# hexabox blog artifact -- CHANGES ## 2026-09-06 -- `--record-point P2`: the record pair at the second point (row 24) - NEW tier `hexabox-evaluate.py --record-point P2` (strings only; 0.49 s here). The six-scale function is not established -- the final forms above live on the one-parameter path -- so nothing in the script can compute the masters at a second point. What exists at P2 = (s12,s23,s34,s45,s15,mm) = (-5,-7,-11,-13,-19,3) is a RECORD PAIR: the three top-sector masters of hexaboxP3P4 through eps^0 evaluated twice by AMFlow, at precision goal 40 and goal 50, shipped as `record_P2/out_goal40.json` (sha256 `f292d9193dcb9410...`) and `record_P2/out_goal50.json` (`28ad93f9a914f360...`) -- the record bytes, unchanged. The tier pins both files and the new comparison module `hexabox_record_pair.py` (`b0d5747b30543d5e...`) by sha256 before reading a value, then re-runs the record's comparison: per re/im component the relative matched digits (the reproducing command's rule, vendored function for function -- masked-AST identical on `parse_arb`, `coeffs_of`, `matched_digits`), structural zeros |value| <= 1e-40 on either side named and not counted (30 components, 27 significant; the 3 zeros are m0_eps-4 im, m1_eps-4 im, m2_eps-4 im), the per-order complex-relative minima 93.62 / 84.38 / 75.37 / 66.45 / 57.14 at eps^-4..eps^0, and the component-wise minimum 56.65 d at master 1, eps^+0, im against the bar 56 = the floor of that minimum: PASS. Every recomputed figure is printed beside the record's and asserted equal to two decimals. The reproducing command's own verdict at --min-digits 30 over all 30 components is also printed (27 PASS / 3 FAIL, OVERALL FAIL: its FAILs are the three structural zeros, 0.0 d by its zero-vs-nonzero rule); the basis of record is the component-wise table. - WHAT THE DIGITS MEAN (printed on every run): two precisions of one program agreeing, not an independent record -- none exists at P2; eps^1 and eps^2 were not run; the six-scale function is open (a second point is the gate the program asked for, not the function); the reduction ran at N = 33 prime fields at P2 vs 31 at the first point; the runs' own Arb radii (~110 digits) are NOT a certification. - Controls (measured on copies): `--mutate-record` plants one digit (decimal digit 20 of the master-1 eps^0 imaginary midpoint of the goal-50 output) IN MEMORY, the files untouched -> the component-wise minimum drops to 18.39 d and the gate FAILS by name, exit 1; one byte of a fixture changed on disk, pin unchanged -> refused by pin, exit 3; the module changed, pin unchanged -> exit 3; a fixture missing -> exit 4; the module missing -> exit 4; the fixture tampered AND re-pinned -> the pin passes and the gate itself fails by name, exit 1; `--record-point P1` / `P0` refused, exit 2 / 2; `--mutate-record` alone, or `--record-point P2` with `--point` / `--dps-double`, refused, exit 2 / 2 / 2. Exit codes of the tier: 0 pass; 1 a gate fails by name; 2 refused; 3 a pin mismatches; 4 a pinned file is missing. - Every existing tier is unchanged: the tier is dispatched right after the options are parsed and exits before any final-form machinery is built; the served and the new script print byte-identical output after masking stamps and walls on the default check demo (595 s / 620 s): identical; --point 0.7 (56 s / 47 s): identical; --point s45=-8.3,s15=-15.2,mm=1.7 (49 s / 45 s): identical; --dps-double (137 s / 118 s): identical; --point 0.62 --sec 255 --dps 30 (449 s / 416 s): identical; --point 0.62 --sec 255 (538 s / 485 s): identical (walls served / new, on a shared host). `--help` differs by the two new options only. `hexabox-data.json`, `hexabox-vop-data.json.gz`, `hexabox_vop.py`, `hexabox_vop_lib.py` and `hexabox-expression.md` are byte-identical. - NEW `MANIFEST.sha256` for the bundle (sha256sum -c from this directory; `_snippet.md` unpinned; this file pinned -- re-emit after any later entry) and this CHANGES.md (created with this entry). `hexabox-evaluate.py` sha256 `84c7d28f4b778157...` (was `e5f840f9e156f27a...`). ## 2026-09-07 -- the REACH CHECK of the sec255 layer recursion (`--kmax`; row 24) - NEW in `hexabox_vop.py` (sha256 `b9eed7da27dca077...`, was `c995a5456884666b...`): the recursion V_i^(k) = sum_j sum_(m in SUPP(i,j)) A_ij^(m) V_j^(k-m) reads only the layers m the bundle carries, and a layer m absent from SUPP(i,j) that lies within the reach of the requested layer k -- k - k_min(j) >= m, where k_min(j) is the lowest live layer of the source row j (its first nonzero fit-point seed order plus L_j; -1 for a sunrise row, whose closed containers start there) -- used to be dropped silently. `Vop255.reach_check` now refuses by name (`RuntimeError('VoP reach: ...')`) BEFORE the sum when a coupling's max m present is below k - k_min(j): for every coupling at every layer above the record layer `KMAX_RECORD = 3` (the layer through which this bundle's supports and seeds were computed and checked against the independent oracle), for the top-sector couplings at every layer, and for a row computed above layer 3 with no fit-point seed there (the seeds stop at eps^2 = layer L_i + 2). The check is called at the top of `close_symbolic`, `de_certificate` and `run_numeric` (a projection over every layer, refusing before any layer is computed) and before every block's sum; every other method is unchanged. Once per run it prints the per-row k_min table -- one `[vop/reach]` line per row: k_min and its source, the seeded layers, the couplings consuming the row, the max m needed at K -- and the summary `reach complete for KMAX K: yes/no`. - NEW `hexabox-evaluate.py --kmax K` (sha256 `6df1cc124e529236...`, was `84c7d28f4b778157...`; default 3 = the served `run_numeric(3)`): threaded into Check 2's recursion (and through `--point --sec 255`); Check 2 prints the reach report right after the loader and turns the named refusal into `REFUSED by name -- VoP reach: ...`, exit 1. K < 3 is refused, exit 2 (the served digits need the layers through 3); K other than 3 with `--dps-double`, `--record-point` or `--point --sec 219` is refused, exit 2 (no sec255 recursion runs there). - WHAT THIS BUNDLE READS. Per-row k_min: row 70 at layer -4 (its seed 1/4 at eps^-4), 17 rows at -2, 49 rows (the 8 sunrise rows among them) at -1, 31 rows at 0 -- the k_min distribution {-4: 1, -2: 17, -1: 49, 0: 31}, the deep rows [(70, -4)] (the probe's own REACH_PROBE line). At K = 3 (the default) no coupling is short and no seed is absent (0 / 0; [vop/reach] reach complete for KMAX 3: yes (0 short coupling(s), 0 row(s) without a seed at a computed layer; 294 couplings checked)): the default run is exactly the served one. At K = 5 every one of the 294 top-sector couplings is short at layer 4 -- each support ends exactly at the layer-3 reach, max m present = 3 - k_min(j) -- together with 1122 non-top couplings and 52 rows without a seed at layer 4; the run refuses in 50 s before any layer is computed: `VoP reach: 1416 coupling(s) short of the reach at KMAX 5 and 52 row(s) without a seed at a computed layer -- coupling (95,70) layer 8 absent within the reach of layer 4 (k_min(70) = -4, max m present 7); coupling (96,70) layer 8 absent within the reach of laye...`. At K = 4 the same top-sector couplings refuse (896 short, 0 seeds absent, 38 s). So the eps^1, eps^2 layers of the top sector are NOT established by this bundle; a bundle carrying the layers (and the eps^3, eps^4 seeds) passes the check and the recursion runs to K -- the printed comparison stays eps^-4..eps^0 (the deep-60 oracle ends there). - THE FIVE COUPLINGS OF THE FULL RECORD. Over the untrimmed record bundle of the same recursion (8151 exact entries, sha256 `7db47aab4e10044b...`, read only) the same helper at K = 5 reads exactly the five top-sector couplings whose supports stop below the reach: (95,70) max m 7 of 9 needed (k_min(source) -4); (96,70) max m 7 of 9 needed (k_min(source) -4); (97,0) max m 4 of 6 needed (k_min(source) -1); (97,2) max m 4 of 6 needed (k_min(source) -1); (97,70) max m 7 of 9 needed (k_min(source) -4) -- the (i,70) three at the record's expansion ceiling m = 7 against the layer-9 need of the deepest source, the two row-97 sunrise couplings at the fit ceiling m = 4 against 6; and 392 non-top couplings whose supports end below the layer-4/5 reach (whether those higher layers vanish identically is not established by either bundle). - NOT a short coupling: an absent m BELOW a coupling's max m present (a zero coefficient of the exact expansion; no coupling of this bundle has such a gap), and a non-top coupling whose support ends below the layer-3 reach (350 of them: the default run's oracle agreement establishes those absent layers as zero coefficients -- the bundle carries no per-entry expansion order, so such a complete expansion cannot be told from a dropped layer below layer 3; the check therefore covers the top-sector couplings at every layer and every coupling above layer 3). - Controls (measured on copies): the served bundle with ONE in-reach layer dropped (`exactA` entry `95,70,7`, the highest layer of the coupling (95,70), consumed at layer 3 with the live source V_70^(-4)): the cured default REFUSES by name in 45 s, exit 1 -- `VoP reach: 1 coupling(s) short of the reach at KMAX 3 and 0 row(s) without a seed at a computed layer -- coupling (95,70) layer 7 absent within the reach of layer 3 (k_min(70) = -4, max m present 6): the bundle's expansion stops below the requested layer; enter the layers or lower --kmax` -- while the served bytes on the same planted bundle compute the whole recursion and fail only at its end, by the independent comparison of Check 2: m0_eps+0 1.27 d against the bar 45 d (the served bundle reads m0_eps+0 56.54 d, m1_eps+0 56.76 d, m2_eps+0 56.91 d), an AssertionError traceback, exit 1 after 445 s -- a digit mismatch, not a named coupling; where no oracle covers the layer (eps^1, eps^2) that drop is silent, which is what the check is for; `--kmax 2` -> exit 2 (`--kmax 2: REFUSED -- the served digits need the sec255 layers through 3 (eps^0 of the top sector); pass --kmax 3 (the default) or higher`); `--kmax 5 --record-point P2` / `--dps-double` / `--point 0.7` -> exit 2 / 2 / 2; the served PINS path is unchanged: one byte of `record_P2/out_goal50.json` -> exit 3, `record_P2/out_goal40.json` missing -> exit 4; `--record-point P2` before / after byte-identical (exit 0 / 0). The served bytes with `--kmax 5` run the KMAX-3 demo unchanged (the knob is unknown to them: exit 0, 414 s) -- a served-bytes `--kmax` run is not a KMAX-5 result. - Every existing tier is unchanged: the served and the new bytes print byte-identical output after masking stamps and walls, plus the designed `[vop/reach]` lines in Check 2 (100 lines: the 98-row table and the summary): the default check demo (442 s / 442 s): identical plus 100 reach-report lines; --point 0.7 (41 s / 40 s): identical; --dps-double (81 s / 88 s): identical; --point 0.62 --sec 255 --dps 30 (305 s / 293 s): identical plus 100 reach-report lines; --record-point P2 (0 s / 0 s): identical (walls served / new, on a shared host at loadavg 71.60 / 71.13). `--help` differs by the `--kmax` option only. `hexabox-data.json`, `hexabox-vop-data.json.gz`, `hexabox_vop_lib.py`, `hexabox_record_pair.py`, `record_P2/*` and `hexabox-expression.md` are byte-identical. - `MANIFEST.sha256` re-emitted by the bundle's generator (two rows move: `hexabox_vop.py`, `hexabox-evaluate.py`; this file re-pinned). ## 2026-09-07 -- the eps^1, eps^2 SUCCESSION of the sec255 bundle (`--kmax 5` gated; row 24) - THE SUCCESSION, by object. `hexabox-vop-data.json.gz` (sha256 `04bfd5f45c625ae8...`, was `35c91bc11f762196...`) is the gated candidate bundle of the eps^1, eps^2 gate of record (its bytes `c4d86690801bcef6...`, re-cut only in provenance strings: 6 leaves differ, all of them strings of `_provenance`; every numeric and rational leaf byte-equal, asserted at build): the FULL exact A (8151 entries; the 5018 served before byte-equal, the other 3133 reachable only above layer 3; the build receipt vendored as `vendor_row24_eps12/BUILD_RECEIPT.json`), the 28 CANDIDATE KERNELS entered from 11 exact candidate files vendored beside (`vendor_row24_eps12/KERNELS_CANDIDATE_v2_*.json`: (86..91,70) and (95..97,70) at m = 8, 9, (97,0) and (97,2) at m = 5..9; exact rationals reconstructed on 101 path nodes, every record layer reproduced exactly; the bundle's entries byte-equal to the files, checked at every `--kmax 4 / 5` run), and the 196 fit-point seed cells at orders [3, 4] for all 98 rows (the 506 served cells kept byte for byte; 0 moved). `D_spec`, `hybrid_kernels`, `sun_p2`, `path`, `real_poles`, the interim seed cache and `_fold` are the served ones. The bundle's `_provenance.item56_succession` block states all of this and the record layer below. - THE GATE OF RECORD (`vendor_row24_eps12/GATE_EPS12.json`, sha256 `607db54afff0e76a...`; stamp 2026-09-07T05:27:52Z): the layer recursion on the gated bytes at KMAX 5, NC 220, engine dps 85 / 115, at the verification point against BOTH records (`vendor_row24_eps12/ORACLE_goal30.json` / `ORACLE_goal60.json`, the AMFlow evaluations of record at precision goals 30 and 60): eps^1 40.21 d, eps^2 35.29 d, eps^-4..eps^0 control 44.59 d (complex-relative, the verdict rule; real-part convention eps^1 39.2 d, eps^2 34.97 d); the goal-30 record is the floor (its own precision there), the goal-60 record and the served strings agree to 57.05 d and more, the two-precision pair to 71.34 d and more; planted digit-20 control 21.31 d FAIL. Rule: GATED iff min over masters and over {vs goal-60 string, vs goal-30 value, vs goal-60 out, two-precision pair} >= 30 d at BOTH eps^1 and eps^2. - NEW `hexabox-evaluate.py --kmax 4 / 5` (sha256 `495f762fea4d800f...`, was `6df1cc124e529236...` with the reach check, `84c7d28f4b778157...` served): the 16 vendored objects are pinned (missing -> exit 4, mismatch -> exit 3, before any check runs), the recursion runs to layer 4 / 5, the served eps^-4..eps^0 comparison prints unchanged, then every master's eps^1 (and eps^2) endpoint against the served 60-digit strings, the goal-60 record and the goal-30 record -- the gate's convention, the real-part reading in brackets -- with the gate's rule (bar 30 d at every order computed; FAIL by name, exit 1) and the record's figures beside. `--kmax K --dps-double` (K >= 4) is the two-precision pair: Check 2 twice, the deeper pass first (the engine library's constant registry is per process and tolerates only a coarser re-registration), the second pass reading the first as its fourth reference. `--mutate-eps12` plants one digit of the served eps^1 string of master 0 in memory. The RECORD LAYER: the reach check's `KMAX_RECORD` is the engine's class default 3 (the served bundle's) unless this script declares it -- it declares 5 for the succeeded bundle, by sha256, right after the loader (the gate of record checked that bundle's layers through 5). - WHY THE DECLARATION (measured with the reach-check engine): under the class default the succeeded bundle REFUSES at `--kmax 5` -- `386` non-top couplings short (`0` top-sector), the (61,61) class whose supports end at m = 1..4 against a record ceiling of 7 (`146` at `--kmax 4`) -- the same class the served default reads as complete expansions below layer 3 (350 of them); the gate of record reproduces both records through eps^2 with those layers as they are, so on this bundle they are complete expansions above layer 3 too, by the oracle's reading, and the record layer is 5. With it declared: `--kmax 5` reads 0 short couplings and 0 rows without a seed; `--kmax 6` refuses by name -- measured: exit 1 in 36 s, 368 distinct couplings short by the engine's summary (its reach table lists 374 entries: 334 in the m-present class = the probe's count, 54 of them top-sector at the exact reconstruction's ceiling m = 7 and 280 non-top, plus 40 in the sunrise-source class -- a layer-6 source above the containers' last layer 5 -- with 6 couplings in both classes), `VoP reach: 368 coupling(s) short of the reach at KMAX 6 and 0 row(s) without a seed at a computed layer -- coupling (95,70) layer 10 absent within the reach of layer 6 (k_min(70) = -4, max m present 9); coupling (96,70) layer 10 absent within the reach of layer 6 (k_min(70) = -4, max m present 9); coupling (97,70) layer 10 absent within the reach of layer 6 (k_min(70) = -4, max m present 9)...`; the untrimmed record bundle before the kernels were entered reads exactly the audited five short at 5 ((95,70) (96,70) (97,0) (97,2) (97,70): the probe's own REACH_PROBE line). On the SERVED bundle nothing changes: `--kmax 5` refuses as before (1416 short, 52 rows without a seed; measured on the cured bytes over the served bundle: exit 1 in 44 s, `VoP reach: 1416 coupling(s) short of the reach at KMAX 5 and 52 row(s) without a seed at a computed layer -- coupling (95,70) layer 8 absent within the reach of layer 4 (k_min(70) = -4, max m present 7); coupling (96,70) layer 8 absent within the reach of layer 4 (k_min(70) = -4, max m present 7); coupling (97,70) layer 8 absent within the reach of layer 4 (k_min(70) = -4, max m present 7)...`). - MEASURED (copies, one 200% scope each, a shared host at loadavg 65.30): `--kmax 5` at the served `--dps 90` (engine dps 115, NC 220 = the gate's dps-115 pass) in 581 s, exit 0: eps^+1 40.21 d at m1_eps1 vs goal-30 record (record 40.21 d: ==), eps^+2 35.29 d at m1_eps2 vs goal-30 record (record 35.29 d: ==), the eps^+0 control vs the goal-30 record 44.59 d; per master: m0_eps+1 served string 57.09 d [re 57.42]; goal-60 record 57.09 d [re 57.42]; goal-30 record 40.22 d [re 39.26]; m1_eps+1 served string 57.19 d [re 57.70]; goal-60 record 57.19 d [re 57.70]; goal-30 record 40.21 d [re 39.20]; m2_eps+1 served string 57.23 d [re 57.35]; goal-60 record 57.23 d [re 57.35]; goal-30 record 40.22 d [re 39.29]; m0_eps+2 served string 57.05 d [re 57.46]; goal-60 record 57.05 d [re 57.46]; goal-30 record 35.31 d [re 35.02]; m1_eps+2 served string 57.16 d [re 57.49]; goal-60 record 57.16 d [re 57.49]; goal-30 record 35.29 d [re 34.97]; m2_eps+2 served string 57.17 d [re 57.78]; goal-60 record 57.17 d [re 57.78]; goal-30 record 35.29 d [re 35.00]; `EPS^1,2 GATE (--kmax 5): eps^+1 40.21 d, eps^+2 35.29 d vs bar 30 d over three references x 3 masters -> ESTABLISHED; the two-precision pair by --dps-double`. `--kmax 4` in 603 s, exit 0: eps^+1 40.21 d (PASS). `--kmax 5 --dps 45 --dps-double` (engine dps 115 first, then 80: the gate's own pair class) in 1222 s, exit 0: eps^-4..eps^0 pair, min over the 15 coefficients: 71.44 d (independent-oracle agreement 56.54 / 56.54 d: the served strings cap it); eps^+1 pair, min over the 3 masters: 69.58 d; the gate's floor over four references 40.21 d; eps^+2 pair, min over the 3 masters: 66.22 d; the gate's floor over four references 35.29 d; working precision 90 -> 45 dps (engine 115 -> 80; wall 627.9 s -> 586.3 s). The served default on the succeeded bundle (420 s / served bytes on the served bundle 462 s, exit 0 / 0): every digit line byte-identical (m0_eps+0 56.54 d, m1_eps+0 56.76 d, m2_eps+0 56.91 d; min over 15 coefficients 56.54 d; served 56.54 d) -- after masking stamps and walls and removing the reach lines the two outputs differ by 3 line(s): the loader's entry count (`5018 exact entries + 3 certified-numeric, 54 blocks` on the served bundle -> `8179 exact entries + 3 certified-numeric, 54 blocks` on the succeeded bundle) and the added `[succession] ... record layer 5 declared` line; the KMAX-3 layers consume no added seed cell (orders 3, 4 lie above the layer-3 reach of every coupling that reads them). - CONTROLS (copies): `--kmax 5 --mutate-eps12` exit 1 in 702 s -- m0_eps+1 served string 19.71 d [re 18.71]; goal-60 record 57.09 d [re 57.42]; goal-30 record 40.22 d [re 39.26]; `EPS^1,2 FAIL by name: below the bar 30 d: m0_eps1 vs served string 19.71 d (the planted digit of --mutate-eps12)`; a digit planted in `vendor_row24_eps12/ORACLE_goal60.json` with the pin re-forged: exit 1 in 630 s -- m0_eps+1 served string 57.09 d [re 57.42]; goal-60 record 19.71 d [re 18.71]; goal-30 record 40.22 d [re 39.26]; `EPS^1,2 FAIL by name: below the bar 30 d: m0_eps1 vs goal-60 record 19.71 d`; a vendored file missing exit 4 (`PIN MISSING: vendor_row24_eps12/KERNELS_CANDIDATE_v2_item56_86_70_20260907T050708Z.json is not beside this script -> exit 4`); a vendored byte with the pin unchanged exit 3 (`PIN MISMATCH: vendor_row24_eps12/ORACLE_goal30.json sha256 06afceec72b6eb45... != pinned 92b3be0b6044a8e9... -> exit 3`); one byte of the bundle flipped: no in-code pin covers the bundle (the served form: its `MANIFEST.sha256` row is the tamper check, and fails) -- the loader stops on the broken stream, exit 1 in 37 s (`gzip.BadGzipFile: CRC check failed 0x266ce109 != 0x967619fc`); `--kmax 2` exit 2; `--kmax 5 --record-point P2` exit 2; `--mutate-eps12` alone exit 2; the served PINS path unchanged (a fixture byte exit 3, a fixture missing exit 4). - Every existing tier unchanged (served bytes on the served bundle vs the cured bytes on the succeeded bundle, byte-identical after masking stamps and walls, plus the reach-check lines): --point 0.7 (40 s / 38 s) identical; --dps-double (90 s / 89 s) identical; --record-point P2 (0.4 s / 0.4 s) identical; --point 0.62 --sec 255 --dps 30 (277 s / 330 s) DIFFERS by 3 line(s); the same tier with `--kmax 5` (473 s, exit 0): EPS^1,2 GATE (--kmax 5): eps^+1 31.19 d, eps^+2 31.19 d vs bar 30 d over three references x 3 masters -> ESTABLISHED; the two-precision pair by --dps-double. `--help` differs by the `--kmax` text and `--mutate-eps12` (vs the reach-check bytes: 12 lines added, 4 removed; vs the served bytes: 14 added, 1 removed). `hexabox_vop.py` (sha256 `294be9589cff5e50...`, was `b9eed7da27dca077...`) differs by its docstring only; `hexabox-data.json`, `hexabox_vop_lib.py`, `hexabox_record_pair.py`, `record_P2/*` and `hexabox-expression.md` are byte-identical. - NOT ESTABLISHED by these objects (the record's own list): - the four m>=5 top-row kernels (97,0,5), (97,2,5), (97,0,6), (97,2,6): exact candidates gated ESTABLISHED by this receipt's gate of record; nothing missing - nothing for the eps^1, eps^2 layers at P0safe: ESTABLISHED by this receipt's gate of record (40.21 and 35.29 digits vs the goal-30 record, 57 digits vs the goal-60 record: keys floors / table) - the per-node wall at scale (one pilot node only) - the true degrees of (97,0,m) and (97,2,m) at m = 5, 6: now MEASURED exactly (the candidate files' layer degrees: (97,2) (174,176) / (199,201); (97,0) (207,209) / (236,238)); the 146 couplings whose record support stops at m <= 4: whether their higher layers vanish identically is not measured (the gate of record reproduces both oracles with them as they are, so nothing beyond enters at this precision) - the bivariate lift's m>=5 layers as kernels (the paper's own fence: rank-two kernel, gauge independence measured false; the lift object not located here) - the 187 samples of record (deleted 07-02; the D_spec provenance) - `MANIFEST.sha256` re-emitted by the bundle's generator with the vendor group added (18 rows under `vendor_row24_eps12/`, read from the directory's own `VENDOR_MANIFEST.sha256`); the bundle, evaluator, engine and CHANGES rows move. ## 2026-09-09 -- the row-24 batch: the two-precision gate-point strings served (`--gatepoint`) and the sec255 recursion on exact kernels and from-definition seeds (`--boundary-regenerate`; row 24) - PART A, THE DATA SHELF. `vendor_row24_gatepoint/DATA_C24g60_pair_strings_20260909T075018Z.json` (sha256 `fc71767e5d7ead42...`; 298168 B; 98 rows) is served VERBATIM as the two-precision boundary object of the row at the verification point: every master's goal-30 and goal-60 Arb-ball strings at every order eps^-4..eps^4 with the matched digits per component -- the data leg of the settled receipt `8a3c9183d633a417...` (its `data_file` block names this file by sha256) and of the PAIR v2 object `bb0b69e312ea86f6...` (the floors below are its keys). NEW `hexabox-evaluate.py --gatepoint` pins the file (missing -> exit 4, mismatch -> exit 3), recomputes the matched digits of every component from the two strings with the record pair's own `matched_digits` (pinned module), skips the components the record marks null and prints the floors from its own table -- measured (copies, one 200% scope, seconds): all_98_through_eps0 48.38 d (floor 48), all_98_through_eps2 42.23 d (floor 42), all_98_all_orders 32.82 d (floor 32), top_sector_all_orders 34.39 d (floor 34); per order eps^-4 49, eps^-3 49, eps^-2 49, eps^-1 49, eps^+0 48, eps^+1 45, eps^+2 42, eps^+3 38, eps^+4 32; 1298 digit cells recomputed, 0 recomputed digit counts differing from the stored ones by more than 0.05 -- read against the PAIR v2 keys (script-emitted from the object; the integer floors 48 / 42 / 32 through eps^0 / through eps^2 / all orders are the row's Table-2 cell pin): `Gate point: PASS (the recomputed floors equal the PAIR v2 keys: 48 / 42 / 32; two precisions of one program, not an independent record).` (exit 0). The recomputed floors EQUAL the PAIR v2 keys on every line. `--gatepoint --mutate-gatepoint` (one digit of a goal-60 string planted in memory): `GATE POINT FAIL by name: 4 floor(s) differ from the PAIR v2 keys: all_98_through_eps0 : recomputed min 20.18 d (floor 20; at master 0 eps^+0 re) vs the PAIR v2 key min 48.4 floor 48: FAIL (the planted digit of --mutate-gatepoint)` (exit 1). The digits are a two-precision agreement of one program (the goal-30 member bounds them); no independent record exists at these orders for the 95 non-top masters. The group carries its own README.md and VENDOR_MANIFEST.sha256 (gen_vendor_manifest_v2.py: the eps12 group's form with the group name and description read from the README). - PART B, THE R5 LEG. THE THREE KERNELS (97,0,m), m = 2, 3, 4, that the served bundle carries as certified-numeric rational fits (`hybrid_kernels`) are now served EXACT beside it: `vendor_row24_kernels/KERNELS_CANDIDATE_item56_97_0_20260907T041028Z.json` (sha256 `adbae0c89d3db900...`; the exact object of the eps^1, eps^2 succession's factored read, layers 2..7, exact by CRT + rational reconstruction on 101 path nodes, 8 withheld nodes reproduced; its layers 2..7 byte-equal to the served candidate file `vendor_row24_eps12/KERNELS_CANDIDATE_v2_item56_97_0_20260907T043901Z.json`, which enters m = 5..9), `vendor_row24_kernels/KERNELS_CANDIDATE_item56_97_2_20260907T040525Z.json` (sha256 `752b050c0877963e...`; the (97,2) sibling, layers 5..7) and the gate of record in its v4 form `vendor_row24_kernels/GATE_ITEM56_EPS12_20260907T052752Z.json` (sha256 `1ef0b8a96ddebacb...`; the same object as the served GATE_EPS12.json, every numeric leaf equal; re-cut by field, cure 3 below). THE FROM-DEFINITION SEEDS: `vendor_row24_seeds/fresh_strings_447_fromdef_20260908T053054Z.json` (sha256 `c353b8d589f70256...`) carries the 447 sec255 fit-point boundary constants regenerated from definition at working precisions 90 and 120 (four checkpointed legs; the four leg receipts `LEG_LANDING_wave12_dps120_20260907T235745Z...` / `LEG_LANDING_wave12_dps90_20260907T201119Z...` / `LEG_LANDING_wave3_dps120_20260908T053011Z...` / `LEG_LANDING_wave3_dps90_20260908T024214Z...` vendored with ONLY their host string fields re-cut to "withheld" (a served file carries no person; 2 field(s) in `LEG_LANDING_wave12_dps120...`, 2 field(s) in `LEG_LANDING_wave12_dps90_...`, 4 field(s) in `LEG_LANDING_wave3_dps120_...`, 3 field(s) in `LEG_LANDING_wave3_dps90_2...`; every other field as written; the receipts as emitted named by sha256 in the seeds README and in the evaluator's `REGEN['vendored_from']`), the comparison `FROMDEF_COMPARE_447_20260908T053054Z.json` and the regeneration receipt `BOUNDARY_REGENERATE_447_fromdef_20260908T053054Z.json` vendored beside; all ten objects re-cut by field, cure 3 below); read entry by entry against the served objects (tag `row,j` positional, eps order = the tag's `eps_order` field, the bundle's own key convention): the dps-90 and dps-120 strings are identical on 447/447 tags (re; the imaginary parts likewise but for 39 structural zeros), the shortest string carrying 78 significant digits (tag 38,2; the longest 80); against the served bank the `re` strings are identical on 447/447 tags (`im` 411, the rest structural zeros differing as noise) -- the 447/447 identity of the settled receipt, by object; against the served bundle's 70-digit seeds the dps-120 strings agree to 69.32 d at worst (63,3:re:eps0; 855 significant components) -- the bundle's own truncation, and the figure the served text called the boundary certificate. 447 of the bundle's 702 seed cells are covered; the other 255 (eps^-4: 24, eps^-2: 27, eps^-1: 8, eps^3: 98, eps^4: 98) keep the bundle's values -- and of the 59 kept cells at eps^-4..eps^-1 (in the value path of every regenerate run) 49 components are structural zeros, 35 short terminating decimals (exact rationals as printed) and 34 SIGNIFICANT components on 24 cells carry the served 70-digit strings of closed-form constants not yet entered exactly (rows 39..41, 58..60, 79..82 at eps^-2, pi/6- and pi/4-class constants; rows 71..72, 86..97 at eps^-4, rationals such as 1/24), so those strings stay in the regenerate recursion's input (the 196 kept eps^3, eps^4 cells, 374 significant components, enter with --kmax 4 / 5 only). The from-definition strings are printed at 80 digits (mp.nstr(x, 80) under workdps(140), the stage_assemble_boundary.py form); the certificate is the printed length. - NEW `hexabox-evaluate.py --boundary-regenerate` (sha256 `45ba7434e10fae02...`, was `fe3eecdbc5b19c30...`): every .json of the two groups pinned (missing -> exit 4, mismatch -> exit 3, before any check runs), the (97,0) layers 2, 3, 4 asserted byte-equal to the served candidate file's, the served fits read against the exact kernels at five interior probe points (measured: worst agreement (97,0,2) 68.01 d, (97,0,3) 68.20 d, (97,0,4) 68.55 d), the 447 covered seeds replaced by the dps-120 strings (255 kept), and the sec255 recursion of Check 2 run on the regenerated bundle (written under `--regen-dir DIR`, default `./hexabox_regen_/` in the working directory, never removed by this tool -- the caller owns the directory; the served bundle untouched): the loader reads `8182 exact entries + 0 certified-numeric, 54 blocks`, no certified-numeric kernel enters (asserted -- the served default asserts the opposite), and the run prints the SEED CERTIFICATE >= 78 d (the printed length of the shortest identical string; the served 70-digit seeds vs the dps-120 strings 69.32 d), the kept-cell census and the TRUE INPUT CAP before the served-form recursion, certificates, [BOUND] and oracle lines. MEASURED (copies, one 200% scope each, a shared host): `--boundary-regenerate` in 9:36.51 (exit 0): sec255 15-coefficient check 56.54 d (the served default on the same host 56.54 d in 9:35.53: the oracle's 60 digits cap both), sec219 40.63 d, `worst trailing-8 spectral tail bound 1.75e-53 (table (97, 3, 12)) < tol 1.0e-46 = 10^-(min(dps,36)+10)`; `--boundary-regenerate --kmax 5` in 14:22.40 (exit 0): `EPS^1,2 GATE (--kmax 5): eps^+1 40.21 d, eps^+2 35.29 d vs bar 30 d over three references x 3 masters -> ESTABLISHED; the two-precision pair by --dps-double` (the served `--kmax 5` on the same host: `EPS^1,2 GATE (--kmax 5): eps^+1 40.21 d, eps^+2 35.29 d vs bar 30 d over three references x 3 masters -> ESTABLISHED; the two-precision pair by --dps-double` in 14:23.84). THE TRUE INPUT CAP: the regenerate tier removes the three fits from the value path and lifts the seed cap on the 447 replaced cells to the printed length of the from-definition strings (>= 78 d), but the 34 kept significant components above still carry the served 70-digit strings, so the input cap of the regenerate recursion is min(78, the served floor 69.32 d on those components) = 69.32 d -- NOT 78 d -- until they are entered exactly at the working precision (an open point for a later succession; they are closed-form constants; not built here); the served floor 69.32 d is the measured agreement of the served 70-digit strings with the from-definition strings over the 855 covered significant components (one printing rule for every served cell). The tier prints that cap on its NOTE line (measured, cure 1 re-run 9:32.29, exit 0): `the input cap of this recursion is min(the seed certificate >= 78 d on the 447 replaced cells, the served floor 69.32 d on the 34 significant components of 24 kept cells at eps^-4 / eps^-2 that still carry the served 70-digit strings) = 69.32 d until those components are entered exactly; the fits are out of the value path; the oracle comparison below stays capped by the oracle's 60 digits.`; it does not raise the printed oracle agreement, which the oracle's own 60 digits bound. The engine's own loader cross-check line reads `[vop] boundary seeds: 447 derived values cross-checked on load against the retired interim strings, worst agreement 69.35 digits (threshold 60).` under this tier where the served default reads 85.8 digits: the 80-digit replaced strings are read against the retired 70-digit interim cache the bundle carries as a load-time cross-check (threshold 60 d holds; the cache is not an input of the recursion) -- informational. The KNOWN GAP paragraph of the docstring is retired for a statement of what each tier runs (the served default and --point tiers run the bundle's certified-numeric fits of the (97,0,2..4) kernels; --boundary-regenerate runs the exact layers); the served default's NOTE line names the kernel lift; `--regen-dir` without `--boundary-regenerate` is refused (exit 2). Refusals: `--boundary-regenerate` with `--record-point` / `--point` / `--dps-double` exit 2 (measured 2 / 2 / 2); `--gatepoint` with `--kmax 5` / `--boundary-regenerate` exit 2 / 2; `--mutate-gatepoint` alone exit 2. - CONTROLS (copies): one digit planted in the exact kernel file (the file's bytes): `PIN MISMATCH: vendor_row24_kernels/KERNELS_CANDIDATE_item56_97_0_20260907T041028Z.json sha256 c966a4889937bba4... != pinned d223992d5ee27c02... -> exit 3` (exit 3; with `--kmax 5` exit 3); the seeds file missing: `PIN MISSING: vendor_row24_seeds/fresh_strings_447_fromdef_20260908T053054Z.json is not beside this script -> exit 4` (exit 4); `--record-point P2 --mutate-record` exit 1; `--kmax 5 --mutate-eps12` exit 1 (`EPS^1,2 FAIL by name: below the bar 30 d: m0_eps1 vs served string 19.71 d (the planted digit of --mutate-eps12)`); `--kmax 2` exit 2. - EVERY SERVED TIER UNCHANGED (the served bytes vs the cured bytes on the same bundle, captures masked of stamps and walls): before_recordP2 vs after_recordP2: 0 differing line(s); before_mutate_record vs after_mutate_record: 0 differing line(s); before_default vs after_default: 2 differing line(s); before_kmax5 vs after_kmax5: 2 differing line(s); before_mutate_eps12 vs after_mutate_eps12: 2 differing line(s); before_help vs after_help: 20 differing line(s); after_default vs regen_k3: 36 differing line(s); after_kmax5 vs regen_k5: 36 differing line(s) (`--help` differs by the three new options' text). Masked AST of hexabox-evaluate.py against the served bytes: 4 unit(s) differ (, FunctionDef run_sec255_live, FunctionDef run_point_255, If __name__ == '__main__': the docstring, the regenerate option's help text, the REGEN pin block, the regenerate seams of Check 2 -- the bundle path, the certified-numeric assertion, the NOTE lines -- the --point closing note and the dispatch), 14 added (Expr _ap.add_argument('--boundary-regenerate', Expr _ap.add_argument('--gatepoint', action=', Expr _ap.add_argument('--mutate-gatepoint', a, If ARGS.gatepoint and (ARGS.boundary_regenerate or ARGS.record_point is not None or ARGS.point is not None or ARGS.dps_double or (ARGS.kmax != 3) or ARGS.mutate_eps12 or ARGS.mutate_record), If ARGS.mutate_gatepoint and (not ARGS.gatepoint), If ARGS.boundary_regenerate and (ARGS.record_point is not None or ARGS.point is not None or ARGS.dps_double), Assign REGEN, Assign REGEN_STATE, FunctionDef regen_pins, FunctionDef regen_bundle_path, Assign GATEPOINT, FunctionDef run_gatepoint, Expr _ap.add_argument('--regen-dir', If ARGS.regen_dir is not None and (not ARGS.boundary_regenerate)), 0 removed; every other unit byte-identical. `hexabox_vop.py`, `hexabox_vop_lib.py`, `hexabox-data.json`, `hexabox-vop-data.json.gz`, `hexabox_record_pair.py`, `record_P2/*`, `vendor_row24_eps12/*` and `hexabox-expression.md` are byte-identical (the expression's Section 6 still describes the fits; the served bundle keeps them). - NOT ESTABLISHED by these objects: the exact kernels beyond the 101-node reconstruction (candidates reproducing both oracle records, no proof); the seeds beyond the printed length of the strings; the 255 cells outside the chain's coverage; any oracle agreement above the oracle's 60 digits; the 95 non-top masters at eps^1..eps^4 beyond the two-precision agreement. - `MANIFEST.sha256` re-emitted by the generator's v3 (the v2 form with the three groups, each read from its own VENDOR_MANIFEST.sha256 and its objects); the evaluator and CHANGES rows move; the 11 vendored objects and the three READMEs / VENDOR_MANIFESTs enter. - CURE 1 (2026-09-09, on the first verify of this entry's delivery; the evaluator `4ce37c81e068fa7d...` succeeds the delivered `94bdcd611e7e9fff...`, text / pin / path units only): the regenerate tier's certificate clause had said the served 70-digit strings were out of the value path -- false by object: 34 significant kept components on 24 cells at eps^-4 / eps^-2 stay in the recursion's input (the census above, counted from the objects at every run) -- cured to the true input cap 69.32 d everywhere (the docstring, the NOTE line, the summary line, this entry, the seeds README). The four leg receipts' host strings re-cut to "withheld" (their pins re-cut, the originals by sha256 in the seeds README, the VENDOR_MANIFEST header and `REGEN['vendored_from']`). The regenerated bundle now lands under `--regen-dir` (default `./hexabox_regen_/`); the 'three certified-numeric kernels' wording at the docstring's precision-model, inputs and reach-check paragraphs and the --point closing note re-cut to what each tier runs. Re-run on the cured bytes (copies, one 200% scope each, a shared host): `--boundary-regenerate` 9:32.29 (exit 0; pins OK 10 files; `[vop] bundle loaded: 8182 exact entries + 0 certified-numeric, 54 blocks (5.7s)`; `from-definition seeds (fresh_strings_447_fromdef_20260908T053054Z.json; working precisions [90, 120]): 447 tags; the dps-90 and dps-120 strings identical on 447/447 tags (re), the shortest such string 78 significant digits (tag 38,2) -> SEED CERTIFICATE >= 78 d on every covered cell`; `the served 70-digit seeds read against the dps-120 strings: min 69.32 d at 63,3:re (eps^0) over 855 significant components (39 structural zeros |x| <= 1e-40 named by count, not counted)`; `kept cells at eps^-4..eps^-1 (in the value path of this recursion): 59 cells = 49 structural-zero components + 35 short terminating decimals (exact rationals as printed) + 34 SIGNIFICANT served 70-digit strings on 24 cells (closed-form constants not yet entered exactly): eps^-4: rows 71, 72, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97; eps^-2: rows 39, 40, 41, 58, 59, 60, 79, 80, 81, 82`; `kept cells at eps^3, eps^4 (in the value path with --kmax 4 / 5 only): 196 cells = 18 structural zeros + 0 short + 374 served 70-digit strings on 196 cells`; `TRUE INPUT CAP of this recursion: min(the seed certificate >= 78 d on the 447 replaced cells, the served floor 69.32 d on the 34 kept significant components) = 69.32 d until those components are entered exactly`; fits vs exact kernels worst (97,0,2) 68.01 d, (97,0,3) 68.20 d, (97,0,4) 68.55 d; `sec255 top-sector 15-coefficient check, recursed live: 56.54 d`; `sec219 min independent check, transported live: 40.63 d`; `sec255 recursion on regenerated inputs (--boundary-regenerate): the (97,0,2..4) kernels exact, 447 seeds from definition; seed certificate >= 78 d (447/447 tags identical at the two working precisions); served 70-digit seeds vs from-definition min 69.32 d; 34 kept significant components on 24 cells keep the served 70-digit strings -> input cap 69.32 d; fits vs exact kernels worst (97,0,2) 68.01 d, (97,0,3) 68.20 d, (97,0,4) 68.55 d`); `--record-point P2` exit 0 / `--mutate-record` exit 1; `--gatepoint` exit 0 / `--mutate-gatepoint` exit 1; `--help` exit 0; a digit planted in a re-cut leg receipt exit 3, a re-cut leg receipt missing exit 4; the option refusals exit 2 / 2 / 2 / 2 / 2 / 2 and `--regen-dir` alone exit 2; `--kmax 2` exit 2. The served default and `--kmax 5` tiers were not re-run at the cure: against the delivered bytes the masked AST differs in 7 unit(s) (, Expr _ap.add_argument('--boundary-regenerate', Assign REGEN, FunctionDef regen_bundle_path, FunctionDef run_sec255_live, FunctionDef run_point_255, If __name__ == '__main__') with 2 added (Expr _ap.add_argument('--regen-dir', default=, If ARGS.regen_dir is not None and (not ARGS.boundary_regenerate)), 0 removed -- print, docstring, pin-constant and path units only; their figures above stand. Not this entry's: hexabox-expression.md Section 6 and the page's boundary-data clause. - CURE 2 (2026-09-09, on the second verify of this entry's delivery; the evaluator `d3311c6c49205ebb...` succeeds the CURE 1 `4ce37c81e068fa7d...`, print / docstring / label units only -- masked AST: 4 units differ (, Assign REGEN, FunctionDef regen_bundle_path, FunctionDef run_sec255_live), 0 added, 0 removed, 112 identical): two lows of the second verify. (a) The tier's TRUE INPUT CAP line, its NOTE line, one REGEN label, two docstring sentences and the seeds README had attributed the served floor 69.32 d TO the 34 kept significant components; the figure is measured over the covered components and only BOUNDS the kept strings (they have no from-definition twin) -- every site now says so, the printed lines carrying the covered count from the run. (b) The run-time kept-cell census printed its buckets under the static label `eps^-4..eps^-1`; the orders present in each bucket are now collected at run time and the labels computed from them. Re-run on the cured bytes (copies, one 200% scope each, a shared host): `--boundary-regenerate` 8:36.83 (exit 0, peak RSS 4701308 kB; pin OK: vendor_row24_kernels/GATE_ITEM56_EPS12_20260907T052752Z.json sha256 65d5566cb74da059...): `from-definition seeds (fresh_strings_447_fromdef_20260908T053054Z.json; working precisions [90, 120]): 447 tags; the dps-90 and dps-120 strings identical on 447/447 tags (re), the shortest such string 78 significant digits (tag 38,2) -> SEED CERTIFICATE >= 78 d on every covered cell`; `kept cells at eps^-4/eps^-2/eps^-1 (the orders <= 0, in the value path of this recursion): 59 cells = 49 structural-zero components + 35 short terminating decimals (exact rationals as printed) + 34 SIGNIFICANT served 70-digit strings on 24 cells (closed-form constants not yet entered exactly): eps^-4: rows 71, 72, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97; eps^-2: rows 39, 40, 41, 58, 59, 60, 79, 80, 81, 82`; `kept cells at eps^3/eps^4 (the orders > 0, in the value path with --kmax 4 / 5 only): 196 cells = 18 structural zeros + 0 short + 374 served 70-digit strings on 196 cells`; `TRUE INPUT CAP of this recursion: min(the seed certificate >= 78 d on the 447 replaced cells, the served floor 69.32 d measured over the 855 covered significant components and bounding the 34 kept significant components, which have no from-definition twin) = 69.32 d until those components are entered exactly`; `the input cap of this recursion is min(the seed certificate >= 78 d on the 447 replaced cells, the served floor 69.32 d measured over the 855 covered components and bounding the 34 significant components of 24 kept cells at eps^-4 / eps^-2 that still carry the served 70-digit strings) = 69.32 d until those components are entered exactly; the fits are out of the value path; the oracle comparison below stays capped by the oracle's 60 digits.`; `[vop] boundary seeds: 447 derived values cross-checked on load against the retired interim strings, worst agreement 69.35 digits (threshold 60).`; `sec255 top-sector 15-coefficient check, recursed live: 56.54 d`; `[BOUND] certified transport truncation bounds (trailing-8 spectral tail, L1-propagated; cert pass at dps+25, NC=80): eps^-2 1.02e-91, eps^-1 7.19e-79, eps^+0 2.56e-77, eps^+1 5.4e-76, eps^+2 4.85e-72`; `sec255 recursion on regenerated inputs (--boundary-regenerate): the (97,0,2..4) kernels exact, 447 seeds from definition; seed certificate >= 78 d (447/447 tags identical at the two working precisions); served 70-digit seeds vs from-definition min 69.32 d; 34 kept significant components on 24 cells keep the served 70-digit strings -> input cap 69.32 d; fits vs exact kernels worst (97,0,2) 68.01 d, (97,0,3) 68.20 d, (97,0,4) 68.55 d`; masked against the CURE 1 capture 6 line(s) differ (the re-cut lines and the run's own paths). The quick tiers (`--record-point P2` (+ `--mutate-record`), `--gatepoint` (+ `--mutate-gatepoint`), `--help`, `--kmax 2`) exit 0 / 1 / 0 / 1 / 0 / 2, each masked-identical to its CURE 1 capture (0 differing lines). The served default and `--kmax 5` tiers were not re-run (no numeric unit moves). `MANIFEST.sha256` and the seeds `VENDOR_MANIFEST.sha256` re-emitted by the v3 generators. Not this entry's (unchanged): hexabox-expression.md Section 6 and the page's boundary-data clause; entering the 34 kept closed-form constants exactly at the working precision (lifts the regenerate cap from 69.32 d to the seed certificate 78 d). - CURE 3 (2026-09-09, on the gate of this entry's delivery; the evaluator `45ba7434e10fae02...` succeeds the CURE 2 `d3311c6c49205ebb...`, pin-constant and docstring units only -- masked AST: units_orig=116 units_patched=116 identical=114 differs=2 added=0 removed=0): the ten vendored objects of `vendor_row24_kernels/` and `vendor_row24_seeds/` carried working narrative and absolute paths in string values; every string VALUE of those objects is re-cut by field (one producer, run twice on a copy: idempotent; the file's own serialization json.dumps(indent=1) asserted on the pre-cut bytes): a narrative value -> "withheld" (6 field(s)), a value that is a path -> its basename with the sha256 of the file it named or "(directory)" (66 field(s)); a sentence whose only hit is a hyphenated numerical term is kept as written (2 field(s), the two kernel objects' certification rule); every numeric leaf, every machine-label value (28) and every key name (62 with a hit) as emitted. The gate-point data file `DATA_C24g60_pair_strings_20260909T075018Z.json` (`fc71767e5d7ead42...`) stays byte for byte. By object: `GATE_ITEM56_EPS12_20260907T052752Z.json` `65d5566cb74da059...` -> `1ef0b8a96ddebacb...` (1 narrative field(s) withheld, 3 path field(s) re-cut; 0 machine-label value(s) and 0 key name(s) kept); `KERNELS_CANDIDATE_item56_97_0_20260907T041028Z.json` `d223992d5ee27c02...` -> `adbae0c89d3db900...` (1 narrative field(s) withheld, 2 path field(s) re-cut, 1 numerical-term field(s) kept as written; 0 machine-label value(s) and 0 key name(s) kept); `KERNELS_CANDIDATE_item56_97_2_20260907T040525Z.json` `5679228f87735129...` -> `752b050c0877963e...` (1 narrative field(s) withheld, 2 path field(s) re-cut, 1 numerical-term field(s) kept as written; 0 machine-label value(s) and 0 key name(s) kept); `BOUNDARY_REGENERATE_447_fromdef_20260908T053054Z.json` `2785b15146f70469...` -> `48294da70bfa1c2b...` (0 narrative field(s) withheld, 4 path field(s) re-cut; 0 machine-label value(s) and 4 key name(s) kept); `FROMDEF_COMPARE_447_20260908T053054Z.json` `27b5d0e6234816e2...` -> `cedafa9e212ee1b5...` (0 narrative field(s) withheld, 4 path field(s) re-cut; 0 machine-label value(s) and 5 key name(s) kept); `LEG_LANDING_wave12_dps120_20260907T235745Z.json` `459e247e3a740750...` -> `1492cd38bfe0c750...` (1 narrative field(s) withheld, 10 path field(s) re-cut, 2 host field(s) withheld since cure 1; 5 machine-label value(s) and 12 key name(s) kept); `LEG_LANDING_wave12_dps90_20260907T201119Z.json` `753c4cccc0e358a4...` -> `3af67d435a676b72...` (0 narrative field(s) withheld, 10 path field(s) re-cut, 2 host field(s) withheld since cure 1; 7 machine-label value(s) and 12 key name(s) kept); `LEG_LANDING_wave3_dps120_20260908T053011Z.json` `3a11a43bc2df47c9...` -> `3266298b0e3b9454...` (1 narrative field(s) withheld, 16 path field(s) re-cut, 4 host field(s) withheld since cure 1; 9 machine-label value(s) and 12 key name(s) kept); `LEG_LANDING_wave3_dps90_20260908T024214Z.json` `7739ffdaca73d3d0...` -> `925479a92608cd4e...` (1 narrative field(s) withheld, 13 path field(s) re-cut, 3 host field(s) withheld since cure 1; 7 machine-label value(s) and 12 key name(s) kept); `fresh_strings_447_fromdef_20260908T053054Z.json` `7961fd60d749804a...` -> `c353b8d589f70256...` (0 narrative field(s) withheld, 2 path field(s) re-cut; 0 machine-label value(s) and 5 key name(s) kept). The objects as emitted are named by sha256 as `vendored_from` in the two READMEs and in `REGEN['vendored_from']` (the count form, all ten); the ten REGEN pins follow; both VENDOR_MANIFESTs by gen_vendor_manifest_v3.py; `MANIFEST.sha256` by gen_hexabox_manifest_v4.py (the v3 form with the v4 gate's role sentence re-cut: 'four path strings un-cut' is no longer what the object is). Re-run on the cured bytes (copies, one 200% scope each, a shared host): `--boundary-regenerate` 8:51.71 (exit 0, peak RSS 4703744; pins OK 10 files at the new shas, e.g. `pin OK: vendor_row24_kernels/GATE_ITEM56_EPS12_20260907T052752Z.json sha256 1ef0b8a96ddebacb...`); the census, certificate, TRUE INPUT CAP and NOTE lines IDENTICAL to the CURE 2 capture (masked of stamps and the run's own paths: 24 differing line(s) = the 20 pin lines at the cured shas and 4 wall-time figures of the run itself; with the pin sha16 and the wall-time figures masked: 0); `exact kernel layers 97,0,2, 97,0,3, 97,0,4 of KERNELS_CANDIDATE_item56_97_0_20260907T041028Z.json: byte-equal to layers 2, 3, 4 of the served candidate file KERNELS_CANDIDATE_v2_item56_97_0_20260907T043901Z.json: 3/3`; `TRUE INPUT CAP of this recursion: min(the seed certificate >= 78 d on the 447 replaced cells, the served floor 69.32 d measured over the 855 covered significant components and bounding the 34 kept significant components, which have no from-definition twin) = 69.32 d until those components are entered exactly`; `All checks passed. Every digit count above was measured in this run.`. The quick tiers (`--record-point P2` (+ `--mutate-record`), `--gatepoint` (+ `--mutate-gatepoint`), `--help`, `--kmax 2`) exit 0 / 1 / 0 / 1 / 0 / 2, each masked-identical to its CURE 2 capture (0 differing lines at most); the option refusals exit 2 / 2 / 2 / 2 / 2 / 2 and `--regen-dir` alone exit 2; a digit planted in the re-cut (97,0) kernel object: `PIN MISMATCH: vendor_row24_kernels/KERNELS_CANDIDATE_item56_97_0_20260907T041028Z.json sha256 541ed5b3b561d0cb... != pinned adbae0c89d3db900... -> exit 3` (exit 3); a re-cut leg receipt missing: `PIN MISSING: vendor_row24_seeds/LEG_LANDING_wave3_dps120_20260908T053011Z.json is not beside this script -> exit 4` (exit 4). The served default and `--kmax 5` tiers were not re-run (no numeric unit moves). Not this entry's (unchanged): the three path fields of the gate-point data file (kept verbatim by the gate). ## 2026-09-11 -- `vendor_row24_pathC/`: the Path-C connection of the third kinematic segment vendored (six exact fixed-d0 slices, their P3 gate receipts, the generic-d connection, the node manifest, the instruments, the self-check); `hexabox-evaluate.py` line 2 names the configuration p1^2 = p3^2 = m^2 (X1); `hexabox-expression.md` section 4: the 437-letter alphabet's per-source counts and the one identified new even letter; its header names the family as the evaluator's line 2 does - `hexabox-evaluate.py` 45ba7434e10fae02... -> 93298ecefea0de55...: line 2 of the module docstring FROM `Two-mass non-planar hexa-box (two-loop, five-point, p3^2 = p4^2 = m^2) --` TO `One-mass-pair non-planar hexa-box (two-loop, five-point, p1^2 = p3^2 = m^2; p2^2 = p4^2 = p5^2 = 0) --` (item X1 of the 2026-09-11T12:18:07Z draft: the label carried the adjacent crossing's masses; the code's kinematics are unchanged). A comment: every top-level code unit is identical by string-masked syntax tree (116 units; changed: none), the plain masked-AST read names only the module docstring. No printed value moves: the default tier run before (the served bytes) and after (these bytes) on scratch copies in 200%-CPU scopes side by side -- exit 0 / 0, wall 14:36.63 / 14:43.80, `All checks passed. Every digit count above was measured in this run.` in both; the two outputs differ in 0 lines once timing lines are masked (242 / 242 lines); `--record-point P2` and `--gatepoint` likewise exit 0 / 0 with 0 / 0 differing masked lines. - `hexabox-expression.md` a3b24d2b072bd5a1... -> d6b08ea93654ff12..., section 4 (the two pastes of 2026-09-11T10:52:00Z, receipt ALPHABET_COUNTS_20260911T105121Z.json cf8124d943ae19f6..., every count read again here from ALPHABET_6VAR.json 46419a9cc0b009fe...): the working alphabet's sources FROM 'the one-mass non-planar hexa-box alphabet (344), the massless pentagon alphabet (49), the two-mass four-point alphabet (2), and 12 genuinely new two-mass five-point letters' (344 + 49 + 2 + 12 = 407, not 437) TO 'the one-mass non-planar hexa-box alphabet (374: 344 rational + 30 algebraic), the massless pentagon alphabet (49), the two-mass four-point alphabet (2), and 12 genuinely new two-mass five-point letters' (374 + 49 + 2 + 12 = 437; by the object: 374 one-mass letters = 344 rational + 30 algebraic, 49 + 2 + 12 others, 437 in all = 404 rational + 33 algebraic, 127 confirmed in the maximal cut); and FROM '6 new even letters not in the 437-letter union: X_8 = -4 Gram3(p3,p4,p5)/s45 plus five more irreducible degree-2 letters' TO 'one new even letter identified in the six scales and not in the 437-letter union: X_8 = -4 Gram3(p3,p4,p5)/s45; five more irreducible degree-2 path factors are recorded as candidates (their six-scale forms not identified)'. NOT APPLIED from the first paste: the clause '(7 rational, 5 algebraic)' after the 12 new letters -- by the same object the 12 split 9 rational (mm, r1_app, r2_app, sig_r1_app, sig_r2_app, Gram5_p1p3, mm2_s12s23, P_a2, 2mm-s12-s23) + 3 algebraic (r_Gram5, W_odd_L1, W_odd_L2) by type and 7 + 5 by source list (NEW_2m5pt / NEW_2m5pt_lifted), so the clause as worded does not match the object and 344 + 49 + 2 + 7 would not give the 404 rational letters the same sentence states; left for the authors' ruling (one clause, one later line). THE HEADER (cure 1): the comment line 2 FROM 'Two-mass non-planar hexa-box (two-loop five-point, p1^2 = p3^2 = m^2)' TO 'One-mass-pair non-planar hexa-box (two-loop five-point, p1^2 = p3^2 = m^2; p2^2 = p4^2 = p5^2 = 0)' and the title line FROM '# Two-mass non-planar hexa-box (two-loop five-point)' TO '# One-mass-pair non-planar hexa-box (two-loop five-point)' -- the family named as `hexabox-evaluate.py` line 2 now names it; the body's 'two-mass five-point letters / masters' are class names against the massless and one-mass sets and stay. Every other line of the file identical. - NEW `vendor_row24_pathC/` (30 files: the 28 objects of the 2026-09-11T12:18:07Z draft's tables 3a-3e and 4, README.md, VENDOR_MANIFEST.sha256 6d9f11d66c7275e1... by gen_vendor_manifest_v3.py). The transport equation dY/du = A(u) Y of the 98 masters along Path C from Pfit = (-3, -5, -7, -2, -11, 1) to P3 = (-5, -7, -9, -2, -11, 1): the six exact fixed-d0 slices = THE CERTIFIED TRANSPORT (d0 = 13/3 `PATHC_DE_d013_3_20260911T051448Z.json.gz` 78ac7d79fbeab1b6..., d0 = 9/2 `PATHC_DE_d09_2_20260911T035535Z.json.gz` 11f86f163eeec04b..., d0 = 5 `PATHC_DE_d05_20260911T040607Z.json.gz` 32f74a9fb9e4296c..., d0 = 11/2 `PATHC_DE_d011_2_20260911T041800Z.json.gz` 5940ab2b632192cc..., d0 = 6 `PATHC_DE_d06_20260911T043033Z.json.gz` 9a4b140510234336..., d0 = 7 `PATHC_DE_d07_20260911T050120Z.json.gz` f1f1df291e1e73b6...), each 1416 nonzero entries P(u)/Q(u) over Q reconstructed from 176 nodes; the P3 gate receipts (d0 = 13/3 `HELDOUT_GATE_P3_fixed_d_d013_3_20260911T115727Z.json` 664e4420887ecd56..., d0 = 9/2 `HELDOUT_GATE_P3_fixed_d_d09_2_20260911T115727Z.json` 3d4b3525bd5c6a98..., d0 = 5 `HELDOUT_GATE_P3_fixed_d_d05_20260911T101320Z.json` cd53ccfac14cf2ea..., d0 = 11/2 `HELDOUT_GATE_P3_fixed_d_d011_2_20260911T115728Z.json` 5a27b860ebf73141..., d0 = 6 `HELDOUT_GATE_P3_fixed_d_d06_20260911T104425Z.json` 462c5e84747e086e..., d0 = 7 `HELDOUT_GATE_P3_fixed_d_d07_20260911T110254Z.json` 144e63258880ada9...) and their summary `HELDOUT_GATE_P3_fixed_d_SUMMARY_20260911T115728Z.json` 995984ee9377299a... -- verdict PASS: at d0 = 13/3, 9/2, 11/2 all 98 masters compared with the independent AMFlow evaluation at P3 agree to 62.5 / 63.6 / 61.7 digits complex-relative (67.2 / 66.6 / 64.2 on the real parts), floor 61.7, pass bar 50; the integer d0 = 5, 6, 7 are not certification slices (1 / 0 / 0 of 98 compared: the masters carry poles there); the gate's completion receipt `LANDING_GATE_P3_fixed_d_20260911T110615Z.json` 31a7afe815d307cb...; the generic-d connection v2 `PATHC_CONNECTION_generic_d_20260911T112703Z.json.gz` 990a8a168845d58f... (a supplementary object, not the certified transport: 1416 entries, u-coefficients exact rational in d, max d-degree 19, fitted on 38 slices, checked exactly at the two withheld slices d0 = 70/11: 1414 EXACT, 2 degree d; d0 = 41/11: 1416 EXACT) with its completion receipt `LANDING_generic_d_connection_v2_20260911T112716Z.json` 7cae58164a0da065...; the authors' README `README_pathC_connection.md` 51e74be6d1f96854... (byte for byte) and manifest v3 `MANIFEST_pathC_connection_20260911T114239Z.json` 39c69a39b018983e...; the instruments `loo_read_B2_v4_20260911T015655Z.py` 4f967b91d8e4efda..., `pathc_transport_arb_B2.py` 8411036c3b9f744a... with its DRY `DRY_transport_arb_pathC_d09_2_20260911T045629Z.json` 4551bf056d6e20d7... (DRY PASS), the gate drivers `heldout_gate_P3_fixed_d_B2_v7_20260911T115212Z.py` 6fb5d900b07612d6... and `heldout_gate_P3_fixed_d_B2_v5_20260911T104424Z.py` b19d93005f02e57e..., the slice builder `pathc_slices_pieces_B2_20260911T083855Z.py` 8c8ed54f938b2b7b..., the fits `bivariate_connection_B2.py` edb9763fa0574594... and `bivariate_connection_B2_three_20260911T110958Z.py` a0e1f43de4f39d76...; the node manifest `NODES_pathC_176_20260911T121807Z.json` c0ff1dabbe9dc78c...; the self-check `selfcheck_pathC_B2.py` 1a59441a35886d2f.... VENDORING RULE (this bundle's rule of 2026-09-09 for vendored receipts, applied by field): 1 of the 28 objects serve byte for byte (`README_pathC_connection.md`); the other 27 carry re-cut string values -- a path value -> the basename of the file it named with that file's sha256, a narrative value carrying working vocabulary or a machine label -> "withheld", the authors' statistics term for a check never used in any fit inside a value kept as emitted, every numeric leaf, exact coefficient string and key name as emitted; the seven gzipped objects re-cut the same way inside (their `entries` member identical, asserted), re-serialized in their own compact form, re-compressed with a zero timestamp; the node manifest's fetch field replaced by the sentence 'available from the authors on request'; the eight scripts as register successions (narrative words and the record's directory literals re-cut; the environment variable naming the computation's root directory reads B2_ROOT_ABS in the slice builder and the two fit instruments (cure 1; a name inside a string literal and comments, string-masked code units unchanged); the toolkit import of the leave-one-out read names RATFIT_DIR, module ratfit 6fedd9b01e5c7842... not shipped; each states its changes at the end of its docstring; all eight compile). README.md names every object AS EMITTED by sha256 (`vendored_from`) -- those are the shas of the draft's tables. NOT SHIPPED: the 176 AMFlow node objects the slices were reconstructed from (561018998 bytes) -- listed by tag, u, sha256 and bytes in the node manifest, available from the authors on request; the further fit slices of the generic-d build; the AMFlow-at-d0 leg outputs the gate driver read (named by sha256 inside each receipt). - THE SELF-CHECK, a runnable succession of the script of record (its three default paths name its own directory; it ends `SELF-CHECK PASS` or `SELF-CHECK FAIL BY NAME: ...` with exit 1; cure 1: with no node object present part (2) prints its not-exercised line only, and the leave-one-out module -- which needs python-flint -- is loaded only when a node object is present, so the shipped form runs on python3 alone). MEASURED in 200%-CPU scopes on a scratch copy of this tree: `python3 vendor_row24_pathC/selfcheck_pathC_B2.py` exit 0, wall 0:00.17, peak 17248 kB: `(1) the residue at u = 1: 14 polar entries on rows [37, 38, 41, 60, 69, 78, 82] x cols [4, 7]`; `R^2 == 0: True | rank R: 1 (rows proportional)`; `the no-log (kernel) condition at u = 1: y[7] = 1 * y[4] (indicial exponents 0; a regular solution has R Y(1) = 0)`; `(2) no node object present under vendor_row24_pathC/node_objects: the sample reproduction was not exercised (the 176 node objects are listed by sha256 in NODES_pathC_176_20260911T121807Z.json beside this file; they are not shipped)`; `SELF-CHECK PASS`. The same with the user site-packages hidden (no python-flint importable): exit 0, `SELF-CHECK PASS`. With the 176 node objects of record placed as --nodes-dir (read-only; not shipped): exit 0, wall 0:01.79: `(2) THE SLICE REPRODUCES THE SAMPLES: 4248/4248 exact (exact to all digits)` -- `SELF-CHECK PASS`. Controls: one coefficient of the polar entry (82,4) of the 13/3 slice changed in a copy -> exit 1: `SELF-CHECK FAIL BY NAME: rank R > 1 (the polar rows of the residue are not proportional)`; one coefficient of the entry (1,1) changed in a copy, with the node objects -> exit 1: `SELF-CHECK FAIL BY NAME: 3 of 4248 node samples not reproduced exactly [('1,1', '1/4'), ('1,1', '1/3'), ('1,1', '2/3')]`. - `MANIFEST.sha256` re-emitted by gen_hexabox_manifest_v6.py (= gen_hexabox_manifest_v4.py, the generator of record, + the vendor_row24_pathC/ group read from its VENDOR_MANIFEST.sha256 and its objects, one header line, the PRODUCER line (v5); + the role sentence of `hexabox-expression.md` naming the family as the file's header now does and four instrument role sentences of the group (v6, cure 1)): the served rows kept byte for byte but `hexabox-evaluate.py`, `hexabox-expression.md`, `CHANGES.md` (re-pinned) and the 30 new rows; `sha256sum -c MANIFEST.sha256` exits 0. The previous shas 45ba7434e10fae02... / a3b24d2b072bd5a1... were held by MANIFEST.sha256 only (hexabox-evaluate.py: CHANGES.md, MANIFEST.sha256; hexabox-expression.md: MANIFEST.sha256) -- no in-code pin, no superseded copy (this bundle carries none). - NOT DONE here, stated: (i) the clause '(7 rational, 5 algebraic)' above; (ii) the BOUNDARY REGENERATE paragraph's 'an open point for a later succession' sentence in `hexabox-evaluate.py` is left as served: its subject is the 34 significant fit-point seed components that carry closed-form constants, which no object of this delivery enters exactly (the group vendored here is the fixed-d transport of the third segment; the exact (97,0,2..4) kernel layers it might be read against are already served under vendor_row24_kernels/ and run by --boundary-regenerate; the kernel succession that retires the numeric fits in the default tiers is a separate, later entry with code changes, and it keeps the seed cap); (iii) `--kmax 5`, `--boundary-regenerate` and the other long tiers were not re-run (unchanged code; their last measured walls stand in the 2026-09-09 entry); (iv) the page and article sentences of the same receipt are not bundle files. ## 2026-09-11 -- the (97,0,2..4) succession: numeric fits -> exact layers; the KNOWN GAP retired (`hexabox-vop-data.json.gz` succeeded, the previous bytes beside as `superseded_04bfd5f45c625ae8/`; row 24) - `hexabox-vop-data.json.gz` 04bfd5f45c625ae8a2c4a05b054ab37e7c5fbc7c50f0fa3bbbf6d65cdf2fbbe9 -> f9e64518cb2e9ef35dfb827c37de8ddf463025c428102487a6c71a6f8f7321ea (14616865 -> 14694623 bytes; the previous bytes kept byte for byte as `superseded_04bfd5f45c625ae8/hexabox-vop-data.json.gz` with `README.md` 86310a9fb1eb9639... and `SHA256SUMS` 9b2cd097f30c903c...). The three top-row kernels (97,0,m), m = 2, 3, 4 -- the KNOWN GAP of every earlier release, carried under `hybrid_kernels` as certified-numeric mpf rational fits (degrees 93/93 / 93/93 / 93/93) and run by the served default and `--point` tiers -- enter `exactA` EXACT: `exactA['97,0,m'] = [P, Q]`, the coefficient strings as they stand (Fraction-parsable, Q monic, low to high in t), from layers 2, 3, 4 of `vendor_row24_kernels/KERNELS_CANDIDATE_item56_97_0_20260907T041028Z.json` (adbae0c89d3db900...; the object as emitted d223992d5ee27c02...; fmpq rationals by CRT + rational reconstruction on 101 path nodes, 8 withheld nodes reproduced, 14 primes, 854 CRT bits; degrees (P,Q) (120,122), (149,151), (178,180)), asserted equal by exact list equality to layers 2, 3, 4 of `vendor_row24_eps12/KERNELS_CANDIDATE_v2_item56_97_0_20260907T043901Z.json` (13f543565bf26ce4..., the file that entered (97,0) m = 5..9 on 2026-09-07) and to the object as emitted (VK = VE = record: m 2 True, m 3 True, m 4 True); `hybrid_kernels` = {} (the key kept); 8179 -> 8182 exact entries + 3 -> 0 numeric kernels; `_provenance.hybrid_kernels` re-written to the fact, `_provenance.exactA` gains one clause (the entry count), `_fold.hybrid_kernels` retired with its earlier text kept verbatim inside it (the served string itself, its two em dashes as characters), a top-level `_succession_2` block naming the succeeded sha256, the three entered keys with their source objects, the emptied keys, the fits-vs-exact check of record and the order of 2026-09-11T14:05:15Z (section A; 241be174633fe3a4...); every other key, numeric and rational leaf, seed cell and string byte-equal (asserted at build); serialization as the served file's (json.dumps default form, gzip level 9) with header timestamp 0 -- a second build reproduces the bytes (asserted; uncompressed 37778643 -> 37968127 bytes, 327a0343581b428f... -> e6c0241626521729...). THE OBJECT CHECK OF RECORD (efed77cfba95f877..., 2026-09-11T13:40:49Z): the exact layers against the served fits at 7 path points (t = 1/20, 1/4, 19/50, 3/5, 7/10, 9/10, 1) at working precisions 90 AND 130: floor 68.15 digits (per kernel (97,0,2) 68.15 / (97,0,3) 68.38 / (97,0,4) 68.69; the two precisions agree to 0.01), planted control (one exact coefficient scaled by 1 + 1e-40) seen at every point, FAIL by name; the four files carry identical layers 2, 3, 4; the served m >= 5 layers are the vendored v2 object. Re-read at build at t = 1/4 and 9/10 at working precision 90: (97,0,2) 70.04, 70.64; (97,0,3) 70.36, 69.53; (97,0,4) 69.68, 69.98 (floor 69.53; each within 0.05 of the record's dps-90 figure at the same point). - `hexabox-evaluate.py` 93298ecefea0de55... -> bcd3172ec2fbac15... (2115 -> 2101 lines). CODE: B5 -- the default tier's assertion is now `assert V.hybrid_used == [] and len(V.HYBRID) == 0` in EVERY tier (the served form asserted the three numeric kernels had fired unless --boundary-regenerate; on the succeeded bundle it would raise); B7 -- `regen_bundle_path()` part (i) no longer swaps layers in: it asserts `hybrid_kernels == {}` and, per key of REGEN['kernels'], `exactA[key] == [P, Q]` of the vendored object (the identity every tier now relies on; printed as `kernels (97,0,2, 97,0,3, 97,0,4): ... 3/3`), part (ii) the seeds unchanged; the fit-vs-exact probe reading is DROPPED with the fits (our call: the fits are in no tier's value path; their agreement with the exact layers is recorded once, above and in `superseded_04bfd5f45c625ae8/README.md`; a served tier reading an unpinned superseded copy at run time was not wanted), so the closing summary line's 'fits vs exact kernels worst ...' clause becomes 'the bundle's (97,0,2..4) layers equal the vendored exact object (asserted; no numeric kernel)' and REGEN keeps 'probe_t' as emitted, unread (comment says so); B8 -- SUCCESSION['bundle']['hexabox-vop-data.json.gz'] re-pinned 04bfd5f45c625ae8a2c4a05b054ab37e7c5fbc7c50f0fa3bbbf6d65cdf2fbbe9 -> f9e64518cb2e9ef35dfb827c37de8ddf463025c428102487a6c71a6f8f7321ea (full values), the previous sha kept as 'served_before_2' beside 'gated_bytes' / 'served_before' (this pin declares the record layer 5 on the engine; a bundle of another sha runs with record layer 3 -- it is not an exit-3 pin; exit 3 / 4 stay the vendored-JSON pins). TEXT (docstring, help, prints), one clause each: B1+B1b docstring FUNCTION CLASS ('analytic, nothing bottoms out in stored floats, EXCEPT -- in the served default tiers -- t ...' -> 'analytic, nothing bottoms out in stored floats, and every kernel of the recursion is an exact fmpq rational, E ...'); E3 docstring Check 3a (83-term sentence) ('coefficient of every top master is an 83-term exact iterated-integral closed form with ZER ...' -> 'coefficient of every top master is an 83-term exact iterated-integral closed form with ZERO numeric seeds; on ...'); B2 docstring THE THREE KERNELS block ('THE THREE KERNELS (97,0,m), m = 2, 3, 4 (2026-09-09; the KNOWN GAP of the releases before ...' -> 'THE THREE KERNELS (97,0,m), m = 2, 3, 4 (the KNOWN GAP of earlier releases, retired): the bundle carries them ...'); B7-doc CLI comment of --boundary-regenerate ('python3 hexabox-evaluate.py --boundary-regenerate # the default check demo with the sec255 ...' -> 'python3 hexabox-evaluate.py --boundary-regenerate # the default check demo with the sec255 recursion on the 44 ...'); B3 docstring PRECISION MODEL tier sentence ('this cap); sec255 seeds = 70 digits plus, in the served default and --point tiers, the bun ...' -> 'this cap); sec255 seeds = 70 digits in the served default and --point tiers (every kernel exact, THE THREE KER ...'); B3 docstring Inputs sentence ('(exact rational graded path DE: the full 8151 exact entries + the 28 gated candidate kerne ...' -> '(exact rational graded path DE: the full 8151 exact entries + the 28 gated candidate kernels + the three (97,0 ...'); B4 docstring REACH CHECK gap count ('eps^4). Not a short coupling: an absent m below a coupling's max m present (the bundle's c ...' -> 'eps^4). Not a short coupling: an absent m below a coupling's max m present (on the succeeded bundle of 2026-09 ...'); B4 docstring REACH CHECK entry count ('lines (the loader line and the reach table count this bundle's 8179 entries). ...' -> 'lines (the loader line and the reach table count this bundle's 8182 entries). ...'); B8 docstring EPS^1, EPS^2 SUCCESSION bundle sha ('of record (c4d86690801bcef6..., re-cut only in provenance strings to the shipped 04bfd5f45 ...' -> 'of record (c4d86690801bcef6..., re-cut only in provenance strings to 04bfd5f45c625ae8..., itself succeeded 202 ...'); B7-doc BOUNDARY REGENERATE part (i) ('with --kmax 4 / 5) re-run on REGENERATED INPUTS, everything else as served: (i) the three ...' -> 'with --kmax 4 / 5) re-run on REGENERATED INPUTS, everything else as served: (i) the three kernels (97,0,m), m ...'); B7-doc BOUNDARY REGENERATE 'removes the three fits' clause ('then print in the served form; the oracle comparison stays capped by the oracle's own 60 d ...' -> 'then print in the served form; the oracle comparison stays capped by the oracle's own 60 digits: the tier lift ...'); B7-doc BOUNDARY REGENERATE 'keeps the fits' clause ('the exact kernels beyond the 101-node reconstruction (candidates reproducing both oracle r ...' -> 'the exact kernels beyond the 101-node reconstruction (candidates reproducing both oracle records, no proof); t ...'); B7-doc --boundary-regenerate help ('help="sec255 recursion on REGENERATED inputs: the three (97,0,m) kernels EXACT from vendor ...' -> 'help="sec255 recursion on REGENERATED inputs: the 447 from-definition fit-point seeds of " "vendor_row24_seeds ...'); B7-doc REGEN kernels comment (''kernels': ['97,0,2', '97,0,3', '97,0,4'], # the three certified-numeric fits of the bundl ...' -> ''kernels': ['97,0,2', '97,0,3', '97,0,4'], # the three (97,0,m) layers the bundle carries exact since 2026-09- ...'); B7-doc REGEN probe_t comment (''probe_t': ['1/7', '2/9', '3/8', '5/11', '7/10'], # interior probe points for the fit-vs-e ...' -> ''probe_t': ['1/7', '2/9', '3/8', '5/11', '7/10'], # the probe points of the retired fit-vs-exact reading (the ...'); B7-doc REGEN labels[0] ('(CRT + rational reconstruction on 101 path nodes, 8 withheld nodes reproduced) in place of ...' -> '(CRT + rational reconstruction on 101 path nodes, 8 withheld nodes reproduced), carried exact by the bundle it ...'); B7-doc REGEN labels[2] (''the oracle comparison stays capped by the oracle\'s 60 digits: this tier removes the thre ...' -> ''the oracle comparison stays capped by the oracle\'s 60 digits: this tier lifts the seed cap on the 447 replac ...'); B6-regen regenerate-branch NOTE ('print(" NOTE: no certified-numeric kernel entered this recursion: the three (97,0,m) kerne ...' -> 'print(" NOTE: every kernel of this recursion is an exact rational (the bundle's exactA; the three (97,0,m) lay ...'); B6-regen regenerate-branch 'fits out of the value path' clause ('f"exactly; the fits are out of the value path; the oracle comparison below stays capped by ...' -> 'f"exactly; the oracle comparison below stays capped by the oracle's 60 digits.") ...'); B6 code default-tier NOTE lines ('print(" NOTE: the 3 certified-numeric kernels above are the ONLY non-exact kernels;") prin ...' -> 'print(" NOTE: every kernel of this recursion is an exact rational; the stored boundary-seed strings") print(" ...'); B3-point run_point_255 trailing note ('print(" seed strings and, for eps^-2..eps^0, the bundle's certified-numeric fits of the") ...' -> 'print(" seed strings; every kernel of this tier is an exact rational, the (97,0,2..4)") print(" layers include ...'). Every other in-code pin unchanged (the vendored .json pins of SUCCESSION / REGEN / GATEPOINT name unchanged files; `hexabox_record_pair.py` and `hexabox_vop.py` carry no pin of the data bundle). String-masked syntax-tree census against the served bytes (every str constant and f-string masked): 116 top-level units, 112 identical, changed `assign SUCCESSION`, `def regen_bundle_path`, `def run_sec255_live`, `if __name__ == '__main__'`, added none, removed none -- the recursion's value path (`Vop255`, `run_numeric`, `endpoint`, the certificates, `run_sec219`, `run_exact_functions`, `run_closed_forms`) untouched; `run_point_255` differs in string constants only. py_compile OK. - `hexabox_vop.py` 294be9589cff5e50... -> 6137855a10de03ec...: the engine's header, B9 ('Known limitation: all kernels are exact fmpq rationals EXCEPT the three disclosed certified-numeric fits ...' -> 'All kernels are exact fmpq rationals (bundle["exactA"]); bundle["hybrid_kernels"] is empty since the (97,0,2..4) succession and the numeric-kernel path below is kept only to read superseded bundles, whose output it labels.'); the loader label ('N exact entries + M certified-numeric') and the numeric-kernel path kept as served; string-masked census 12/12 units identical. py_compile OK. - `hexabox-expression.md` d6b08ea93654ff12... -> 2ed4fc48da8e6ea9... (406 -> 414 lines), the order's literal text: B10 Sec. 1 summary ('above). Section 2a lists those closed forms; three kernels stay certified-numeric (rows (9 ...' -> 'above). Section 2a lists those closed forms; every kernel of the top-sector recursion is an exact rational fun ...'); E2 Sec. 2a the eps^-4 layer as rational functions (inserted after the endpoint rationals) ('m2[eps^-4] = -854177 / 8639400 ...' -> 'm2[eps^-4] = -854177 / 8639400 On the path the eps^-4 layer is a rational function of t: with D(t) = m^2 (-s15 ...'); C1 Sec. 2a the 'UT (canonical)' label ('In the UT (canonical) normalization, ghat = (sqrt45709 * g0, sqrt45709 * g1, g2) ...' -> 'In the eps-factorized endpoint rotation, ghat = (sqrt45709 * g0, sqrt45709 * g1, g2) ...'); B11 Sec. 2a Tier 2 sentence ('precision. These are closed forms (not value-fits), verified at 59.67-61.07 digits at thos ...' -> 'precision. These are closed forms (not value-fits), verified at 59.67-61.07 digits at those orders, with every ...'); D1 Sec. 4 the Leviathan flag ('101 -> 75). One flag: the top block's odd radical is the quartic Q4 = 3721 t^4 + 6724 t^3 ...' -> '101 -> 75). The top block's odd radical is the quartic Q4 = 3721 t^4 + 6724 t^3 + 11824 t^2 + 16400 t + 7040 ( ...'); B12 Sec. 6 the first bullet ('- Three top-sector kernels stay certified-numeric: the path-DE entries (97,0,m) for m = 2, ...' -> '- Every kernel of the shipped recursion is an exact fmpq rational. The three path-DE entries (97,0,m), m = 2, ...'); D2+C2 Sec. 6 the Q4 bullet and its parenthesis ('- The top block's odd radical is Q4 = 3721 t^4 + 6724 t^3 + 11824 t^2 + 16400 t + 7040 (va ...' -> '- The top block's odd radical is Q4 = 3721 t^4 + 6724 t^3 + 11824 t^2 + 16400 t + 7040 (value 45709 at t = 1) ...'); B13 Sec. 7 the live-evaluation bullet ('printed to show the results are functions of the kinematics. The three certified-numeric k ...' -> 'printed to show the results are functions of the kinematics. ...'); beyond the order's pairs, the Sec. 2a 'Shipped live (2026-07-03)' parenthesis the succession turned false ('(trimmed to the 5018 layer-reachable entries; every kernel exact fmpq except the three disclosed fits)' -> '(8182 exact entries after the kernel successions of 2026-09-07 and 2026-09-11; every kernel an exact fmpq rational)'; the entry count read from the data bundle). BEFORE E2 was written the three rational functions were checked in exact arithmetic: at t = 0 they equal -437/13860, 409/1980, -33437/13860 (the seeds the text names) AND the bundle's own fit-point seed strings of rows 95, 96, 97 at eps^-4 to 70.88 / 69.78 / 69.70 digits (imaginary parts <= 1e-60); at t = 1 they equal the endpoint rationals -571/1079925, 46591/8639400, -854177/8639400 read from the file above the insertion; D(0) = 2772, D(1) = 1748450; 105 = -s12 s23 s34 at (-3,-5,-7). C2 and D2 were cut as one block (their FROMs share the '(The UT' seam). Em dashes: -2 (two of the FROMs carried one each). - `_snippet.md` (the unpinned companion, proposed page text) 6d7df399dd066779... -> 80dd65b6cd424c40...: E1 the single-path sentence ('the explicit solution is constructed along a single path through the six-scale space rathe ...' -> 'the explicit solution is constructed along kinematic paths through the six-scale space rather than over the wh ...'); B14 Honest scope ('Three kernels of the top-sector recursion remain certified-numeric fits — their true degre ...' -> 'Every kernel of the top-sector recursion is an exact rational function of the path parameter — the three top-r ...'); beyond the order's pairs, two sentences the expression file's C1 and D1 / D2 re-cuts had turned false: the normalization label ('In the canonical uniform-weight normalization ...' -> 'In the $\varepsilon$-factorized endpoint rotation ...', the rest of the sentence kept; the form the page's own line already carries) and the $Q_4$ sentence ('And the quartic $Q_4$ is not found as a Landau singularity of the alphabet, so its identif ...' -> 'The quartic $Q_4$ is the five-point Gram determinant restricted to the path, $Q_4(t)=\mathrm{Gram}_5(s(t))$ identically in $t$, and the direct Euler-characteristic test finds the drop from 101 to 90 on its locus, so the identification is settled.'); all four quoted in the delivery record for the page (em dashes 21 -> 20). `vendor_row24_kernels/README.md` be8ef9c6cbffaabf... -> 58a3da0c3a1a9898...: B15 first sentence ('The served bundle `hexabox-vop-data.json.gz` carries the three kernels (97,0,m), m = 2, 3, ...' -> 'The served bundle `hexabox-vop-data.json.gz` carries the three kernels (97,0,m), m = 2, 3, 4, EXACT in `exactA ...'); B15+ 'served as fits' clause ('Its layers 2, 3, 4 are the three kernels served as fits; its layers 2..7 ...' -> 'Its layers 2, 3, 4 are the three kernels the served bundle carries in `exactA` (served as fits before 2026-09- ...'); B15+ 'keeps the fits' clause ('no proof); the served bundle keeps the fits. ...' -> 'no proof); the numeric fits of the earlier bundles are kept under `superseded_04bfd5f45c625ae8/`. ...') (the order asked for the first sentence; the two further clauses would have turned false on the succeeded bundle); its `VENDOR_MANIFEST.sha256` f6149d4ee492073c... -> 71fabb464f195ce6... re-emitted by gen_vendor_manifest_v3.py (the group's producer of record; the PRODUCER stamp line and the README.md row move, nothing else). `vendor_row24_eps12/README.md` faade173f943688d... -> 781d3c870783e1aa... (not in the order: the pin-holder census found its line 3 naming the data bundle by the old sha256 -- re-pinned to f9e64518cb2e9ef35dfb827c37de8ddf463025c428102487a6c71a6f8f7321ea... with the succession stated; its BUILD_RECEIPT bullet's 'still served as such' likewise): PIN eps12 README line 3 (the data bundle's sha256) ('The served `hexabox-vop-data.json.gz` (sha256 `04bfd5f45c625ae8...`) is the SUCCEEDED bund ...' -> 'The served `hexabox-vop-data.json.gz` (sha256 `f9e64518cb2e9ef3...`; until the (97,0,2..4) succession of 2026- ...'); PIN eps12 README BUILD_RECEIPT bullet ('are the three certified-numeric kernels (97,0,2..4), still served as such, and the six m > ...' -> 'are the three kernels (97,0,2..4), then served as certified-numeric fits and entered exact on 2026-09-11, and ...'); its `VENDOR_MANIFEST.sha256` a77450b17e3e687d... -> 5fef37f8593202b4... re-emitted by gen_vendor_manifest.py (that group's producer of record; stamp line + README.md row). `sha256sum -c` exits 0 in both groups. - MEASURED (scratch copies of the served tree and of this tree, one 200%-CPU / 8G scope each on a shared host, side by side; captures masked of timing lines and scratch paths). The default check demo BEFORE / AFTER: exit 0 / 0, wall 9:07.87 / 8:59.56, peak RSS 4690332 / 4690896 kB; the loader `8179 exact entries + 3 certified-numeric` -> `8182 exact entries + 0 certified-numeric`; the reach header `3 absent layers below a coupling's max m present` -> `0`; the three `[vop/T2] CERTIFIED-NUMERIC kernel (97, 0, m) entered the recursion` lines gone; the NOTE `NOTE: the 3 certified-numeric kernels above are the ONLY non-exact kernels;` -> `NOTE: every kernel of this recursion is an exact rational; the stored boundary-seed strings (50 / 70 digits) cap endpoint agreement above eps^-4 (--boundary-regenerate replaces the 447 covered seeds).`; the 15 top-sector coefficients against the independent deep-60 oracle IDENTICAL before / after in every printed digit of the value (24) and of the agreement (m0_eps-4 57.88 / 57.88; m0_eps-3 57.50 / 57.50; m0_eps-2 57.83 / 57.83; m0_eps-1 57.54 / 57.54; m0_eps+0 56.54 / 56.54; m1_eps-4 57.84 / 57.84; m1_eps-3 57.46 / 57.46; m1_eps-2 57.89 / 57.89; m1_eps-1 57.65 / 57.65; m1_eps+0 56.76 / 56.76; m2_eps-4 58.00 / 58.00; m2_eps-3 57.52 / 57.52; m2_eps-2 58.08 / 58.08; m2_eps-1 57.75 / 57.75; m2_eps+0 56.91 / 56.91); min over 15 = 56.54 / 56.54 d; sec219 40.63 / 40.63 d; the other summary lines identical (`sec219 min independent check, transported live: 40.63 d`; `sec255 top-sector 15-coefficient check, recursed live: 56.54 d`; `eps^-4 exact functions (zero seeds) vs independent oracle: 55.6 d`; `Named boundary constants vs independent oracle, live: 69.1 d`; `sec223 18-coefficient check (archived transport values): 32.86 d`); the two outputs differ in 8 / 5 lines, all of them the designed ones above. Re-run on this entry's final bytes (the data bundle f9e64518cb2e9ef3..., the evaluator bcd3172ec2fbac15...; the retired `_fold` note decoded, the pin re-pointed): exit 0, wall 8:47.03, peak RSS 4693708 kB, `[succession] bundle f9e64518cb2e9ef3... is the succeeded bundle: record layer 5 declared (the gate of record checked its layers through 5; the engine's class default is 3)`, the loader `8182 exact entries + 0 certified-numeric`, the 15 values and agreement figures identical to the AFTER run in every printed digit, min over 15 = 56.54 d, `All checks passed`; against the AFTER run the output differs in 1 / 1 line, the succession line only. `--kmax 5` BEFORE / AFTER: exit 0 / 0, wall 13:35.95 / 13:47.04, peak RSS 6296232 / 6300940 kB; `EPS^1,2 GATE (--kmax 5): eps^+1 40.21 d, eps^+2 35.29 d vs bar 30 d over three references x 3 masters -> ESTABLISHED; the two-precision pair by --dps-double` in both (record: eps^+1 40.21 d, eps^+2 35.29 d); the 15 lower-order figures identical; 8 / 5 differing lines, the same designed set. `--boundary-regenerate` AFTER (its code changed, B7): exit 0, wall 9:14.04, peak RSS 4688564 kB; 10/10 vendored pins OK; `exact kernel layers ... byte-equal to layers 2, 3, 4 of the served candidate file: 3/3`; `kernels (97,0,2, 97,0,3, 97,0,4): the bundle's exactA layers equal layers 2, 3, 4 of KERNELS_CANDIDATE_item56_97_0_20260907T041028Z.json: 3/3`; SEED CERTIFICATE >= 78 d, served seeds vs from-definition min 69.32 d, TRUE INPUT CAP 69.32 d (as served); `regenerated bundle written ...: 8182 exact entries + 0 certified-numeric`; min over 15 = 56.54 d; `All checks passed`; against the AFTER default it differs only in the regenerate tier's own lines (the loader's cross-check reads 69.35 vs 85.8 digits and the sunrise-seed line as documented under BOUNDARY REGENERATE). `--point 0.62 --sec 255 --dps 30` BEFORE / AFTER: exit 0 / 0, wall 6:07.09 / 5:55.64; the 15 printed function values at t = 0.62 identical (e.g. m2[eps^+0](t) = (7.20241730715912683292491 - 50.6187090793567204533155j)); the trailing note now reads `seed strings and, for eps^-2..eps^0, the bundle's certified-numeric fits of the (97,0,2..4) kernels -- this tier runs the served fits; --point is refused with --boundary-regenerate)` / `seed strings; every kernel of this tier is an exact rational, the (97,0,2..4) layers included -- --point is refused with --boundary-regenerate)`. The string tiers BEFORE / AFTER: `--record-point P2` exit 0 / 0, `--gatepoint` 0 / 0, `--kmax 2` 2 / 2 (0 / 0 / 0 differing masked lines), `--help` 0 / 0 (9 lines differ: the --boundary-regenerate help); `--regen-dir` alone 2, `--boundary-regenerate --point` 2. NOT RUN (the 15-minute cap on documented walls): `--boundary-regenerate --kmax 5` (14:22 documented 2026-09-09), `--kmax 5 --dps-double` (1222 s documented 2026-09-07). - PLANTED CONTROLS (a scratch copy of this tree whose data bundle has one exact coefficient changed: exactA['97,0,3'] P[5] scaled by (1 + 10^-40), the object check's planted form; that copy's sha256 50554155ccf3fef5...). The default tier: `[succession] bundle 50554155ccf3fef5... is not the succeeded bundle (f9e64518cb2e9ef3...): the engine's record layer 3 stands`, then the recursion runs and the independent-oracle comparison FAILS BY NAME -- `sec255 check FAILED at m0_eps-1: 40.43 d <= bar 45.0 d (strict; rel 3.68e-41 vs 10^-bar/2 5.0e-46)` -- exit 1 (wall 8:26.65): the planted 1e-40 shows at 40.43 d where the unplanted layer reads 57.54 d. `--kmax 5` on the same copy: the record layer is not declared (the sha is not the pinned one), the reach check runs at record layer 3 and REFUSES BY NAME before any layer is computed -- `REFUSED by name -- VoP reach: 386 coupling(s) short of the reach at KMAX 5 and 0 row(s) without a seed at a computed layer -- coupling (70,70) layer 2 absent within the r...` -- exit 1 (wall 0:46.89). - `MANIFEST.sha256` re-emitted by gen_hexabox_manifest_v7.py 90817da7d7f2f512... (= gen_hexabox_manifest_v6.py f541d5cc7db1ad4f..., the generator of record, + the minimal change, 8 lines of v6 replaced: the data bundle's (97,0,2..4) layers asserted exact against the vendored (97,0) object with `hybrid_kernels` empty and `_succession_2` present; the superseded group read from that block, checked against its own `SHA256SUMS`, not walked; the role sentences of the data bundle, of the evaluator's --boundary-regenerate and of the (97,0) kernel object re-cut to the fact; one header line `# unpinned companion group: superseded_04bfd5f45c625ae8/ (...)`; the PRODUCER line; every other emitted line byte-identical): the served rows kept byte for byte but `hexabox-vop-data.json.gz`, `hexabox-evaluate.py`, `hexabox_vop.py`, `hexabox-expression.md`, `CHANGES.md`, `vendor_row24_kernels/README.md`, `vendor_row24_kernels/VENDOR_MANIFEST.sha256`, `vendor_row24_eps12/README.md`, `vendor_row24_eps12/VENDOR_MANIFEST.sha256` (re-pinned); `_snippet.md` stays the unpinned companion; `sha256sum -c MANIFEST.sha256` exits 0; `sha256sum -c SHA256SUMS` inside `superseded_04bfd5f45c625ae8/` exits 0. py_compile of all 12 .py files of the tree: OK (no pre-existing failure); no .sh file in the tree. - NAMING: the order writes `superseded_/`; this bundle follows the site's convention for superseded copies (the directory named by the old file's sha16, `superseded_04bfd5f45c625ae8/`, with `README.md` and `SHA256SUMS`), as the sibling bundles do. `_succession_2` is a top-level key of the data bundle beside `_provenance` and `_fold` (the loader reads named keys only). - NOT DONE here, stated: (i) the page's two sentences (its lines 85 / 91: the Scope sentence and the kernels sentence) and the article's four D2 pastes are not files of this bundle and fold only after it is installed; (ii) three sentences outside the order's pairs that the succession had turned false -- `hexabox-expression.md` Sec. 2a 'Shipped live (2026-07-03)' and, in `_snippet.md`, the normalization label and the $Q_4$ 'stays open' sentence -- were re-cut above rather than left; the page's own copies of the two `_snippet.md` sentences are the page's; (iii) `--boundary-regenerate --kmax 5` and `--kmax 5 --dps-double` were not re-run (documented walls above the cap; their code path is the one exercised by `--boundary-regenerate` and `--kmax 5` separately, both exit 0 here); (iv) the 34 kept seed components of closed-form constants (BOUNDARY REGENERATE's open point) are untouched -- this succession changes kernels, not seeds; (v) `vendor_row24_kernels/README.md` line 1 and `vendor_row24_eps12/README.md` line 1 keep the label 'two-mass' of their emission date (the family label X1 re-cut elsewhere on 2026-09-11); not in the order. ## 2026-09-11 -- the endpoint-rotation naming pass: the working label 'UT-basis' retired on two lines of `hexabox-expression.md` and one docstring line of `hexabox-evaluate.py` (row 24) - `hexabox-expression.md` 2ed4fc48da8e6ea966333f519187c4a241d7849a471881cfac1495071c5d85d2 -> 43c488aefe8f8b5af70639361546b93a55b33b3cf2b18a8eaf91f67e27724cc4 (414 lines, count unchanged; lines 400 and 401 only). Sec. 7 'Reproducing the result', the item 'Named boundary constants, evaluated live': line 400 'UT-basis' -> 'endpoint-rotation'; line 401 'exact-in-eps UT' -> 'exact-in-eps endpoint' (the phrase closes on line 402 with 'rotation)', so it now reads 'the exact-in-eps endpoint rotation'). The sentence whole, BEFORE: '- **Named boundary constants, evaluated live.** The three eps^-4 rationals, the UT-basis eps^-4 rationals and the eps^-3 pi-rational imaginary parts are computed at runtime (rational arithmetic + pi + the exact-in-eps UT rotation) and verified against BOTH the live recursion output and the independent oracle (69.1-70.7 digits vs the oracle).' AFTER: '- **Named boundary constants, evaluated live.** The three eps^-4 rationals, the endpoint-rotation eps^-4 rationals and the eps^-3 pi-rational imaginary parts are computed at runtime (rational arithmetic + pi + the exact-in-eps endpoint rotation) and verified against BOTH the live recursion output and the independent oracle (69.1-70.7 digits vs the oracle).' Why: the article (its p. 112), the site page and this file's own Sec. 2a (line 176: 'In the eps-factorized endpoint rotation, ghat = (sqrt45709 * g0, sqrt45709 * g1, g2)') call the object the eps-factorized endpoint rotation; 'UT-basis' was the working name, left on these two lines when Sec. 2a was re-named earlier today. - `hexabox-evaluate.py` bcd3172ec2fbac15f4c6c0ee58fc9e180dd40524ced9c80390e0321b1ebff19e -> cdc3d9147491a38e52fe56eef901801cfa309d7d4ff25d00c0e267aeb03b8b7a (2101 lines, count unchanged; line 66 only): the module docstring's Check 3b sentence -- the same named-boundary-constants description as the expression file's item above (both name the exact eps^-4 rationals, the eps^-3 pi-rational imaginary parts, the runtime computation and the independent oracle; asserted before the edit) -- 'UT-basis' -> 'endpoint-rotation'. BEFORE: 'Check 3b -- named boundary constants: the exact eps^-4 rationals, UT-basis eps^-4 rationals and eps^-3 pi-rational imaginary parts are computed from rational arithmetic + pi at runtime and verified BOTH against the live recursion output of Check 2 and against the independent oracle.' AFTER: 'Check 3b -- named boundary constants: the exact eps^-4 rationals, endpoint-rotation eps^-4 rationals and eps^-3 pi-rational imaginary parts are computed from rational arithmetic + pi at runtime and verified BOTH against the live recursion output of Check 2 and against the independent oracle.' VALUE PATH UNTOUCHED: string-masked AST per top-level unit 116/116 identical (0 changed, 0 added, 0 removed); unmasked, the one differing unit is the module docstring; py_compile OK; the docstring reaches no output (`--help` prints an argparse literal, and no print names the docstring). No superseded copy is kept: this bundle's `superseded_/` convention holds the previous bytes of a pinned DATA object whose values a tier read (`superseded_04bfd5f45c625ae8/` holds the earlier `hexabox-vop-data.json.gz`); the evaluator's own byte moves of 2026-09-09 and of the two entries above were re-pins without a kept copy, and so is this one. - CENSUS, not change -- the remaining sites of /\bUT\b|UT-basis|UT basis/ (as written) and /uniform.transcendental|canonical/ (any case) in the bundle's prose, scripts (docstrings, comments, print strings, code), data strings and READMEs after this pass: 11. `hexabox-evaluate.py` line 1881, a code comment ('# UT basis: ghat = diag(sqrt45709, sqrt45709, 1) . T(eps) . (m0,m1,m2)'), and lines 1882, 1883, 1884, 1885, 1894, 1896, the local identifier `UT = S["ut"]` reading the data key `ut` (6 lines); `hexabox-data.json` line 540, the `_src` string of that `ut` block ('closed-form UT-basis constants (eps^-4 closed, eps^-3 imaginary part) + the exact-in-eps rotation T(eps) series coefficients, orders 0,1 (only n<=1 contribute at eps^-4/-3)'); and 3 generic uses of 'canonical' in `hexabox-expression.md` Sec. 3 (lines 226, 237, 240: the constant / dlog-form sense). None is printed at runtime; none is changed here: the comment, the identifier and the data string name the same rotation and are listed for a later ruling (renaming the identifier or the data key would be a code / pinned-data change, not a wording pass). `_snippet.md`, `hexabox_vop.py`, `hexabox_vop_lib.py`, `hexabox_record_pair.py`, `superseded_04bfd5f45c625ae8/README.md`, `vendor_row24_eps12/README.md`, `vendor_row24_gatepoint/README.md`, `vendor_row24_kernels/README.md`, `vendor_row24_pathC/README.md`, `vendor_row24_pathC/README_pathC_connection.md`, `vendor_row24_seeds/README.md`: 0 sites. - MEASURED (one 200%-CPU / 8G scope on a shared host; captures compared with timing tokens masked). The default check demo on this tree: exit 0, wall 10:56.08, peak RSS 4694256 kB; `[succession] bundle f9e64518cb2e9ef3... is the succeeded bundle: record layer 5 declared (the gate of record checked its layers through 5; the engine's class default is 3)`; `Named boundary constants vs independent oracle, live: 69.1 d`; `All checks passed. Every digit count above was measured in this run.`; against the default-tier capture of the served bytes (exit 0, wall 8:47.03, peak RSS 4693708 kB -- the re-run on the previous entry's final bytes) the two outputs are IDENTICAL line for line once timing tokens are masked (239 lines each, 0 differing); the run wrote nothing into its tree. `--help` on the served bytes / on this tree: exit 0 / 0, 70 lines, identical. NOT RUN, none of their code, data or text having changed: `--boundary-regenerate` (documented above: exit 0, wall 9:14.04), `--kmax 5` (documented above: wall 13:35.95 / 13:47.04), the two together (14:22 documented 2026-09-09), and the string tiers `--record-point P2`, `--gatepoint`, `--point`, `--kmax 2`; the moved line is documentation only and reaches no tier's output. - `MANIFEST.sha256` re-emitted by gen_hexabox_manifest_v8.py 396f42f7004af5b2... (= gen_hexabox_manifest_v7.py 90817da7d7f2f512..., the generator of record, + the minimal change: a docstring paragraph, an optional `--base-manifest=PATH` changed-set assertion -- the rows that moved against the manifest it succeeds must lie in {`hexabox-expression.md`, `hexabox-evaluate.py`, `CHANGES.md`} with none added or gone --, the PRODUCER line naming v8 and this pass, one clause of the final print; 4 lines of v7 replaced, 23 lines new; every other emitted line byte-identical): the two rows above and `CHANGES.md` re-pinned, every other row and every header line but the PRODUCER line byte-identical to the served manifest; `_snippet.md` stays the unpinned companion and `superseded_04bfd5f45c625ae8/` the unpinned companion group, both untouched; `sha256sum -c MANIFEST.sha256` exits 0. Planted control of the assertion: a scratch copy of the staged tree, taken after this entry was appended (so its `CHANGES.md` row differs from the served manifest's as well), with one byte appended to `hexabox_vop_lib.py` -> `AssertionError: rows moved outside this pass's changed set ['CHANGES.md', 'hexabox-evaluate.py', 'hexabox-expression.md']: moved ['CHANGES.md', 'hexabox-evaluate.py', 'hexabox-expression.md', 'hexabox_vop_lib.py'], added [], gone []`, exit 1, nothing written (the copy's manifest untouched); the moved list depends only on which rows differ from the served manifest, not on this entry's bytes. py_compile of all 12 .py files of the tree: OK (no pre-existing failure); no .sh file in the tree. Holders of the two retired sha256 values anywhere in the bundle (text, scripts, the data bundles decompressed): `CHANGES.md` and `MANIFEST.sha256` -- the manifest is re-emitted and this file's history lines stay as written; no script PINS dict, README, VENDOR_MANIFEST, data object or snippet names either file; the evaluator's SUCCESSION block pins the data bundle (keys `bundle`, `gated_bytes`, `served_before`, `served_before_2`) and the vendored objects, not the expression file and not itself; the site page names neither sha256. - NOT DONE here, stated: (i) the site page's sentences are not files of this bundle (its line 67 already names the epsilon-factorized endpoint rotation); (ii) the 8 label sites of the census (one comment, 6 identifier lines, one data string) are unchanged by design -- census only, for a later ruling; (iii) `--boundary-regenerate` and `--kmax 5` were not re-run (documented walls above; no code, data or tier text changed); (iv) no superseded copy of the evaluator (the convention above). - 2026-09-29 (release cleanup; no value, key structure or numeric leaf changed): the vendored receipts re-cut once more for the public release -- in `vendor_row24_gatepoint/DATA_C24g60_pair_strings_20260909T075018Z.json` the three absolute path values -> their basenames; in the four `vendor_row24_seeds/LEG_LANDING_*.json` the compute-host labels -> neutral letters (hostA / hostB) in values and key names, and the one remaining narrative `label` -> "withheld"; `vendor_row24_seeds/README.md` states the re-cut. The evaluator's in-code pins (REGEN fixtures, the gate-point pin), the two directories' VENDOR_MANIFEST.sha256, their README.md sha256 lines and this bundle's MANIFEST.sha256 rows were re-emitted for the new bytes (sha256sum); NOTICE and LICENSE added and entered in the manifest. Checksums (sha256, first 16 hex) of the scripts and top-level files whose bytes moved: `hexabox-evaluate.py` cdc3d9147491a38e... -> 834b6691770c4948...; `vendor_row24_gatepoint/DATA_C24g60_pair_strings_20260909T075018Z.json` fc71767e5d7ead42... -> 2045567bf9c52d39...; `vendor_row24_seeds/LEG_LANDING_wave12_dps120_20260907T235745Z.json` 1492cd38bfe0c750... -> dd72beb3aa11bf5e...; `vendor_row24_seeds/LEG_LANDING_wave12_dps90_20260907T201119Z.json` 3af67d435a676b72... -> 58457f3a7bff6543...; `vendor_row24_seeds/LEG_LANDING_wave3_dps120_20260908T053011Z.json` 3266298b0e3b9454... -> 82108e0e4630bcb0...; `vendor_row24_seeds/LEG_LANDING_wave3_dps90_20260908T024214Z.json` 925479a92608cd4e... -> 16fb65e69f888668....