# vendor_row24_pathC -- the Path-C connection of the 98 masters on the third kinematic segment: six exact fixed-d0 slices (the certified transport), their gate receipts at P3, the generic-d connection, the node manifest, the instruments and the self-check (row 24, the one-mass-pair non-planar hexa-box; 2026-09-11)

WHAT THIS IS.  The transport equation dY/du = A(u) Y of the 98 master integrals of the two-loop five-point non-planar hexa-box (p1^2 = p3^2 = m^2; p2^2 = p4^2 = p5^2 = 0) along the straight segment Path C from Pfit = (s12, s23, s34, s45, s15, m^2) = (-3, -5, -7, -2, -11, 1) to P3 = (-5, -7, -9, -2, -11, 1), u in [0, 1].  `README_pathC_connection.md` (the authors' README, byte for byte) states the objects and what each certifies; `MANIFEST_pathC_connection_20260911T114239Z.json` is the authors' manifest of every object by sha256 as emitted.  This directory is DATA and INSTRUMENTS OF RECORD: `hexabox-evaluate.py` does not read it; its own check is `selfcheck_pathC_B2.py` below.

THE HEADLINE, read from `HELDOUT_GATE_P3_fixed_d_SUMMARY_20260911T115728Z.json`: verdict PASS; at the three half-integer d0 = 13/3, 9/2, 11/2 all 98 masters are compared at P3 and agree with the independent AMFlow evaluation there to 62.5 / 63.6 / 61.7 digits complex-relative (67.2 / 66.6 / 64.2 on the real parts) at worst per slice, floor 61.7 (pass bar 50); at the integer d0 = 5, 6, 7 the masters carry poles and no certification is made (d0 = 5: 1 of 98 compared; d0 = 6: 0 of 98 compared; d0 = 7: 0 of 98 compared).

VENDORING RULE.  Every object below is the authors' emission with its string VALUES re-cut by field for serving (a path value -> the basename of the file it named with that file's sha256, or '(directory)'; a narrative value carrying working vocabulary or a machine label -> "withheld"; a value whose only such word is the authors' statistics term for a check point never used in any fit -> kept as written; every numeric leaf, every exact coefficient string and every key name as emitted).  The gzipped objects were decompressed, re-cut the same way (only PRODUCER / slice / part path fields move; the `entries` member -- the mathematics -- is identical, asserted at build), re-serialized in their own compact form and re-compressed with a zero timestamp.  The scripts are register successions (narrative words and the record's directory literals re-cut; each states its own changes at the end of its docstring and compiles).  The objects AS EMITTED are named by sha256 in the `vendored_from` lines at the end; `VENDOR_MANIFEST.sha256` pins the served bytes.

## 1. The six fixed-d0 slices = the certified transport

The exact 98 x 98 connection at each fixed d0: every nonzero entry (1416) an exact rational function P(u)/Q(u) over Q (coefficient strings low to high), reconstructed from the 176 node objects and read leave-one-out (the v4 read: every entry exact at each d0).  Certified at P3 at the three half-integer d0; the integer d0 are not certification slices.

| file | sha256 (served) | bytes | role |
|---|---|---|---|
| `PATHC_DE_d013_3_20260911T051448Z.json.gz` | `78ac7d79fbeab1b6491e1793bc9c6c77fe53d0af9c0409c9f76c420e2b8116d0` | 355739 | the slice at d0 = 13/3 (a certification slice: 98/98 compared at P3) |
| `PATHC_DE_d09_2_20260911T035535Z.json.gz` | `11f86f163eeec04bc4ed4e05dc71be526be213868deb6461f7d5a2d69999929a` | 324616 | the slice at d0 = 9/2 (a certification slice: 98/98 compared at P3) |
| `PATHC_DE_d05_20260911T040607Z.json.gz` | `32f74a9fb9e4296c2da78cb459dc050200416b11abb1406f60e6a58e3d34625d` | 318933 | the slice at d0 = 5 (integer d0: not a certification slice) |
| `PATHC_DE_d011_2_20260911T041800Z.json.gz` | `5940ab2b632192ccc49d360f777c577a878153900c64b0fd4bbb118cd385b4e2` | 366070 | the slice at d0 = 11/2 (a certification slice: 98/98 compared at P3) |
| `PATHC_DE_d06_20260911T043033Z.json.gz` | `9a4b1405102343362550316d2280528c5ec3e086fa64b9581c6dbe42b2f084ef` | 301905 | the slice at d0 = 6 (integer d0: not a certification slice) |
| `PATHC_DE_d07_20260911T050120Z.json.gz` | `f1f1df291e1e73b6ffe84983ab5c558b6118972881bcb49e7ccd1f1dad4e2b17` | 347485 | the slice at d0 = 7 (integer d0: not a certification slice) |

## 2. The gate receipts at P3 (Re + Im at the half-integer d0) and their summary

Per d0: the AMFlow boundary at Pfit transported to u = 63/64 by the arb stepper at two precisions, matched to the regular Frobenius family at the simple pole u = 1 (residue nilpotent, kernel relation y7 = y4), compared master by master with an independent AMFlow evaluation at P3 on the full complex values; the return trip and the planted wrong-boundary control (failing by name) inside each receipt.

| file | sha256 (served) | bytes | role |
|---|---|---|---|
| `HELDOUT_GATE_P3_fixed_d_d013_3_20260911T115727Z.json` | `664e4420887ecd56dd22b1678446fd531662cb3cad5990c3feacb870781a6916` | 135267 | the receipt at d0 = 13/3: 98/98 compared, 62.5 digits complex-relative (67.2 real parts), PASS |
| `HELDOUT_GATE_P3_fixed_d_d09_2_20260911T115727Z.json` | `3d4b3525bd5c6a9825c518924c32deec322a865217a006cf65459ca5fd9b7dfa` | 135086 | the receipt at d0 = 9/2: 98/98 compared, 63.6 digits complex-relative (66.6 real parts), PASS |
| `HELDOUT_GATE_P3_fixed_d_d05_20260911T101320Z.json` | `cd53ccfac14cf2ea83f8701931733374607ff4c15688478eaec51e264a6f82a7` | 35001 | the receipt at d0 = 5: 1 of 98 compared -- not a certification slice (the masters carry poles at integer d0) |
| `HELDOUT_GATE_P3_fixed_d_d011_2_20260911T115728Z.json` | `5a27b860ebf7314125fba0b3b7fe5ad63ceff7294574766e5d085afba804616a` | 135279 | the receipt at d0 = 11/2: 98/98 compared, 61.7 digits complex-relative (64.2 real parts), PASS |
| `HELDOUT_GATE_P3_fixed_d_d06_20260911T104425Z.json` | `462c5e84747e086e9d51ac1b2949b6c47e06e5002939d04b77ab6e2b8ed83288` | 33297 | the receipt at d0 = 6: 0 of 98 compared -- not a certification slice (the masters carry poles at integer d0) |
| `HELDOUT_GATE_P3_fixed_d_d07_20260911T110254Z.json` | `144e63258880ada9c8ed09cb0b801aeddba6a3a10a2ecebe87f19ddf14718dbc` | 32952 | the receipt at d0 = 7: 0 of 98 compared -- not a certification slice (the masters carry poles at integer d0) |
| `HELDOUT_GATE_P3_fixed_d_SUMMARY_20260911T115728Z.json` | `995984ee9377299abdcd6fe470972a066e67358d1592f6795de2ac6c4010e681` | 8730 | the summary over the six d0 (its `legs` name the six receipts by sha256 as emitted): verdict PASS, floor 61.7 digits complex-relative over the 98/98 slices |
| `LANDING_GATE_P3_fixed_d_20260911T110615Z.json` | `31a7afe815d307cbf5d54ced2c09030b946afff75246376f21216e5e61d7b2b0` | 26237 | the completion receipt of the P3 gate (the twelve AMFlow-at-d0 legs, the six first-emission receipts and the first summary by sha256; host and narrative fields withheld) |

## 3. The generic-d connection v2 (a supplementary object, not the certified transport)

| file | sha256 (served) | bytes | role |
|---|---|---|---|
| `PATHC_CONNECTION_generic_d_20260911T112703Z.json.gz` | `990a8a168845d58f72bf461fe6d92b390e386679512710b0900a1d899dcaf6d8` | 1947510 | the same matrix with every u-coefficient an exact rational function of d (max d-degree 19), fitted on 38 fixed-d0 slices and checked entrywise exactly at two withheld slices never used in any fit: d0 = 70/11: 1414 EXACT, 2 degree d; d0 = 41/11: 1416 EXACT; 1416 nonzero entries, 0 failed |
| `LANDING_generic_d_connection_v2_20260911T112716Z.json` | `7cae58164a0da065b635fd25cb2f4738bd3bc3716eb5d33c1ab7d7ce6a4f21ea` | 2276 | its completion receipt (v2: the object, the v1 object it succeeds and the three-entry parts by sha256) |

## 4. The instruments and the authors' README / manifest

| file | sha256 (served) | bytes | role |
|---|---|---|---|
| `README_pathC_connection.md` | `51e74be6d1f9685485d926a987ab547f838e26647cc6cdd27583ab045fff38ff` | 3149 | the authors' README of the Path-C connection (v2), byte for byte |
| `MANIFEST_pathC_connection_20260911T114239Z.json` | `39c69a39b018983e6714d385df50019a6a158ecef3be6b835dbaa0d401427248` | 63511 | the authors' manifest v3 (2026-09-11T11:42:39Z) of every object by sha256 as emitted: the 176 node objects, the six slices, the first-emission gate receipts and summary, the generic-d object and its parts, 15 instruments; path fields re-cut |
| `loo_read_B2_v4_20260911T015655Z.py` | `4f967b91d8e4efdab6ad15f136b0f9324efef3f5b82258b312946209925e0578` | 16197 | the leave-one-out read v4 (the slice-certification instrument: Thiele over the nodes with withheld nodes reproduced exactly; the exact Cauchy form on a died table) |
| `pathc_transport_arb_B2.py` | `8411036c3b9f744ab42ca221b15df8bb9528136d58a074360dceb0134f8a5933` | 23211 | the arb Taylor stepper (python-flint balls; h <= rho/3 from the nearest denominator root; the regular Frobenius family at u = 1; `run` / `dry`) |
| `DRY_transport_arb_pathC_d09_2_20260911T045629Z.json` | `4551bf056d6e20d73061e4d217af0b78c9596cfd34fab1147ac46a02aa07b272` | 3325 | the stepper's DRY on the exact d0 = 9/2 slice: DRY PASS -- pair 83.1, reversal 124.2, linearity 126.9 digits; the planted entry: FAIL BY NAME; the wrong boundary: FAIL BY NAME |
| `heldout_gate_P3_fixed_d_B2_v7_20260911T115212Z.py` | `6fb5d900b07612d684b72d91a9f7da9ecad07f98d790ff5d5424a27af162a883` | 46333 | the gate driver v7 (pieces A-E and F1/F2 for the imaginary parts; assemble / assemble_im): the driver of the receipts in section 2 |
| `heldout_gate_P3_fixed_d_B2_v5_20260911T104424Z.py` | `b19d93005f02e57e589fb8b177d4f3fa7c9f78b186ff3144c8f140e6b39d2bd8` | 37712 | the gate driver v5 (the driver of the first-emission real-part receipts the manifest v3 names); kept for the record |
| `pathc_slices_pieces_B2_20260911T083855Z.py` | `8c8ed54f938b2b7b3421872600b8e694470cc0bff8c6ef59256c8f2b073bfb45` | 20308 | the slice builder (the exact fixed-d0 connection from the node objects; the first stage of the generic-d build) |
| `bivariate_connection_B2.py` | `edb9763fa0574594b23a39cf6adb556a419f737f87b888f4b38a705ac8ff1e1a` | 12194 | the generic-d fit / assemble (the second stage: each u-coefficient interpolated in d exactly over the fit slices, checked at the withheld slices) |
| `bivariate_connection_B2_three_20260911T110958Z.py` | `a0e1f43de4f39d76b27264b981c6844afb4cdd97ff2a7e49dde07337b3ec4219` | 12242 | the three-entry FULL_TYPE variant of the fit for the top-row entries (95,0), (96,0), (97,0) |

## 5. The node objects (NOT shipped) and the self-check

| file | sha256 (served) | bytes | role |
|---|---|---|---|
| `NODES_pathC_176_20260911T121807Z.json` | `c0ff1dabbe9dc78c461c3f61ce9815ee094bebd8f02ecdbd19ec8d1909e615d8` | 49157 | the node manifest: the 176 AMFlow node objects at rational u (tag, u, sha256, bytes; 561018998 bytes in all) the slices were reconstructed from |
| `selfcheck_pathC_B2.py` | `1a59441a35886d2fa91ea49e431ca8552d4ff1acaf696ede4c77943066bc5a17` | 6597 | the self-check (a runnable succession; see below) |

The 176 node objects (561018998 bytes) are too large for this bundle and are NOT shipped; they are available from the authors on request, listed by sha256 in `NODES_pathC_176_20260911T121807Z.json`.  Placed under `vendor_row24_pathC/node_objects/<tag>/<tag>.json` they are read by the self-check's sample reproduction and by the instruments' defaults.

THE SELF-CHECK.  `python3 vendor_row24_pathC/selfcheck_pathC_B2.py` (python3 alone when no node object is present; python-flint for part (2) once node objects are placed; seconds on one core) reads the d0 = 13/3 slice beside it and (1) proves the no-log condition at u = 1 exactly over Q: the residue R of every polar entry, R^2 = 0, rank 1, the kernel relation y7 = c y4 printed with c exact; (2) with node objects present under `vendor_row24_pathC/node_objects/`, reproduces the AMFlow samples at u = 1/4, 1/3, 2/3 exactly entry by entry (without them it says so and skips the comparison); (3) prints the entry degrees.  It ends `SELF-CHECK PASS` (exit 0) or `SELF-CHECK FAIL BY NAME: ...` (exit 1).  Options: `--slice FILE`, `--nodes-dir DIR`, `--u a/b,c/d,...`.  CHANGES.md carries the measured run.

NOT IN THIS DIRECTORY: the eps-expanded layers on this segment (the transport is at fixed d); the 176 node objects; the further k/13 slices and the k/11 fit slices of the generic-d build (build data, named by sha256 in the manifest v3); the AMFlow-at-d0 leg outputs the gate driver read (named by sha256 inside each receipt).  The instruments other than the self-check are vendored as the record of method: they compile, and run only with those inputs placed as their docstrings state.

## The objects as emitted (by sha256) and what moved

- vendored_from: `PATHC_DE_d013_3_20260911T051448Z.json.gz` <- sha256 `3b38f849064cbcaa2ecee542604a51a5715cb580afd1be89cdb96453579967eb` (2 path field(s) re-cut inside; entries identical; uncompressed sha256 as emitted 9a0176d9477a6a0a4baabb9f06edcc73d9f28e0ec7c5876cd373f782a41ad467)
- vendored_from: `PATHC_DE_d09_2_20260911T035535Z.json.gz` <- sha256 `6d4168dbc12ae2e3121338a9e6e9f852c4892320afe1e871da2667da70042415` (2 path field(s) re-cut inside; entries identical; uncompressed sha256 as emitted be7d7796ffccd51c7edb6127177c333120502d14ae4bf72fa4bbe17fec69fc00)
- vendored_from: `PATHC_DE_d05_20260911T040607Z.json.gz` <- sha256 `cebe05808da5dec7438b837b8fc522c78d6ebb6d1b2f25ce2b984d1273fd2e93` (2 path field(s) re-cut inside; entries identical; uncompressed sha256 as emitted db53ef70ee70d1463cae8d336f22394a5760544bd9b6059fb4bc679e170046f3)
- vendored_from: `PATHC_DE_d011_2_20260911T041800Z.json.gz` <- sha256 `037033ffb3381b0faac08375e0090c97ba456b682b3bf8aee501ca9a79f2d7b4` (2 path field(s) re-cut inside; entries identical; uncompressed sha256 as emitted bfad0bb310fb24819733ba38e501ef064c81609b54cc5e373ea88612ce4f2f57)
- vendored_from: `PATHC_DE_d06_20260911T043033Z.json.gz` <- sha256 `09943c6167f446e744125996a92895a7cf0c51e5f445f518baca0215c9f05119` (2 path field(s) re-cut inside; entries identical; uncompressed sha256 as emitted 75bcd5fd3995e4996e6526963c363daf1aead06e18b1929de5dc323c8a9a3233)
- vendored_from: `PATHC_DE_d07_20260911T050120Z.json.gz` <- sha256 `f5f3c8eb0a82b2636b747254c43fb8810caa70501f5b46abf3a652640948640f` (2 path field(s) re-cut inside; entries identical; uncompressed sha256 as emitted ec6402eb8c4dbe7de62fae4a5b0d0b1016825e7f176ad4d64306069787280cc3)
- vendored_from: `HELDOUT_GATE_P3_fixed_d_d013_3_20260911T115727Z.json` <- sha256 `39322a72a641faedc5cc93fbea23d6e08c3c9241a754f5ef0a3fa1bfe381c87e` (16 field(s) re-cut: 15 path, 1 withheld; 1 value(s) carrying the authors' statistics term kept as written)
- vendored_from: `HELDOUT_GATE_P3_fixed_d_d09_2_20260911T115727Z.json` <- sha256 `bfb6ad380bdb212dbdcbcc7de3cc513b997621d14e3d59d76584959defb159d5` (16 field(s) re-cut: 15 path, 1 withheld; 1 value(s) carrying the authors' statistics term kept as written)
- vendored_from: `HELDOUT_GATE_P3_fixed_d_d011_2_20260911T115728Z.json` <- sha256 `0385d084a4adefbb842c69a4ea6787c62da6584f34f8e16cfa3111d98967ae36` (16 field(s) re-cut: 15 path, 1 withheld; 1 value(s) carrying the authors' statistics term kept as written)
- vendored_from: `HELDOUT_GATE_P3_fixed_d_d05_20260911T101320Z.json` <- sha256 `dde3e954f36e88a878f87f7f71a524a0f3449f5816a60cb3ef420f3d39abd94b` (13 field(s) re-cut: 12 path, 1 withheld; 1 value(s) carrying the authors' statistics term kept as written)
- vendored_from: `HELDOUT_GATE_P3_fixed_d_d06_20260911T104425Z.json` <- sha256 `8b97edcd1e0a6b623266d947b2c088ae1bb5f5873bcec6d0c4c95947154906bd` (13 field(s) re-cut: 12 path, 1 withheld; 1 value(s) carrying the authors' statistics term kept as written)
- vendored_from: `HELDOUT_GATE_P3_fixed_d_d07_20260911T110254Z.json` <- sha256 `7cd6d64b3e36fd207c85d2f6cf4a496a9a6fda7dda584082ef896b8c35366c9a` (11 field(s) re-cut: 11 path, 0 withheld; 1 value(s) carrying the authors' statistics term kept as written)
- vendored_from: `HELDOUT_GATE_P3_fixed_d_SUMMARY_20260911T115728Z.json` <- sha256 `ad3e683f5008dfb55ec189d5bbf4042621f98825843f9b507e24bd30af37bede` (7 field(s) re-cut: 7 path, 0 withheld; 1 value(s) carrying the authors' statistics term kept as written)
- vendored_from: `LANDING_GATE_P3_fixed_d_20260911T110615Z.json` <- sha256 `14a3e00e94fba5ba963c5bb4d6017a8becbef8ac301d06a881adcb4dd4a19955` (55 field(s) re-cut: 38 path, 17 withheld)
- vendored_from: `PATHC_CONNECTION_generic_d_20260911T112703Z.json.gz` <- sha256 `840f95f82a6ed6cf35e4bbbf0bc0370ce54afed223431cf7ea01fa36dc9415fd` (151 path field(s) re-cut inside; entries identical; uncompressed sha256 as emitted 156375fb1273546bfa5ce2864870f259d1d5ed7fa3af00b73abd34567342b084)
- vendored_from: `LANDING_generic_d_connection_v2_20260911T112716Z.json` <- sha256 `dee42fbcb0dded5c432b4fde2796f5392bae007134e9d9db1b18912347fe49be` (8 field(s) re-cut: 5 path, 3 withheld)
- `README_pathC_connection.md`: served byte for byte as emitted (sha256 `51e74be6d1f9685485d926a987ab547f838e26647cc6cdd27583ab045fff38ff`).
- vendored_from: `MANIFEST_pathC_connection_20260911T114239Z.json` <- sha256 `07f3ad4d2d795175fa7880a863f56fbd5e1ae08e49bfcf46d2a07dfb265bde84` (233 field(s) re-cut: 230 path, 3 withheld; 1 value(s) carrying the authors' statistics term kept as written)
- vendored_from: `loo_read_B2_v4_20260911T015655Z.py` <- sha256 `acffaea70fa8c6afe96c94037f037bab5569cacf030ae601d53eb868a426c513` (register succession: 5 substitution(s), 14 diff lines; string-masked code units changed main, thiele_loo)
- vendored_from: `pathc_transport_arb_B2.py` <- sha256 `183eb738e4256e2b8712f7359037aa88beeb1009da50596ad54de201e97e05fb` (register succession: 1 substitution(s), 6 diff lines; string-masked code units changed none)
- vendored_from: `DRY_transport_arb_pathC_d09_2_20260911T045629Z.json` <- sha256 `fabe4f097bb392f38ef61b0a0f9d2ff08ef8cc79395c2d963d1b03410820a0ae` (1 field(s) re-cut: 1 path, 0 withheld)
- vendored_from: `heldout_gate_P3_fixed_d_B2_v7_20260911T115212Z.py` <- sha256 `73243e44386fb156c35e6b6a76d8576a612bd73b00238f033b87eb60c39bd2e3` (register succession: 6 substitution(s), 20 diff lines; string-masked code units changed leg, piece)
- vendored_from: `heldout_gate_P3_fixed_d_B2_v5_20260911T104424Z.py` <- sha256 `ff56cfe283f2295956332a8c3a30206ef6db63016d8f4a6ebee45945427c4b04` (register succession: 4 substitution(s), 16 diff lines; string-masked code units changed leg, piece)
- vendored_from: `pathc_slices_pieces_B2_20260911T083855Z.py` <- sha256 `04e69977a4141751d82467848af1af2e664015c9f1eacbc8caba1e31cecc63ad` (register succession: 5 substitution(s), 12 diff lines; string-masked code units changed build)
- vendored_from: `bivariate_connection_B2.py` <- sha256 `6805ddd7422913401bf710047002df332fc5c90ec00841ed768b7b628e97f13f` (register succession: 2 substitution(s), 6 diff lines; string-masked code units changed none)
- vendored_from: `bivariate_connection_B2_three_20260911T110958Z.py` <- sha256 `4ee076a0148bb94c78ea1888fa557dc26aaedb96ad91829b5cc29c32eeba769e` (register succession: 2 substitution(s), 6 diff lines; string-masked code units changed none)
- vendored_from: `NODES_pathC_176_20260911T121807Z.json` <- sha256 `965273fc09eedec26e476bde2d74393f52005c3ee4119a65af4f01a1ed15c06b` (179 field(s) re-cut: 178 path, 0 withheld, 1 special)
- vendored_from: `selfcheck_pathC_B2.py` <- sha256 `eedb46fe8d2efea11a79aa47a4381b571e8095675b12646e6b2a51c2769c657e` (register succession: 9 substitution(s), 23 diff lines; string-masked code units changed main)

Pins: none of these files is pinned in-code by hexabox-evaluate.py (data and instruments of record, not an evaluator tier); VENDOR_MANIFEST.sha256 here and the bundle's MANIFEST.sha256 list every file by sha256

`VENDOR_MANIFEST.sha256` lists every file of this directory; the bundle's `MANIFEST.sha256` pins this directory's files too.