{ "what": "LBL3X K3 subsector (sec15 equal-mass 3-loop banana block, 9 masters x eps^-3..0): exact rational u-DE + closed-form u=0 MUM seed + 3 named resonance constants. Everything needed to evaluate m13(u) to arbitrary precision as a PF-operator period series.", "provenance": { "ban_de": "/lbl3x_bootstrap/ban_de_poly.json sha256[:16]=934a156a867d9967", "u0_closed_forms": "/lbl3x_fulla/PSLQ15_RESULTS.json (tag u0, all reverified dps210) sha=d412706b91fc7183", "m3e0_literal": "cache; derived, runtime chain 2026-07-06 (build-record sec 6 gate PASSED 19:41: agreement 225.3d = the old reference's certified floor, internal two-prec cert ~240d, synthetic-truth 241.0d; zero AMFlow in the loop) -- compare-on-load gated vs mum_constants_derived_record. Pre-demotion provenance: /lbl3x_fulla/ring15_pslq/out_u0_hi.json (AMFlow goal-220) sha=3d27ae684467bbb8; PSLQ NULL vs 49-member conductor-15 CM ring (honest named constant)", "mum_constants": "cache; derived, runtime chain 2026-07-06 (build-record sec 6 gate PASSED 19:41: agreement 223.6-226.7d vs this string's own certified floor, internal two-prec certs 236-240d, synthetic-truth 239-241d; zero AMFlow in the loop) -- compare-on-load gated vs mum_constants_derived_record. Pre-demotion provenance: solved (this campaign, mum_match.py method) vs archived out_ic2_hi sha=d9d66f4ac1b6b09e; overdetermined 36-eq/3-unknown, rel resid 1.2e-225; PSLQ NULL (PSLQ_R4, 3 MUM targets)", "normalization": "raw AMFlow (with Euler-gamma); closed forms quoted e^{3*gamma*eps}-stripped" }, "ban_de": { "masters": [ { "family": "BAN", "indices": [ 1, 1, 1, 0, 0, 0, 0, 0, 0 ] }, { "family": "BAN", "indices": [ 1, 1, 1, 1, 0, 0, 0, 0, 0 ] }, { "family": "BAN", "indices": [ 1, 1, 1, 1, -2, 0, 0, 0, 0 ] }, { "family": "BAN", "indices": [ 1, 1, 1, 1, 0, 0, 0, -2, 0 ] }, { "family": "BAN", "indices": [ 1, 1, 1, 1, -1, 0, 0, 0, 0 ] }, { "family": "BAN", "indices": [ 1, 1, 1, 1, 0, -1, 0, 0, 0 ] }, { "family": "BAN", "indices": [ 1, 1, 1, 1, 0, 0, -1, 0, 0 ] }, { "family": "BAN", "indices": [ 1, 1, 1, 1, 0, 0, 0, -1, 0 ] }, { "family": "BAN", "indices": [ 1, 1, 1, 1, 0, 0, 0, 0, -1 ] } ], "N": 9, "NEPS": 4, "D_coeffs_asc": [ "0", "64", "-20", "1" ], "M": [ [ [ [], [], [], [], [], [], 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"synthetic_truth_control_digits": {"MUM1": 239.1, "MUM2": 239.8, "MUM3": 239.1, "M3_eps0": 241.0}, "gate_bars_digits": {"MUM1": 215, "MUM2": 215, "MUM3": 215, "M3_eps0": 215}, "cache_support_dps": 215, "derive_support_dps": 225, "leg4_dir": "row21_leg4", "env_override": "ROW21_LEG4_DIR", "ban_towers_sha256": {"BAN_TOWER_dps280.json": "290dd705c1f193e452893dd9b9e2655e809f6465c8388db1c84f9470f2a5a81e", "BAN_TOWER_dps245.json": "c3cda1bd69f26e66e2cc54843fb1dfc2f1ce26c181fb1e516af144291ef1ae7c"}, "mum_match_v2_sha256": "e1bce3989b8f86119178275ee0c2a68425a7b5e7e86f303ec1adebf0f9c1652a", "mum_match_v2_vendored_from_sha256": "7052b98016e73666de8f8b4e98c9861bb6162a1fe039ef01a08c31fd88120aa4", "import_shim_sha256": "7b4c1c38363c87e2c01d5daf42a6975804aaad4a0f55edb751e65b58e72cbac6", "refresh_recipe": "base-point refresh (lbl3x_recompute): build_vacuum_exact.py -> GRID-v2 m2-DE transport (boundary sentinel mandatory) -> solve_towers.py -> step5_ban_tower.py -> mum_match_v2.py; higher dps needs a higher-bprec transport rerun, cost ~ dps^(1+[0,0.6])"}, "mum_constants_closed_forms": {"wired": "2026-07-08 row21-k3-wiring (decision record 02:2x; form-record sec 3, gated CONFIRM)", "status_law": "pole tower + complete K3 sector exact; two named residual classes with certificates", "basis": ["1", "pi^2", "zeta3", "g", "g*pi^2", "g^2", "g^3"], "basis_note": "g = EulerGamma; e^{3*gammaE*eps}-stripped normalization (eval_row21 conventions)", "coeffs": {"MUM1": ["-61/12", "-1/12", "7/2", "9/2", "0", "-3/2", "0"], "MUM2": ["89/48", "11/16", "23/6", "-361/24", "-5/8", "99/8", "-15/4"], "MUM3": ["-71/24", "5/24", "13/3", "-11/4", "-1/4", "15/4", "-3/2"], "M3_eps0": ["36143/288", "647/72", "-10", "0", "0", "0", "0"]}, "provenance": {"MUM1": "DE-forced, route-K pivot-gauge + PWW base points, oracle-free (form-record sec 3; 223.6d vs gate-cache)", "MUM2": "BAN momentum-shift identities m7==m8==(4/3)m0+((u+8)/6)m1 -> rank-2 exact solve, 1281/1281 rows (226.7d vs gate-cache)", "MUM3": "same route as MUM2 (224.3d vs gate-cache)", "M3_eps0": "DE frame condition B0.a0=0, route K (225.3d vs gate-cache)", "artifacts": ["/lbl3x_form/phase1//DERIVE.json", "/lbl3x_form/phase1/mum23/MUM23_RESULTS.json", "/lbl3x_form/phase2a/VERIFY_LEDGER.json"], "controls": "gamma-mixing cross-predictions 12/12; two-precision identical; non-rational synthetic negatives loud (39-39.5d collapse at injected 1e-40*pi); independent fresh-eyes verifier reproduces all depths"}, "gate_rule": "serve the closed forms, runtime-evaluated; compare-gate vs the demoted gate-cache strings to >= bar_i = min(dps, floor_i) - 5 digits PER CONSTANT (10:2x clamp; floor_i = measured_cache_floor_digits), else K3SeedClosedFormGateError (named, fail-closed)", "gate_cache_role": "mum_constants_mybasis + M3_eps0_stripped_named are DEMOTED to gate-cache: never deleted, never served, compare-only; mum_constants_derived_record stays the import-time tamper reference and the --derive-constants oracle", "measured_cache_floor_digits": {"MUM1": 223.6, "MUM2": 226.7, "MUM3": 224.3, "M3_eps0": 225.3}, "ceiling_note": "RESOLVED by the 10:2x per-constant clamp: bar_i = min(dps, floor_i) - 5 with floor_i from measured_cache_floor_digits (223.6/226.7/224.3/225.3 d for MUM1/MUM2/MUM3/M3_eps0) -- honest deep requests at ANY dps serve with the bar capped at each constant's measured cache floor (no false-raise; measured: dps 240 serves 4/4); the flat min(dps,231)-5 bar and its by-construction dps>=229 raise are superseded"}, "mum_constants_mybasis": [ "0.399102400646453308581282849471673639435235040610225113971540545656602731673018060126814655854747124387643723687938862564217553493216121301005537406340349492448642150773196684991105791876795739967451095868153087249019505679422009846", "4.40645606399338436593182405983956145525544043841635410938859534297464061201539415940361863627289338027340521478556573031967162539595409177759744969112176389428526188679791031121924071567906540460457046677940739594471625571920664737", "2.25612579114733877303558520681902934996964442920808053533074816208684918788535055488391682476237280178126658244797502135225585828145901947310201846897267730625518503075674235990135627217553100106675742473670702686104688321347866296" ], "kernel_int_vectors": [ [ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 1, 1, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ], "pivots": [ 28, 30, 35 ], "Kp_inv_exact": [ [ "1", "0", "0" ], [ "0", "1/4", "0" ], [ "0", "0", "1" ] ], "domb_shift_identity": { "statement": "144*u*h(u) = P4A(u)*w + P4B(u)*(theta w) + P4C(u)*(theta^2 w), w=varpi0(u/64) Domb A002895, theta=u d/du; h = m13-eps0 component of the MUM kernel-0 homogeneous tower (the K3 direction of m13)", "A": [ 0, -256, -72, 6, 1 ], "B": [ 0, 640, -672, 30, 2 ], "C": [ 4096, 1280, -672, 20, 1 ], "derivation": "exact Hermite-Pade on 80 exact series orders (this work); re-verified live over 30+ orders" } }