# MANIFEST.sha256 -- files/threshold-banana download bundle # PRODUCER: gen_threshold_banana_manifest_v3.py (the generator of record, succeeding gen_threshold_banana_manifest_v2.py 01cf77fe93c552d5 by the rows of the two threshold-coefficient modules served beside the evaluator -- threshold_hankel_tail.py with calpha_rings.py and fixtures/hankel_tail_fixtures.json, direct_linear_extract.py with fixtures/direct_linear_fixtures.json -- 2026-09-11; v2 succeeded gen_threshold_banana_manifest.py 1ef41b750d762fe5 by one ROLES row for the ancillary data file frobenius_coefficients_rows31_32_20260909T042148Z.json; cure-queue #54 v2, 2026-09-07: the bundle's first manifest, the sunrise form; the vendor_row31_family/ group of the --family tier, its rows read from the served FAMILY_MANIFEST.sha256 and FAMILY_PINS); emitted 2026-09-11T16:13:50Z # verify: sha256sum -c MANIFEST.sha256 (run in this directory; the paths are relative to it) # roles: # threshold-banana-evaluate.py -- the (1,1,1,9) threshold-banana K3 connection coefficient c_{3/2} = -sqrt(3)/(36 pi): the default evaluates the closed form at --dps and runs two fail-closed self-checks (the Route-B Arb oracle literal, a live low-order probe); --derive rebuilds the exact Picard-Fuchs operator, the series, the transport and the projector from scratch; --point evaluates the holomorphic period at any s; --family is Table 2 row 31, the same integral run as a Feynman family: the exact operator identity three ways (the IBP-derived operator, the record's operator, the operator this file derives at runtime), --family --c32 the connection coefficient recomputed from the IBP-derived operator against the record's string and the closed form, --family --oracle the leg-(III) AMFlow points and the III-a/III-b figures (the record's); python3 + mpmath + sympy; the vendor_row31_family/ files are read by --family only # threshold-banana-expression.md -- the (1,1,1,9) result written out: the closed form, the PSLQ relations, the 195-digit Route-B certification, the projector extraction, the caveats # frobenius_coefficients_rows31_32_20260909T042148Z.json -- ancillary data (JSON): Table 2 rows 31 and 32, the Frobenius coefficients of the eps^0 layer of the physical master in the IBP operator's z = 0 Frobenius basis under the particular-solution convention the file states -- the 31-significant-digit strings of record (row 31, the (1,1,1,9) K3 banana: a_0, a_2, a_3; row 32, the (1,1,1,1,16) CY3 banana: a_0, a_1, a_3, a_4, a_5; the coefficient at the floor on each row carried as a bound), the two-precision members in full, the basis' first coefficients, the digit rule and the floor source; emitted by key from its source receipt, named inside the file with its sha256 (f367d80f571f5b4f); read by no tier of threshold-banana-evaluate.py # threshold_hankel_tail.py -- the threshold connection coefficients c_alpha of the banana coalescence sequence DERIVED, not fitted -- K3: c_{3/2}; CY3: c_{5/4}, c_{7/4}; CY4: c_{3/2} (families K3 (1,1,1,9), CY3 (1,1,1,1,16), CY4 (1,1,1,1,1,25)) -- from the non-oscillatory tail of the Bessel-kernel representation after the rotation to the Hankel kernel and the Mellin formula, every step exact over Q: --check reduces the result to the calpha_rings grammar (sign, rational, pi power, radicals, Gamma exponents) and compares it EXACTLY with the recorded structure, reproduces the record's integer-relation vectors from the structure (PSLQ demoted to the check), compares the value with the record strings of the fixtures at --dps and checks the identity c_{alpha+1}/c_alpha = phi_{alpha,1} against the record operator's exact Frobenius coefficient; --selftest adds three planted controls that must fail by name; --derive --masses for any tuple whose largest root is the sum of the others (a tuple with no such root is refused by design); reads calpha_rings.py beside it and fixtures/hankel_tail_fixtures.json, both pinned in-code by sha256 (exit 3 on a mismatch, 4 when absent); python3 + mpmath # direct_linear_extract.py -- the DIRECT LINEAR extraction of the same coefficients at >= 1400-bit ball arithmetic (python-flint), families K3 (1,1,1,9), CY3 (1,1,1,1,16): the multinomial-squared period series generated exactly and annihilated EXACTLY by the record operator of the fixtures (a nonzero residual exits 3), the s-chart D-form, the seed jet above the threshold with a rigorous tail bound, a Taylor transport along the record's path at two precisions, the local Frobenius basis at s = 0 exactly over Q, one r x r linear solve; printed beside: the two-precision agreement, the agreement with the record strings and with the closed form, the size of the unipotent coefficients relative to c_alpha and the projector's digits of record; --selftest adds two planted controls that must fail by name; reads fixtures/direct_linear_fixtures.json pinned in-code by sha256 (exit 3); python3 + python-flint + mpmath + numpy # calpha_rings.py -- the family / mass-tuple / ring table threshold_hankel_tail.py reads (vendored beside it, pinned there by sha256): every recorded closed form a STRUCTURE (sign, rational, pi power, radical exponents, Gamma exponents) evaluated at run time, every expected integer relation DERIVED from the structure, the log and additive ring grammars; python3 calpha_rings.py runs its own selftest; python3 + mpmath # fixtures/ (2 files) -- the record objects of the two modules, copied by object with a source path + sha256 per string (6 sources point at files of this bundle and are checked against the served bytes at emission): hankel_tail_fixtures.json (read by threshold_hankel_tail.py: 7 record strings, the integer-relation pins, the Frobenius coefficients phi_1 and the calpha_rings family per family, families K3, CY3, CY4) and direct_linear_fixtures.json (read by direct_linear_extract.py: the record operators in theta form, the path of record, 9 record strings, the closed forms and the projector's digits of record, families K3, CY3); each pinned in its module by sha256 (exit 3 on a mismatch) # vendor_row31_family/ (25 files) -- the data and engines of threshold-banana-evaluate.py --family (Table 2 row 31, the (1,1,1,9) K3 banana as a Feynman family): family/ the family definition and its symmetry; operator/ the operator identity of record and the record's Picard-Fuchs operator; c32/ the connection-coefficient objects of record and the record's 195-digit string; oracle/ the leg-(III) AMFlow points of the physical master (the four out files verbatim + the two-goal object); threshold/ the III-a/III-b succession (the receipt and its two run objects); engine/ the monodromy-projection move, the record's transport engine, the exact identity units; README.md; every file pinned in the script by sha256 (FAMILY_PINS; exit 3 / 4) and listed in FAMILY_MANIFEST.sha256 there # unpinned companions: CHANGES.md (changelog), _snippet.md (proposed page text) # threshold-banana-evaluate.py carries its Route-B oracle literal in-code; the vendor_row31_family/ files are pinned in-code as well (FAMILY_PINS) and by the directory's own FAMILY_MANIFEST.sha256 # threshold_hankel_tail.py pins calpha_rings.py and fixtures/hankel_tail_fixtures.json in-code by sha256 and direct_linear_extract.py pins fixtures/direct_linear_fixtures.json: a mismatch exits 3 before any number is read; neither module imports or reads threshold-banana-evaluate.py 90255485dac07cc196b448824a35afbf687c35c52dd865c43296b9059c214c38 threshold-banana-evaluate.py 2f02d54d02e3acfe75532f9892df7a157a0f6a1cf3ba1984b26b6e14d17a3c37 threshold-banana-expression.md 12b90aea7709c45232ed442c6aaa6d47b05ff21f1c01a2a18002c93fafe6832b frobenius_coefficients_rows31_32_20260909T042148Z.json 350d3808cd85efe7f47c17c3bb1f71679e20be54e8c1702ec3fdf83489954bec threshold_hankel_tail.py 601735c6fa4e1b322eced2bede662eb839f000a02c7b11689e0678cf10418d07 direct_linear_extract.py f31b186255d2aa1f41166382ed00881d927eafde7c82ded8c9a30d14a745ce46 calpha_rings.py 3aca127c00cb0dd9e4dad3a441c5c801f3ce5a95ab816a4cbff6e3f2be783997 fixtures/hankel_tail_fixtures.json c3bb23092d1367f9eb94f0b250c3a93752593b2ea4f391d11e9f04aa28908e22 fixtures/direct_linear_fixtures.json 769b561d0350dcdf5dd3bbcfbfca03a5b769c70beacee5c7dcfe1f30b535b839 vendor_row31_family/FAMILY_MANIFEST.sha256 aa171eeaa89fd6617a8db571a1f469a18a95e62b0848e35989e4c3c14b4ad069 vendor_row31_family/README.md c367d08f78efb01f4993ec7b80ce0979122343f107dca57210f6e6a8d3b95512 vendor_row31_family/c32/LEGII_S1.json 179239e878794168bcf8b00ce0dc6be948d037403201bd79543ee9af7fd8b7a0 vendor_row31_family/c32/LEGII_S2.json c9fee696bfa5dca2fc146cc49deae8781e898cafaeccf55c65fe81f3a52ef3e7 vendor_row31_family/c32/LEGII_S3pl.json 1be8e07b7a3ffebde19869ac04d4036a32ad59226f963312e3bd7a05ed02c043 vendor_row31_family/c32/LEGII_S3pos.json 580e0ccff323608e91d7180f3f19f57740ad6cb2f7eb93bbe982bbe72b25af71 vendor_row31_family/c32/LEGII_S4_COMPARE.json 9986fe347ec94cb97182b222fbfab41157a6ba2f4bb3055a5f909949f39a39ea vendor_row31_family/c32/c32_record.json 92c80c38d96aca69d9b25c48382ef131a0b6f1a099d1dd51389c53246f7ff359 vendor_row31_family/engine/family_c32.py 58da6ca9ae5c04fc02cd99874a5bc81c4927a3bb962369e921f359c43bd8a3d0 vendor_row31_family/engine/operator_identity.py 9e232419746ff59634b84284aef8171b4d157121773ab00755e0f866ea2d2ce5 vendor_row31_family/engine/transport_engine.py 6390b375b930e9eed77702f91f1be7b271430fac306ba7999d70d504e0d48a2e vendor_row31_family/family/FAMILY_DEF_BAN1119.json 24e71c7f3b5811ac94b136953d323cfdb4581cc466c2d69be688a35fcae7f6e5 vendor_row31_family/family/FAMILY_DEF_BAN1119_sym.json 59cdb215856502dff9dbdcfb17c8fcb3b672c5a53acc602ce7708374d946806e vendor_row31_family/family/FAMILY_DIFF.json f282c46e8908842bb15f8bc96963e8c84f0c797fab24564a0e6c0269077f458a vendor_row31_family/family/SYMMETRY.json 8857f2addb393c1e63820d53f225dca3c49c238711a4750d92906b78c7a82f87 vendor_row31_family/operator/LEGI_OPERATOR_IDENTITY.json 62198a7a0a5b4bbdcccaf1b7948e4006e9c50d2692193ccb6ceb9180f28ff4e3 vendor_row31_family/operator/PF_119_EXACT.json fd2fdb722353a503d6e9c7ed238227c6011ba3e9eb7d1d782372f5848eb1ac0a vendor_row31_family/oracle/LEGIII_TWO_GOAL.json 0f5936dc6699d2b7f52bccc6c3cf8c17c19df4ae9ca835f13889c6a51ad5fa14 vendor_row31_family/oracle/LEGIII_pA_g60.json 30f4b192d379bc7ff6efc5d53b2f115d8710eea21efe878c5e0de70d3c8456b9 vendor_row31_family/oracle/LEGIII_pA_g80.json 11ab26358328a2c8b9eae261b89cf3e73fb41ca895cbe0a889c4b5998b8d0841 vendor_row31_family/oracle/LEGIII_pB_g60.json 726c3da1602a3534da800ea0677171f79fedf46d00300e0a7c66352bdc996fd3 vendor_row31_family/oracle/LEGIII_pB_g80.json f89cc6f2fe59471a3ac392c470e69eede20b091f460904fcdbe5dbc0c7b30789 vendor_row31_family/threshold/LEGIIIab_g60_dps40_20260907T020954Z.json e682604872c65502488924aa8794018c25a4a113f3ad527c538616205d769a5d vendor_row31_family/threshold/LEGIIIab_g80_dps50_20260907T020958Z.json 3cbdb1456da28fe4e328a456293e47a55aa9b9d28087269fed0281824b739f2c vendor_row31_family/threshold/LEG_IIIab_RECEIPT_item54_20260907T030516Z.json