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Explore the foundations and current research.

Follow the published construction into its registered claims, then explore reviewed research questions, attempts and the connections that remain open.

Fine-structure constant

The published foundation in this area

7 authored claim references lead into the original ledger and paper sections. This source record remains available even where no separate reviewed research packet is attached.

Read the foundational statements and sources

The α program contains an explicit fixed-point equation, determinant-line reformulations, and precise finite checks. A positive root is exhibited for the specified equation; finite checks do not establish global uniqueness. make_F ignores c3 and Nfac=8 is selected, so physical origin and transfer to Thomson α remain open.

Starting structure in the Atlas orientation
The specified equation has a positive solution. v3 finite tests support only their checked cases; make_F ignores c3 and Nfac=8 is selected. They do not prove global uniqueness.
Which connection is sought
The open work is a source derivation of the function and its parameters, determinant/Ward origin, and a justified transfer to Thomson α.
How it connects
φ0 and other architectural inputs connect the α branch to flavor and other outputs; this shared dependence limits the independence of matches.

Historical attempts

Original experiment and contract metadata. A reported PASS is a historical verdict, not an independently reviewed result. Only explicit Atlas links are used when filtering by research area.

6 matching attempt records

charged sector readout clock 20261013PARTIAL

Can the original marked E8 charged response realize the alpha factor with exponent5/4 under the same source time and actual clocks?

Conditional original E8 lattice-VOA vacuum with marked D5/A3 sector, regularized charged state and actual C/J matrices; no microscopic source selection.

Original historical attempt metadata. A reported PASS is not a reviewed theorem, a fresh run or physical completion.

  • contract_index.json lines 1–67

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    experiments/theory-contracts/charged-sector-readout-clock-20261013/contract_index.json

    df8084830f684f01ebe0325ac814e7c0d356dc82f6b4da674740dbdad5864e93

  • PROOF.txt lines 1–199

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    experiments/theory-contracts/charged-sector-readout-clock-20261013/PROOF.txt

    26e6480a6304e4da5be96328e70f5f56c5bee1bfde7e58593a34a273016d09e0

  • checker.py lines 1–119

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    experiments/theory-contracts/charged-sector-readout-clock-20261013/checker.py

    bf949d11034c1d17322971b58c712c0bef01bb6a3d0e6aa63aeca6d7d41b45d6

  • source_manifest.json lines 1–24

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    experiments/theory-contracts/charged-sector-readout-clock-20261013/source_manifest.json

    5ce972e36ec7f8f4f7770f6a0ce302f1d6a9020c32e491d25b23cbfa1466695a

  • neutral_source_response.py lines 1–293

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    tfpt_explorer/neutral_source_response.py

    a6a21749cba24ae6c50c1f4e1cf95bf283c69ec9b2167a7089380188c5cd8898

  • current_block_geometry.py lines 1–2015

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    tfpt_explorer/current_block_geometry.py

    c9efcac4ba33d4ee3dc20f8c3c69a0f6ff6b2084893a5edf4aaae6c204d9056b

  • certificate.json lines 1–3631

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    experiments/theory-contracts/compiler-integral-triality-20260918/certificate.json

    a342f865bec164ae6dd54e9e7b7c7cc991efcf7a939dda2ecab586b4a6c6cfe3

  • PROOF.txt lines 1–406

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    experiments/theory-contracts/charged-source-time-audit-20260920/PROOF.txt

    97ddf9206a860c00d797dc62bb23b6d731523ca21c10280592f6c61e8a0b2476

  • README.md lines 1–76

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    experiments/theory-contracts/seam-readout-flow-deck-20261005/README.md

    62c3fee7d8e34745c2199230f1a8fc04d8d90e77a771d9f0d9b787a801edcc48

  • results.json lines 1–125

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    experiments/theory-contracts/charged-sector-readout-clock-20261013/results.json

    548de0930bdfb44e6bc190ba9385b3e37e129e3f47c2f8cdae30f2455d44cfe9

  • findings_overrides.json lines 1–1396

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    verification/findings_overrides.json

    aa67c3ed6617aab61c3c7fa9b29e0412d01ab193c62245491563c376151746a5

contract:charged-sector-readout-clock-20261013

clock jordan response reconstruction 20261015PARTIAL

Do the four actual clock-carrier fields provide a complete source-defined probe menu for arbitrary neutral quadratic response, including off-diagonal alignment?

Original eight-current vacuum Heisenberg sector and same-coordinate C/J/P5; mixed two-point responses to iterated weight-two OPE coefficients. Not a physical detector, charged-sector or complete-source theorem.

Original historical attempt metadata. A reported PASS is not a reviewed theorem, a fresh run or physical completion.

  • contract_index.json lines 1–64

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    experiments/theory-contracts/clock-jordan-response-reconstruction-20261015/contract_index.json

    da1619d093fee40604727a62e3d779ffccb787101cc5b2eb10b32c13240bd0ea

  • PROOF.md lines 1–127

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    experiments/theory-contracts/clock-jordan-response-reconstruction-20261015/PROOF.md

    dd062d2017de70d3b858452a41a7b9089d3b8cb8dd3984af9cec89a6524cdbc0

  • README.md lines 1–14

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    experiments/theory-contracts/clock-jordan-response-reconstruction-20261015/README.md

    da60243a4d0ba19259a857c229b1ac31ed3fb5fda6c9e709e2ddaa0f6e0c72d1

  • checker.py lines 1–127

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    experiments/theory-contracts/clock-jordan-response-reconstruction-20261015/checker.py

    0c5701db514bda4dbf6985bb9e70e39c81df8fea3bcf83f351a462d4d554ad1e

  • certificate.json lines 1–5316

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    experiments/theory-contracts/clock-jordan-response-reconstruction-20261015/certificate.json

    79f6529307c8265ece19d553e84d9bdb325d3b08f009dd0c7dbfcf8634d17dea

  • results.json lines 1–70

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    experiments/theory-contracts/clock-jordan-response-reconstruction-20261015/results.json

    6655ddf954deefa1c042eac72448ba16825fa71915d542fd06aca01272ad2d92

  • findings_overrides.json lines 1–1396

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    verification/findings_overrides.json

    aa67c3ed6617aab61c3c7fa9b29e0412d01ab193c62245491563c376151746a5

contract:clock-jordan-response-reconstruction-20261015

em positive root convexity 20261013PARTIAL

Can the fixed original EM closure function be proved to have exactly one simple positive root without relying on the numerical derivative scan?

All positive alpha for the exact default v3 EM function; mathematical existence, uniqueness and simplicity under fixed inputs, not their physical selection.

Original historical attempt metadata. A reported PASS is not a reviewed theorem, a fresh run or physical completion.

  • contract_index.json lines 1–51

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    experiments/theory-contracts/em-positive-root-convexity-20261013/contract_index.json

    3dfe6542dcf79f59905f20afb2ade4ef8406e7274992eb1cc20ee7cab2792cbd

  • PROOF.txt lines 1–80

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    experiments/theory-contracts/em-positive-root-convexity-20261013/PROOF.txt

    c1ad319037418e7745c287132c4065cf6d963af797c5a4c81f12273e486d7b50

  • README.md lines 1–5

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    experiments/theory-contracts/em-positive-root-convexity-20261013/README.md

    d27f6939d99aa02c2dfba2a7b46bba9c2d6014696fd8572530d9391e0f8ab6ca

  • checker.py lines 1–61

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    experiments/theory-contracts/em-positive-root-convexity-20261013/checker.py

    24b14c59cd5dff98e79920b35c71093127f330ff721b46943b6b0e60811945fb

  • source_manifest.json lines 1–20

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    experiments/theory-contracts/em-positive-root-convexity-20261013/source_manifest.json

    6f09422ccb0a713dbaea94c96834079c9c525b1ff590ef9bb16987435f046b97

  • ORIGINAL_RUN.json lines 1–15

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    experiments/theory-contracts/em-positive-root-convexity-20261013/ORIGINAL_RUN.json

    2963fd109a255fd5fe1945d472649ef7cafa01d221e21760b66d0a168169e307

  • tfpt_1_architecture_e8.tex lines 1–1

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    tfpt_1_architecture_e8.tex

    45a26936328c7464bcca138329e7361eb8ee89a597d29fed281af6785ace43a5

  • v13_open_gates.py lines 1–59

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    verification/v13_open_gates.py

    892b757498342f24d41683c33a65eba3e1e133d41143b72b66ddb518737bd131

  • v3_em_alpha.py lines 1–140

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    verification/v3_em_alpha.py

    22f769d9f89e74e2279c06b11c75d6da4d7455ef185fb2f79869a30932ebc3e8

  • results.json lines 1–56

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    experiments/theory-contracts/em-positive-root-convexity-20261013/results.json

    28518491a71843f025228bc28c183b71f524740b703a7570cc622c9e60086401

  • findings_overrides.json lines 1–1396

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    verification/findings_overrides.json

    aa67c3ed6617aab61c3c7fa9b29e0412d01ab193c62245491563c376151746a5

contract:em-positive-root-convexity-20261013

native mark memory 20261014PARTIAL

Which marking and response memory follow from the original charge source, and can the derived four-grade factor close under the same Hamiltonian and actual clocks?

Original historical attempt metadata. A reported PASS is not a reviewed theorem, a fresh run or physical completion.

  • contract_index.json lines 1–134

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    experiments/theory-contracts/native-mark-memory-20261014/contract_index.json

    cf4ebd4c6bf88c97690a01ee2ad252de024ae7c5af61168447a4230ed4182144

  • PROOF.md lines 1–191

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    experiments/theory-contracts/native-mark-memory-20261014/PROOF.md

    10492f2d34e93ffb8db2593b120ef120401e26bd5acc34db0cd9c7e8f15ec364

  • README.md lines 1–7

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    experiments/theory-contracts/native-mark-memory-20261014/README.md

    bd8db56e48700e7825e0a961c20e23801ecfb2424f723231d51ef4c8463a2036

  • checker.py lines 1–70

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    experiments/theory-contracts/native-mark-memory-20261014/checker.py

    50a3b64a68a585f3eb574b343aff1822210b36c09714469d43f601753ec69d69

  • source_manifest.json lines 1–117

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    experiments/theory-contracts/native-mark-memory-20261014/source_manifest.json

    0d4e140fd36126f58cbe5b739c383d7e1df49dd0c94a60fc1a8f5cd634a4bbda

  • PROOF.md lines 1–250

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    experiments/theory-contracts/charged-lift-round16/PROOF.md

    a02a9cd73bcfd1382e187531dc218f9b422e4d89504fb57ec56643c5c5d9cfc8

  • README.md lines 1–230

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    experiments/theory-contracts/carrier-module-conjugation/README.md

    2f1b9171f4ea03bbe6dc0466834f21d738526b84c559f4008fa17c3e8f42ee70

  • PROOF.md lines 1–285

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    experiments/theory-contracts/local-charge-transport-round20/PROOF.md

    6d7059cc75108be2b7262f030b83e2c14c774a950d2f1ccd0f9c5c1b3b5afb5c

  • checker.py lines 1–397

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    experiments/theory-contracts/local-charge-transport-round20/checker.py

    e5b56b53e3fbb079947d8f420aa45cfd0190e9ac3ccca9fd42f8797a7438d234

  • PROOF.md lines 1–175

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    experiments/theory-contracts/hopping-source-domain-round20/PROOF.md

    b9d5bd67310cfc3176e92e1b72d3609c128566635166adb5df8d582d54bcd624

  • PROOF.md lines 1–157

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    experiments/theory-contracts/scalar-charge-energy-round20/PROOF.md

    f54190fffdf3ccc110c5a66d6da0575c7b8ad96a5a880fcb4b6c01f930ccb7b5

  • PROOF.md lines 1–198

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    experiments/theory-contracts/history-sum-control-round26/PROOF.md

    cd1ea78abaeabd0073fa20e290aebe4599d4a1895552f23d9ef3843064cb6647

  • PROOF.md lines 1–255

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    experiments/theory-contracts/native-source-reconstruction-20261014/PROOF.md

    d16b6af2c90491ac94eeb4ab04a8c96b072d37bb6bc5015b3db85c023f8a96e2

  • certificate.json lines 1–3631

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    experiments/theory-contracts/compiler-integral-triality-20260918/certificate.json

    a342f865bec164ae6dd54e9e7b7c7cc991efcf7a939dda2ecab586b4a6c6cfe3

  • PROOF.txt lines 1–199

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    experiments/theory-contracts/charged-sector-readout-clock-20261013/PROOF.txt

    26e6480a6304e4da5be96328e70f5f56c5bee1bfde7e58593a34a273016d09e0

  • MEMORY-REVIEW.md lines 1–686

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    experiments/theory-contracts/native-mark-memory-20261014/MEMORY-REVIEW.md

    74314123ad648066b1d86de11e0afac53f8165472619b96fda7b30f0eb92c73b

  • MARK-REVIEW.md lines 1–75

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    experiments/theory-contracts/native-mark-memory-20261014/MARK-REVIEW.md

    54b83ea2b6198545558a8efc79fa47eb78b1f9adb609a3ff3cc3837579505651

  • results.json lines 1–30

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    experiments/theory-contracts/native-mark-memory-20261014/results.json

    73fe617ec8ffe29822c40e2a38a8cec20742bc50dfe4ae5eaf78f45387f945bc

  • carry_check.py lines 1–47

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    experiments/theory-contracts/native-mark-memory-20261014/carry_check.py

    1b14d3977e94618e308756b128bfe8de52e1c282cc5b79dd5462f0b8d2868cc7

  • carry-result.json lines 1–33

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    experiments/theory-contracts/native-mark-memory-20261014/carry-result.json

    f5b8e365c11c80967c8469b78ca27fa9e5e3bbaf1aac0e6e31338b34f377aeb8

  • clock_probe.py lines 1–93

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    experiments/theory-contracts/native-mark-memory-20261014/clock_probe.py

    24fba1254dd11738448c9e5baa9035a7f5e966d0e9ea2cbddf77345e7e0646cc

  • clock-result.json lines 1–193

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    experiments/theory-contracts/native-mark-memory-20261014/clock-result.json

    0438eba443d70e8e4546e8d1d45e63b4bfde0b7cb3beeedbf2f11aa61c7e1147

  • CLAUDE-SELECTION-AUDIT.md lines 1–74

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    experiments/theory-contracts/native-mark-memory-20261014/CLAUDE-SELECTION-AUDIT.md

    d154de3d96d6a28a15aa03923916138c587fee96e5816403c285f455ceedb5c5

  • spinor_selection_check.py lines 1–37

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    experiments/theory-contracts/native-mark-memory-20261014/spinor_selection_check.py

    da4f220259918bacdf39cf6a20d89d49cf0bad10b318fca8598854716859bf78

  • spinor-selection-result.json lines 1–67

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    experiments/theory-contracts/native-mark-memory-20261014/spinor-selection-result.json

    2ad935403c7aa44c690a7a474701b7b08a3ec8e50bd2e2952690c49be26f3871

  • CLAUDE-SELECTION-REVIEW.md lines 1–81

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    experiments/theory-contracts/native-mark-memory-20261014/CLAUDE-SELECTION-REVIEW.md

    b7641433e82bc70c7aa10cd2366cae0afaa048094cee0535b1b29e72f5ba0de2

  • TFPT_Gesamtsynthese_2026-09-28.tex lines 1–1

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    tfpt_explorer/docs/session-2026-09-28/TFPT_Gesamtsynthese_2026-09-28.tex

    73097e57a9ba40866a96d110041aea3246085cf54d210096a509fa3de2162510

  • tfpt_3_e8_audit_bootstrap.tex lines 1–1

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    tfpt_3_e8_audit_bootstrap.tex

    8fafa428bf8a079d774692514063c51eb62e4fdeb3897a1db40563433b4a3a7c

  • v624_external_lattice_audit.py lines 1–261

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    verification/v624_external_lattice_audit.py

    71d0e6fbabad7f3d2187d708638371a2df5722f5a9d5eb80d851e205e577cc9b

  • v993_minimal_defect_selector.py lines 1–544

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    verification/v993_minimal_defect_selector.py

    1d39723c8beb6ebc848414a7448c98040c0e3790fd2498d249dee1a682059b2d

  • findings_overrides.json lines 1–1396

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    verification/findings_overrides.json

    aa67c3ed6617aab61c3c7fa9b29e0412d01ab193c62245491563c376151746a5

contract:native-mark-memory-20261014

neutral response tomography 20261013PARTIAL

Which additional native neutral-field responses repair the information lost by the rank-one P0 port, and under which source-alignment assumptions?

Exact vacuum Wick responses of original neutral_source_response.py with fixed native rank5,2,1 projectors and block-scalar quadratic primaries; algebraic identifiability, not physical source selection or susceptibility derivation.

Original historical attempt metadata. A reported PASS is not a reviewed theorem, a fresh run or physical completion.

  • contract_index.json lines 1–70

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    experiments/theory-contracts/neutral-response-tomography-20261013/contract_index.json

    acbd078e43ee66964d7eb3cde62170523cbc97ef1b76d7c589bed6338fab71ef

  • PROOF.txt lines 1–110

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    experiments/theory-contracts/neutral-response-tomography-20261013/PROOF.txt

    2bd7603913979c07743d96e390e8a5891770da3c2df536b7ec24383a23cbe03f

  • README.md lines 1–7

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    experiments/theory-contracts/neutral-response-tomography-20261013/README.md

    3bf65c1ac62d10390384dc585e04d49d3fe3359a0bcbcdc3e160926818a39825

  • checker.py lines 1–129

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    experiments/theory-contracts/neutral-response-tomography-20261013/checker.py

    2b6699d8bfbe6e6465fb1faeb1ce6d1712291e7bd98722ef4fcb29f363e785aa

  • source_manifest.json lines 1–20

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    experiments/theory-contracts/neutral-response-tomography-20261013/source_manifest.json

    1ffdc2720f493025b401c5bf843c0af378bcf58905b3a46ec7bb7c42f1703d3f

  • neutral_source_response.py lines 1–293

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    tfpt_explorer/neutral_source_response.py

    a6a21749cba24ae6c50c1f4e1cf95bf283c69ec9b2167a7089380188c5cd8898

  • PROOF.txt lines 1–91

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    experiments/theory-contracts/neutral-port-identifiability-20261013/PROOF.txt

    a42d419c8d372a749417fe642010317b846cd7fadc183f5fbade04a80d17ddca

  • PROOF.txt lines 1–55

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    experiments/theory-contracts/source-observation-identifiability-20261013/PROOF.txt

    b37b7cc9d0454954938fc348337f4da4d2d5c56f178127ad65d94df887ad672d

  • README.md lines 1–76

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    experiments/theory-contracts/seam-readout-flow-deck-20261005/README.md

    62c3fee7d8e34745c2199230f1a8fc04d8d90e77a771d9f0d9b787a801edcc48

  • results.json lines 1–130

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    experiments/theory-contracts/neutral-response-tomography-20261013/results.json

    7b19c01f5940c4e7a1767c743f52a277b86963768a78e2e33c04b7b0c2cbce85

  • findings_overrides.json lines 1–1396

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    verification/findings_overrides.json

    aa67c3ed6617aab61c3c7fa9b29e0412d01ab193c62245491563c376151746a5

contract:neutral-response-tomography-20261013

source flavor origin 20260920PARTIAL

Do the original global carrier group and actual native cubic select a consistent source-level route to distinct Down/lepton masses and phases?

Original historical attempt metadata. A reported PASS is not a reviewed theorem, a fresh run or physical completion.

  • contract_index.json lines 1–84

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    experiments/theory-contracts/source-flavor-origin-20260920/contract_index.json

    c5893a43e40f48483c7577eac0e1c70e0b477593f3f2cf79d6bb9067aa404fe2

  • PROOF.txt lines 1–233

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    experiments/theory-contracts/source-flavor-origin-20260920/PROOF.txt

    328158deea8bab9ac552c1d4f44eb64f79724264501a5d8a7276e873c5c9b314

  • README.md lines 1–67

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    experiments/theory-contracts/source-flavor-origin-20260920/README.md

    97fb0475cd000953089b6b0a98ca500a71cb22c53f17fe424fb6f31bcde27fd7

  • checker.py lines 1–144

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    experiments/theory-contracts/source-flavor-origin-20260920/checker.py

    da4cc9430e9834d5e9e1008061edce4999c3699f0933f1f9a56e7dee8b998387

  • source_manifest.json lines 1–70

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    experiments/theory-contracts/source-flavor-origin-20260920/source_manifest.json

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  • SPEC.txt lines 1–34

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    Original location and fingerprint

    experiments/theory-contracts/source-flavor-origin-20260920/SPEC.txt

    74929c226d5d07daff059635a24fc0639d3710fe4128d8585361df21869de7b3

  • FLAVOR_REVIEW.txt lines 1–176

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    Original location and fingerprint

    experiments/theory-contracts/source-flavor-origin-20260920/FLAVOR_REVIEW.txt

    f3bb1c0c6bb9a20347e4f21f9ab70a0d2b5f297d8e7118b8fa3a9b36242eaf70

  • GLOBAL_CHARGE_REVIEW.txt lines 1–341

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    Original location and fingerprint

    experiments/theory-contracts/source-flavor-origin-20260920/GLOBAL_CHARGE_REVIEW.txt

    57463740887525fe9dc007005b106af96312c220f2a67ce5bef6acfd571de577

  • tfpt_1_architecture_e8.tex lines 1–1

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    Original location and fingerprint

    tfpt_1_architecture_e8.tex

    45a26936328c7464bcca138329e7361eb8ee89a597d29fed281af6785ace43a5

  • tfpt_2_standard_model.tex lines 1–1

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    tfpt_2_standard_model.tex

    00035c071a4d037ede785fb65cd55dfe1cb34430a935ef534620ba38a40436a6

  • v46_grand_mass_volume.py lines 1–69

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    Original location and fingerprint

    verification/v46_grand_mass_volume.py

    19163c77032de2fd910409cfdfdadc6635ad0ae945c44e89b1751d1d4269fb90

  • v252_full_finite_triple.py lines 1–375

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    Original location and fingerprint

    verification/v252_full_finite_triple.py

    820254440e178430422e50605067775656236602996307f67c9e69124ba5d163

  • certificate.json lines 1–1008

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    experiments/theory-contracts/compiler-vacuum-current-cubic-20260918/certificate.json

    150f27876e19fba789b497d53b1dc02b3d9f2f02704b991cc214cfc8e0ab51eb

  • PROOF.txt lines 1–137

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    Original location and fingerprint

    experiments/theory-contracts/compiler-vacuum-current-cubic-20260918/PROOF.txt

    d65189b806facbb1eb718eec50221bb85b3a8c3417f98fb6627e01c72c98ef62

  • source_pins.json lines 1–25

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    Original location and fingerprint

    experiments/theory-contracts/compiler-vacuum-current-cubic-20260918/source_pins.json

    a6e3588e75768a37747606d57802c358f1fe7b94752e8691f412261320ed779b

  • PROOF.md lines 1–275

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    experiments/theory-contracts/source-boundary-selection-20260920/PROOF.md

    4081e9f7bc19da9cf87234edf361bb0ab29eaf8e5f69d23f7c6708b4512be0ff

  • PROOF.txt lines 1–61

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    Original location and fingerprint

    experiments/theory-contracts/phase-origin-yukawa-defect-20260919/PROOF.txt

    4d3f9e0b24b445e0d72fc7816e6c5aa860c8c8f957cbd997291e704958a154e0

  • certificate.optimized.json lines 1–3013

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    experiments/theory-contracts/source-flavor-origin-20260920/certificate.optimized.json

    3efa28973698464e873b0ae2bde82469a73e1f1bf3543c85a33e63bfe931a9ca

  • certificate.json lines 1–3013

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    Original location and fingerprint

    experiments/theory-contracts/source-flavor-origin-20260920/certificate.json

    3efa28973698464e873b0ae2bde82469a73e1f1bf3543c85a33e63bfe931a9ca

  • findings_overrides.json lines 1–1396

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    Original location and fingerprint

    verification/findings_overrides.json

    aa67c3ed6617aab61c3c7fa9b29e0412d01ab193c62245491563c376151746a5

contract:source-flavor-origin-20260920