403 sections found. Current publication documents are listed before historical material.
Research changelog · TFPT — Introduction and reading guide
The four marks emerge from Gauss–Bonnet — count derived, not assumed ( v216_marks_gauss_bonnet, tfpt_research_contracts, ; ledger QGEO.MARKS.03). The K1 lever of the v215 kill-test (``exactly four marks'') is executed: if the marks are [formula in source] branch points (deficit [formula in source] ) on the flat seam sphere ( [formula in source] , the same [formula in source] as the [formula in source] in [formula in
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documents/changelog/sections/019-source.tex · lines 280 to 299
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Research changelog · TFPT — Introduction and reading guide
QGEO.SYM.01 as a kill-test, not a proof-promise ( v215_seam_deck_killtest, tfpt_research_contracts, / ; ledger QGEO.KILL.01). A foundational symmetry cannot be derived from nothing (Bisognano–Wichmann would presuppose the covariance it should produce), so the bedrock [formula in source] is recast as four independently-falsifiable predictions about the raw seam DtN. The non-circular reduction ( v198/ v199/ v201) gives
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documents/changelog/sections/019-source.tex · lines 300 to 319
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Research changelog · TFPT — Introduction and reading guide
Pillowcase reduction of QGEO.SYM.01 ( v214_seam_pillowcase, tfpt_research_contracts, / ; ledger QGEO.PILLOW.01). The two separately-tracked open QGEO residuals — QGEO.ISO.01 ( v180: the carrier clock is an order- [formula in source] isometry of the seam metric) and QGEO.SUBPRIN.01 ( v201: the DtN sub-principal symbol is mark-local, the seam flat away from the [formula in source] marks) — are shown to be one statement
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documents/changelog/sections/019-source.tex · lines 320 to 342
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Research changelog · TFPT — Introduction and reading guide
[formula in source] formalised as a typed functor with four axioms ( v213_ftransfer_functor, tfpt_research_contracts, ). The four frontier transfers are consolidated into ONE functor [formula in source] , each instance a discrete compiler kernel \ composed with an external continuous solver : (1) [formula in source] -deck equivariance (the Koide multiplier [formula in source] is the deck transfer eigenvalue); (2) Pl\
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documents/changelog/sections/019-source.tex · lines 343 to 359
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Research changelog · TFPT — Introduction and reading guide
Axion DM spine-angle branch [formula in source] ( v211_axion_spine_angle, tfpt_4_frontier, ). A more robust misalignment angle than the determinant-line hilltop [formula in source] ( v185, which over-produces [formula in source] ): the central spine quotient gives [formula in source] exactly (no fit), the finite- [formula in source] solver reaches [formula in source] at [formula in source] , and [formula in source] s
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documents/changelog/sections/019-source.tex · lines 360 to 379
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Research changelog · TFPT — Introduction and reading guide
The cohomology character grading is now Lean-formalised ( CohomologyGrading.lean, ledger FORM.QGEO.03, ). A new module machine-proves the Cohom node of the QGEO proof tree ( v177; audit: pass, no sorry/ admit, axioms propext, Classical.choice, Quot.sound only): the three [formula in source] eigenforms [formula in source] ( [formula in source] ) have pullback character [formula in source] under the clock [formula in s
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documents/changelog/sections/020-source.tex · lines 1 to 17
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Research changelog · TFPT — Introduction and reading guide
The M\"obius uniformisation normal form is now Lean-formalised ( Mobius Uniformisation.lean, ledger FORM.QGEO.02, ). A new module machine-proves the constructive Uniform node of the QGEO proof tree ( v177; audit: pass, no sorry/ admit, axioms propext, Classical.choice, Quot.sound only): the clock [formula in source] has [formula in source] and [formula in source] (order exactly [formula in source] ); the reflection [
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documents/changelog/sections/020-source.tex · lines 18 to 33
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Research changelog · TFPT — Introduction and reading guide
The mark-local [formula in source] implication is now Lean-formalised ( SeamDeckClosure.lean, ledger FORM.QGEO.01, ). A new module in the carrier-rigidity Lean project machine-proves the algebraic core of v201/ v210 ( audit: pass, no sorry/ admit, no domain axioms — \#print axioms [formula in source] propext, Classical.choice, Quot.sound only): (i) the [formula in source] th-root character orthogonality [formula in s
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documents/changelog/sections/020-source.tex · lines 34 to 51
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Research changelog · TFPT — Introduction and reading guide
Mark-local DtN [formula in source] , certified on realistic Steklov profiles and at the state level ( v210_mark_local_dtn, tfpt_research_contracts, ). A numerical sharpening of QGEO.SUBPRIN.01/ v201: a real von-Mises curvature bump summed over the four [formula in source] marks, [formula in source] , builds the Steklov DtN [formula in source] whose off- [formula in source] Fourier support vanishes to [formula in sour
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documents/changelog/sections/020-source.tex · lines 52 to 67
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Research changelog · TFPT — Introduction and reading guide
Muon [formula in source] as a seam vertex ( v204_muon_seam_g2, tfpt_4_frontier, ). The carrier's second-order topological defect [formula in source] projected through the seam-loop phase gives [formula in source] ( [formula in source] vs the dispersive [formula in source] ; [formula in source] vs lattice/CMD-3). The value is exact ; the vertex identification is the \ bridge. Ledger FR.MUONG2.01; Wolfram-mirrored. An
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documents/changelog/sections/020-source.tex · lines 68 to 98
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Research changelog · TFPT — Introduction and reading guide
The M\"obius seam is the boundary Lorentz structure ( tfpt_3, ). Added a paragraph to the ``M\"obius origin of [formula in source] '' section: [formula in source] (Penrose \& Rindler, Spinors and Space-time, Vol. 1, 1.2–1.4), the celestial sphere of null directions via stereographic projection. This gives the self-consistency loop a spacetime meaning — the carrier clock [formula in source] is an elliptic [formula in
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documents/changelog/sections/020-source.tex · lines 99 to 110
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Research changelog · TFPT — Introduction and reading guide
Haloscope coupling tied to [formula in source] ( tfpt_4_frontier, ). Made explicit: in the determinant-line normalization the axion–photon anomaly coefficient is [formula in source] ( [formula in source] ), so the haloscope [formula in source] coupling is set by the same [formula in source] that fixes [formula in source] and [formula in source] — a \ structural relation (the coefficient, not a parameter-free physical
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documents/changelog/sections/020-source.tex · lines 111 to 122
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Research changelog · TFPT — Introduction and reading guide
HOR.EHT.01 ( v203, / / ). The surviving core of the old UFE/black-hole notes ( not the RN-type metric — superseded by the Nariai/seam [formula in source] horizon readouts v101– v104/ v190; only the polarization signature survives): a local achromatic polarization-rotation intercept around a horizon-scale black hole, [formula in source] . The coupling [formula in source] is exact ( , Wolfram-mirrored) — the same top-f
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Research changelog · TFPT — Introduction and reading guide
FR.RAREKAON.01 ( v202, ). The closed TFPT CKM point ( [formula in source] , [formula in source] , [formula in source] , [formula in source] rad; v18/ v88, no flavor fit) feeds the cleanest FCNC probe. With standard external short-distance input (Brod–Gorbahn–Stamou [formula in source] ) it gives [formula in source] and [formula in source] — a \ downstream flavor readout, not a compiler power (the SD functions are ext
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documents/changelog/sections/020-source.tex · lines 140 to 156
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Research changelog · TFPT — Introduction and reading guide
QGEO.SUBPRIN.01 ( v201, / ). The v199 bedrock residual — ``the bounded sub-principal symbol of the raw seam DtN has no off-character (mod 4) matrix elements'' — is reduced one genuine step further: block-diagonality is not an independent postulate. Writing the DtN as [formula in source] with [formula in source] the bounded sub-principal piece [formula in source] multiplication by a curvature [formula in source] (stan
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documents/changelog/sections/020-source.tex · lines 157 to 174
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Research changelog · TFPT — Introduction and reading guide
Axion relic solver ( experiments/ftransfer/axion_relic/relic_solver.py, ). The first real [formula in source] pipeline computation (work package C / review 6.2): a standard misalignment relic with a numerically-computed anharmonic factor [formula in source] at the hilltop. Honest finding: at the predicted [formula in source] the estimate over-produces dark matter, [formula in source] – [formula in source] (robustly [
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documents/changelog/sections/020-source.tex · lines 175 to 198
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Research changelog · TFPT — Introduction and reading guide
v199_seam_state_invariance.py / \ (claim QGEO.STATE.01, work package A). Attacking [formula in source] directly on the raw seam. (1) \ the setup is non-circular: [formula in source] is the Coxeter element of [formula in source] ( [formula in source] , v117), an automorphism of the raw CAR algebra (16 Majoranas) — both carrier-side, no seam geometry. (2) \ for a quasi-free RP state [formula in source] , so [formula in
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documents/changelog/sections/020-source.tex · lines 199 to 221
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Research changelog · TFPT — Introduction and reading guide
v198_modular_commutator_reduction.py \ (claim QGEO.MODULAR.01). The decisive crack on the last residual. (1) \ the DtN principal symbol [formula in source] and the clock [formula in source] are both diagonal in the Fourier basis, so [formula in source] exactly on all of [formula in source] (verified on 33 modes) — the leading-order commutation is free on the whole boundary, never the open part. (2) \ by Tomita–Takesa
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Research changelog · TFPT — Introduction and reading guide
v195_marks_lefschetz_character.py / \ (claim QGEO.MARKS.02). The four seam marks are forced (not posited): [formula in source] fixes only [formula in source] , [formula in source] (the [formula in source] exponents, [formula in source] ) has no trivial component [formula in source] no puncture at a fixed point, and [formula in source] a single free [formula in source] orbit (cross-ratio [formula in source] ). So Mark
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documents/changelog/sections/020-source.tex · lines 242 to 266
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Research changelog · TFPT — Introduction and reading guide
v194_raw_seam_dtn_rp.py \ (claim QGEO.DTN.01). The next hard lever — ``is the raw RP-seam DtN definable from RP data alone?'' (sub-claim 2 of QGEO.ENERGY.02) — was tackled, and the honest result is a reduction, not a closure. (1) \ the commutator [formula in source] closes on the finite cohomology [formula in source] ( [formula in source] , distinct [formula in source] characters; v177). (2) \ the hinge is met: the D
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literal source filename/path in TeX
- cross reference join SeamResidualAxiom.lean
TeX and evidence source explicitly name the same Python identifier; statement equivalence not inferred
- cross reference join MobiusUniformisation.lean
TeX and evidence source explicitly name the same Python identifier; statement equivalence not inferred