The published foundations of TFPT
Read the original registered statements beside their paper sections, assumptions and verification sources. The later reviewed research stays connected through a separate record.
Seam, origin and declared inputs
25 authored claim references in the foundation record. The membership comes from explicit Atlas authoring relations.
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25 matching active claims. Showing at most 20 per page. Original statement text and long numerical details open within each claim.
The declared boundary normalization
TFPT — Introduction and reading guide
Original identifier and classification
AX.P1.01Axiom (declared input; reduces to the anchor a=(1,1,2)+pi)
Topic connection recorded by an authored Atlas relation.
Read the statement, conditions and evidenceThe five slot carrier and its bootstrap conditions
TFPT — Introduction and reading guide
Original identifier and classification
AX.P2.01Axiom (declared input; over-determined bootstrap fixed point, Lean-forced)
Topic connection recorded by an authored Atlas relation.
Read the statement, conditions and evidenceThe explicit D₅ and A₃ lattice construction of E₈
Architecture, E8 and the electromagnetic fixed point
Original identifier and classification
E8.GLU.01Lattice
Topic connection recorded by an authored Atlas relation.
Read the statement, conditions and evidenceThe positive solution of the alpha equation
TFPT — Introduction and reading guide
Original identifier and classification
EM.FP.01Numerical
Topic connection recorded by an authored Atlas relation.
Read the statement, conditions and evidenceThe common anchor and its integer invariants
TFPT — Introduction and reading guide
Original identifier and classification
ANCHOR.GEN.01Identity
Topic connection recorded by an authored Atlas relation.
Read the statement, conditions and evidenceThe ambient gravitational measure problem
TFPT — Introduction and reading guide
Original identifier and classification
QG.AMB.01Open (decoupled general QG; non-TFPT)
Topic connection recorded by an authored Atlas relation.
Read the statement, conditions and evidenceThe conditional entanglement route to linearized gravity
Research contracts
Original identifier and classification
GRAV.ENTROPY.EQUILIBRIUM.01Entanglement-equilibrium gravity [E]/[C]/[O] (parameter-free linearised Einstein 8pi=1/c3; thermo=geo coincidence via |mu4|=|Z2|chi; J3 assembled; entropy density atom-fixed; residual = nonlinear + v_geo)
Topic connection recorded by an authored Atlas relation.
Read the statement, conditions and evidenceInteger constraints from the E₈ invariant degrees
Red-team audit
Original identifier and classification
E8.DEGREE.JOINT.01E8 degree joint-lock [E] (the two structural integers g_car=5, N_fam=3 = unique roots of x^2-8x+15 with coeffs rank E8=8 and h/2=15; all E8 combinatorics fixed by its degrees; consolidation of v6/v66/v355/v431, no new mining)
Topic connection recorded by an authored Atlas relation.
Read the statement, conditions and evidenceRealizing the seam as a physical boundary
Origin Theory
Original identifier and classification
QGEO.REALIZE.01Physical [C] (seam-side identification) + [O] (open realisation)
Topic connection recorded by an authored Atlas relation.
Read the statement, conditions and evidenceThe Coxeter clock and its quarter action
Origin Theory
Original identifier and classification
COX.CLOCK.01Identity (exact)
Topic connection recorded by an authored Atlas relation.
Read the statement, conditions and evidenceThe modular spectral closure assembly
Research contracts
Original identifier and classification
QFT.MSC.01Numerical (assembly certificate) [E]/[C]/[O]
Topic connection recorded by an authored Atlas relation.
Read the statement, conditions and evidenceThe seam realization contract
TFPT — Introduction and reading guide
Original identifier and classification
SEAM.EQUIV.01Contract [E] (typing + firewall + taxonomy) + [O] (the named theorem)
Topic connection recorded by an authored Atlas relation.
Read the statement, conditions and evidenceHow the Coxeter sectors couple
Origin Theory
Original identifier and classification
COX.COUPLE.01Identity/Lattice [E] (cyclotomic Galois) + [C] (verdict)
Topic connection recorded by an authored Atlas relation.
Read the statement, conditions and evidenceThe physical determinant variation required for alpha
Origin Theory
Original identifier and classification
ALPHA.QUILLEN.EXACT.01Named target [E]/[O] (the Quillen determinant-line variation-exactness; a face of SEAM.EQUIV.01, elevates EM.WARD.01's residual to a citable target; no new gate; 2026-08-28: the v974 CHANNEL-SWAP face resolved at the finite level by mu4-character grading, v985; completeness wave: finite KMS rigidity-premise [E] v995, ln-2-rate detline shadow v996 -- continuum Bismut-Freed stays [O])
Topic connection recorded by an authored Atlas relation.
Read the statement, conditions and evidenceThe source of the seam alignment bit
TFPT — Introduction and reading guide
Original identifier and classification
SEAM.BIT.ORIGIN.01Formal/Identity [E] (origin theorem: half-period fixed points, rational descent identity, free-involution census in all three stabiliser types; core solve lambda in {-1, 2, 1/2}; CM dictionary; equivalence tetrad + circularity audit; fermion dichotomy: Utilde^2 = 256 gamma-monomial vs +2^7 scalar in exact Cl(16) Fractions, root counts 2 vs 0, arrangement census 28/21 -- sympy exact, Wolfram-mirrored) + [C] (the one alignment bit: which half-period, i.e. the deck position); SEAM.CLOCK.RIGIDITY.01 and QGEO.REALIZE.01 stay as they are, P2.TYPING.01 R1 unchanged
Topic connection recorded by an authored Atlas relation.
Read the statement, conditions and evidenceWhat the conformal marked seam axioms fix
TFPT — Introduction and reading guide
Original identifier and classification
QGEO.SEAMFORCE.01Exact [E] rigidity/census/genus identities (sympy) + [C] the residue typing
Topic connection recorded by an authored Atlas relation.
Read the statement, conditions and evidenceWhich cyclic orders the marked construction permits
input 5 tfpt 3 e8 audit bootstrap
Original identifier and classification
QGEO.NCENSUS.01Exact [E] ramification/genus/Chevalley-Weil/pinning identities (sympy) + [C] the conditional typing
Topic connection recorded by an authored Atlas relation.
Read the statement, conditions and evidenceThe covered seam and its lattice skeleton
TFPT — Introduction and reading guide
Original identifier and classification
QGEO.COVERSEAM.01Exact [E] combinatorics + mode-sum identities (sympy) + [C] the orbifold residue typing
Topic connection recorded by an authored Atlas relation.
Read the statement, conditions and evidenceThe compiler clock alphabet in G₃₁
Research contracts
Original identifier and classification
E8.G31.CLOCK_ALPHABET.01Exact corpus compression + selectivity audit [typed evidence line: 19/19 checks, zero fails; the honesty line kept (degree-only audits cannot separate G31 from the reducible torus Z8 x Z12 x Z20 x Z24 -- frozen scope the irreducible rank-4 Shephard-Todd list); the Molien uniqueness and the full W(D5)-fence structural refutation CITED (v634), not recomputed; X1/X2 controls fire]; a normal form plus an armed kill rule for a deployed object; NO RH claim; no marker move (Python-only per GATE.WOLFRAM.02)
Topic connection recorded by an authored Atlas relation.
Read the statement, conditions and evidenceThe assumptions needed for geometric modular flow
Research contracts
Original identifier and classification
GRAV.NONCIRCULAR.01Firewall (standing discipline rule, in force; audit census recorded)
Topic connection recorded by an authored Atlas relation.
Read the statement, conditions and evidence