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.
Tests and predictions
20 authored claim references in the foundation record. The membership comes from explicit Atlas authoring relations.
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20 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 evidenceResearch contracts
Research contracts
Original identifier and classification
RH.SPLIT.01Numerical (partial; honest wall)
Topic connection recorded by an authored Atlas relation.
Read the statement, conditions and evidenceResearch contracts
Research contracts
Original identifier and classification
RH.BUNDLE.01Numerical (explicit realisation)
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 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 axion misalignment branch
Frontier and open physical interfaces
Original identifier and classification
DM.AXION.SPINE.01Physical [C] (spine angle = structural rational / NOT observable post-inflationary; relic from f_a + N_DW=1; reframed by FR.DM.02)
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 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 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 formally encoded scalar spectral gap
Origin Theory
Original identifier and classification
FORM.SPECTRALGAP.01Formal [F] (Lean kernel; no extra axioms) -- the scalar core + the finite-dimensional diagonalisable case of the spectral-gap meta-theorem (v383): gap => unique attractor + geometric decay => parameter-free
Topic connection recorded by an authored Atlas relation.
Read the statement, conditions and evidenceThe weight typing premise of the carrier
TFPT — Introduction and reading guide
Original identifier and classification
P2.TYPING.01Formal/Identity [E] (AG arithmetic: Deligne residue-trace degree, BG dictionary, stability skeleton, Schur-Horn lattice points, Biswas Z3-cover -- sympy exact, Wolfram-mirrored) + [C] (R1 module identification, QGEO.SYM territory; R2 unitarity (U)) + [N] reference (R3 analytic monodromy, v117 check 4); AX.P2.01 stays Axiom
Topic connection recorded by an authored Atlas relation.
Read the statement, conditions and evidenceThe gap between a boundary net and local spacetime physics
Research contracts
Original identifier and classification
DIMENSION.UPLIFT.FIREWALL.01Firewall (standing discipline rule, in force; the uplift theorems it names stay Open)
Topic connection recorded by an authored Atlas relation.
Read the statement, conditions and evidenceChiral lattice matter and the mirror sector
Frontier and open physical interfaces
Original identifier and classification
CHIRAL4D.NOMIRROR.01Open (research contract; 1+1D chiral Gauss census executed; SMG mechanism toy-proved [E]; Nielsen-Ninomiya as Gauss statement; 4D Spin(10) theorem stays [O]; no 3+1D closure) | Round-3 v1023 adds an exact finite block lemma [E]/conditional GW reading [C]; NOMIRROR remains Open [O].
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 evidenceThe conditions for full physical completion
TFPT — Introduction and reading guide
Original identifier and classification
TFPT.TOE.COMPLETE.01Open (research contract; named AND of eight gates; no closure, no marker move) | Round-3 v1022-v1025 adds certified subgates and no-gos only; Round-4 v1026-v1030 adds narrow proved and conditional subresults only; all T1-T8 gates and TOE remain Open [O].
Topic connection recorded by an authored Atlas relation.
Read the statement, conditions and evidenceThe finite mirror projector candidate
TFPT — Introduction and reading guide
Original identifier and classification
CHIRAL4D.MIRROR.DET16.01Candidate [C] (exact finite-cluster gapping; open: dynamical gauge fields, domain-wall geometry, 4D volume theorem) | Round-3 v1023 is a separate finite block lemma and does not upgrade DET16.
Topic connection recorded by an authored Atlas relation.
Read the statement, conditions and evidence