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.
Standard Model and flavor
18 authored claim references in the foundation record. The membership comes from explicit Atlas authoring relations.
Search the complete foundation register
18 matching active claims. Showing at most 20 per page. Original statement text and long numerical details open within each claim.
The 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 residue matrix and flavour transport budget
Architecture, E8 and the electromagnetic fixed point
Original identifier and classification
FLAV.R.01Lattice
Topic connection recorded by an authored Atlas relation.
Read the statement, conditions and evidenceThe connected Q, K, R and L flavour operators
Standard Model and flavor structure
Original identifier and classification
FLAV.KQ.01Lattice
Topic connection recorded by an authored Atlas relation.
Read the statement, conditions and evidenceThe dual anchor and solar mixing response
Standard Model and flavor structure
Original identifier and classification
FLAV.SOLAR.01Numerical
Topic connection recorded by an authored Atlas relation.
Read the statement, conditions and evidenceThe family lattice norm in the solar coefficient
Standard Model and flavor structure
Original identifier and classification
FLAV.SOLAR.02Identity
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 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 evidenceParticle charges and anomaly cancellation in one family
Research contracts
Original identifier and classification
CAR.SM.ANOM.01Identity [E] (spectrum+anomaly+RG) + [C]/[O] (S-matrix)
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 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 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