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.
Carrier, families and E8 closure
32 authored claim references in the foundation record. The membership comes from explicit Atlas authoring relations.
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32 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 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 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 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 evidenceAn E₈ singularity model for seam realization
Origin Theory
Original identifier and classification
TOPO.E8.01Lattice/Topology (exact) [E]/[C]
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 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 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 Galois action of the quarter clock
Origin Theory
Original identifier and classification
SEAM.GALOIS.01Seam mu4 = carrier's Galois group [E]/[C]: 30 squarefree => no order-4 cyclic, so the seam mu4 is the Galois side (Z/30)^x=mu4 x Z2; the mu4 factor IS (Z/5)^x=Gal(Q(zeta5)) (carrier), the Z2 IS (Z/3)^x (family/CP); the Frobenius zeta5->zeta5^2 is the explicit order-4 operator G with G C5 G^-1=C5^2, G^4=I; resolves the v409 asymmetry (seam = automorphism, not a hand) [C]
Topic connection recorded by an authored Atlas relation.
Read the statement, conditions and evidence