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.
Interlocking clocks
23 authored claim references in the foundation record. The membership comes from explicit Atlas authoring relations.
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23 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 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 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 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 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 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 evidenceE₈ from the extended Hamming code
input 5 tfpt 3 e8 audit bootstrap
Original identifier and classification
E8.CODE.01Exact [E] code/lattice identities + [C] typed compiler ties (integer combinatorics; Python-only per GATE.WOLFRAM.02).
Topic connection recorded by an authored Atlas relation.
Read the statement, conditions and evidenceThe G₃₁ reflection structure
input 5 tfpt 3 e8 audit bootstrap
Original identifier and classification
E8.ST31.01Exact [E] group/Molien/Springer census + [E, KILL] the numerology kill + honest clock typing (Python-only per GATE.WOLFRAM.02; Lean order identities).
Topic connection recorded by an authored Atlas relation.
Read the statement, conditions and evidenceWhat the code interpretation preserves and loses
input 5 tfpt 3 e8 audit bootstrap
Original identifier and classification
E8.CODESEM.01Exact [E] code/dictionary identities + [E, kill] the 30-census control (exact arithmetic; Python-only per GATE.WOLFRAM.02).
Topic connection recorded by an authored Atlas relation.
Read the statement, conditions and evidenceThe Gaussian code and four bit information space
Architecture, E8 and the electromagnetic fixed point
Original identifier and classification
E8.GAUSSCODE.01Exact [E] SNF/census/semantics identities + [E, kill] three must-fail controls (exact arithmetic; Python-only per GATE.WOLFRAM.02).
Topic connection recorded by an authored Atlas relation.
Read the statement, conditions and evidenceThe finite two qubit stabilizer identification
input 5 tfpt 3 e8 audit bootstrap
Original identifier and classification
E8.CLIFFORD2Q.01Exact [E] finite group/lattice identification (H1-H3) with the H4 layer honestly PARTIAL (the index bit identified as the sqrt2/Hadamard Galois bit, not J <-> -J); no marker move (Python-only per GATE.WOLFRAM.02).
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 evidenceEmbedding the specified finite dynamics in continuous time
Research contracts
Original identifier and classification
DYN.MARKOV.EMBED.01Contract [E] (finite kernel embedding, sympy-exact; v971) + [O] (field level)
Topic connection recorded by an authored Atlas relation.
Read the statement, conditions and evidence