Skip to main content

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.

Follow later research questions in this areaAll foundation areas

Search the complete foundation register

32 matching active claims. Showing at most 20 per page. Original statement text and long numerical details open within each claim.

The 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 evidence

The 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 evidence

The holomorphic restriction of E₈ invariants

Architecture, E8 and the electromagnetic fixed point

Original identifier and classification

E8.QUARTICHALF.01Symbolic [PROOF] mu4-orbit vanishing + [E] G31 invariance/independence/mirror census + [E, kill] complex-structure controls + [cited] Chevalley basic-invariant theorem (exact arithmetic; Python-only per GATE.WOLFRAM.02).

Topic connection recorded by an authored Atlas relation.

Read the statement, conditions and evidence

The 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 evidence

The 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 evidence

The 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 evidence