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.
Search the complete foundation register
334 matching active claims. Showing at most 20 per page. Original statement text and long numerical details open within each claim.
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 evidenceResearch Contract 2 — [formula in source]
Research contracts
Original identifier and classification
E8.WINDING.DECODER.01Honest promotion of an exact integer theorem [typed evidence line: 11/11 checks, zero fails, verdict WINDING-DECODER-EXACT; frozen spec SHA 6a54768d...]
No authored topic assignment in this snapshot.
Read the statement, conditions and evidenceResearch Contract 2 — [formula in source]
Research contracts
Original identifier and classification
E8.SHELL.GLOBAL.01Honest promotion of a proved shell law [typed evidence line: 15/15 checks, zero fails, verdict SHELL-GLOBAL-THEOREM; frozen spec SHA a4b2f6d9...]
No authored topic assignment in this snapshot.
Read the statement, conditions and evidenceResearch Contract 2 — [formula in source]
Research contracts
Original identifier and classification
FORM.E8.SHELL.GLOBAL.01Formal [F] (Lean kernel; the consequence chain from the named ShellSystem hypotheses -- every statement an exact integer identity)
No authored topic assignment in this snapshot.
Read the statement, conditions and evidenceArchitecture, E8 and the electromagnetic fixed point
Architecture, E8 and the electromagnetic fixed point
Original identifier and classification
DOILY.ANCHOR.CLASSIFY.01Exact identity-grade theorem [Identity]: the anchor law characterizes the doily among ALL 35 lines (exclusivity census 15 + 10 + 10); no marker move
No authored topic assignment in this snapshot.
Read the statement, conditions and evidenceThe EM closure: [formula in source] as an explicit fixed point (made explicit here)
Architecture, E8 and the electromagnetic fixed point
Original identifier and classification
SEAM.STATE.RPMIXING.01Measured census [E] (sector-truncated; float64 exploration grade warded by exact identities) + finite KMS rigidity [E] (v995); type-III/continuum stays [O]; no marker moves
No authored topic assignment in this snapshot.
Read the statement, conditions and evidenceThe EM closure: [formula in source] as an explicit fixed point (made explicit here)
Architecture, E8 and the electromagnetic fixed point
Original identifier and classification
ALPHA.QUILLEN.FACES.01Exact/computed witnesses [E] + typed conditional [C]; the target row stays [O]
No authored topic assignment in this snapshot.
Read the statement, conditions and evidenceResearch Programme — the TFPT4D master route (one 4D transfer object instead of twenty formulas)
Research contracts
Original identifier and classification
SEAM.SIMPLECURRENT.GENERATOR.01Open [O] + lattice shadow [E] (v983) + quantitative S1/S2 skeleton [E-measured] + reduction-to-cited-class [C conditional] + MMST criteria 5/7 executed [E-measured] (v994) + C6 written-out [C]; open rest = C7 modular invariance + net-level G2/G3/G4; no closure
No authored topic assignment in this snapshot.
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 charged scaling limit and Type III identification
TFPT — Introduction and reading guide
Original identifier and classification
SEAM.MMST.TYPEIII.CHARGED.01Open (research contract; master scaling-limit theorem; children listed here not back) | Round-3: C1/C2a/TV and scalar C2b subclaims proved [E]; ALG2 implication refuted [X]; CF/DG and ALG-EXH remain Open [O].
Topic connection recorded by an authored Atlas relation.
Read the statement, conditions and evidenceThe hard reduction: the live residual as typed interfaces
TFPT — Introduction and reading guide
Original identifier and classification
SEAM.MILNOR.LOCALRING.01Open (research contract; canonical geometric identification of the raw seam collar with F2[y,z]/(y^2,z^4) unproven; Milnor algebra + exponents classical)
No authored topic assignment in this snapshot.
Read the statement, conditions and evidenceThe hard reduction: the live residual as typed interfaces
TFPT — Introduction and reading guide
Original identifier and classification
E8.DIRECTED.READOUT.01Proven finite statement [E] (Identity, exact over Z/Q via sympy); C7 Gauss-code transform stays OPEN (rem:c7-audit); NO RH claim
No authored topic assignment in this snapshot.
Read the statement, conditions and evidenceThe Coxeter and Euler completion identity
TFPT — Introduction and reading guide
Original identifier and classification
E8.COXETER.EULER.COMPLETION.01Proven finite statement [E] (Identity, exact over Z/Q via sympy) plus Numerical Euler-product checks (mpmath, X=10^5); fence/no-go carry NO marker upgrade; NO RH claim
Topic connection recorded by an authored Atlas relation.
Read the statement, conditions and evidenceResearch Contract — SEAM.BULK4D.RECON.01 (from seam data to a 4D local quantum theory)
Research contracts
Original identifier and classification
BULK.PRIME_COMPLETION.01Open (research contract)
No authored topic assignment in this snapshot.
Read the statement, conditions and evidence