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
114 matching active claims. Showing at most 20 per page. Original statement text and long numerical details open within each claim.
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 evidenceCertifiability and recommended order
Research contracts
Original identifier and classification
FTRANSFER.CLOCKS.01Executed preregistered search target (frozen 2026-08-04 [X]; executed + promoted 2026-08-05, v777): the K1 kill fired exactly as the frozen prior expected (NO-COMMON-CONNECTION); the fibered-groupoid refinement carries; the four observables stay [C]/[O]; no marker move (Python-only per GATE.WOLFRAM.02).
No authored topic assignment in this snapshot.
Read the statement, conditions and evidenceGroup-theoretic audits (optional)
input 5 tfpt 3 e8 audit bootstrap
Original identifier and classification
QGEO.FANODISC7.01Exact [E] machinery; the preregistered break fires -- honest structural negative, correlation typed decorative (Python-only per GATE.WOLFRAM.02).
No authored topic assignment in this snapshot.
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 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 — PRED.JOINTLIKELIHOOD.01 (from hit-counting to overdetermined relations)
Research contracts
Original identifier and classification
PRED.JOINTLIKELIHOOD.01Open (statistics-construction contract; v1 executed [N]; promotion conditions typed)
No authored topic assignment in this snapshot.
Read the statement, conditions and evidenceResearch Contract 1 — [formula in source]
tfpt research contracts
Original identifier and classification
SEAM.EQUIV.SKELETON.01Exact [E] (executable skeleton; fine types Lattice/Numerical for the collar battery, Identity for the S0 mechanism gates)
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 Contract — SEAM.DETLINE.UNIFICATION.01 (the determinant-line unification hypothesis)
Research contracts
Original identifier and classification
SEAM.DETLINE.UNIFICATION.01Open [O] + finite bulk-edge shadow [E] (2+1D/1D QWZ; continuum Bismut-Freed stays Open)
No authored topic assignment in this snapshot.
Read the statement, conditions and evidenceThe common generating functional contract
Research contracts
Original identifier and classification
FTRANSFER.GENERATING.01Open (research contract; finite W[J] derivative identities + transduction shadow executed at 1+1D Z6; no upgrade permitted)
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
GAUGE.DETLINE.FIXPOINT.01Open (research contract; naive grammar extension excluded [E]; genuinely nonabelian structure required -- typed; alpha_s(M_Z) currently an external input)
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 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 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 evidence