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.
Start with the published construction
The foundations include the carrier, E₈, flavour, alpha, quantum structure, gravity and cosmology. Open an area to follow its registered statements into the papers and verification sources.
- Seam, origin and declared inputsBoundary inputs, the common anchor and source selection.
- Carrier, families and E8 closureThe particle carrier, lattice matching and E₈ closure.
- Interlocking clocksFinite clock actions, their couplings and dynamics.
- Standard Model and flavorParticle charges, source mass ratios and mixing.
- Fine-structure constantThe response equation, its root and physical interpretation.
- Quantum and boundary structureCodes, finite quantum geometry and field structure.
- GravityEntanglement, geometric flow and gravity interfaces.
- CosmologyInflation, baryon density and vacuum energy readouts.
- Tests and predictionsWhat the formal and numerical checks establish.
- UniversalraumA common process, state and observable source.
- MetrologyHow dimensionless relations meet physical units.
- SpacetimeFrom internal structure to local physical spacetime.
- Process and compilationCompiler operations, responses and their assumptions.
These are authored navigation links. The complete register contains 783 active claims; 723 do not yet have an authored topic assignment and remain searchable.
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783 matching active claims. Showing at most 20 per page. Original statement text and long numerical details open within each claim.
=150 2026-07-31 (III) (the residual reconstruction bit located and given a canonical witness: the ladder self-consistency selects the compiler [formula in source] uniquely (SELECTOR-FOUND); the split geometry excluded; Priority 2 sharpened + v568 promoted + ledger/paper/diary/website sync)
TFPT — Introduction and reading guide
Original identifier and classification
DIAMOND.BIT.SELECT.01Identity [E] (exact integer/symbolic algebra -- Hermite/Smith lattice comparison, the symbolic dominant-mode identity, the uniqueness census on the 28-member class, the split-complement solve, the candidate tests) + [C] (the anchored ladder selector as candidate canonical selection; its physical justification open) + [O] (the selection mechanism; the F3[V]-character question; Stage B); verdict SELECTOR-FOUND; no marker moves
No authored topic assignment in this snapshot.
Read the statement, conditions and evidence=150 2026-07-31 (XI) (the continuous half of the cross-ratio check executed and closed: UNIFLOW-DEGENERATE ( v575 promoted) — the native exports are forced degenerate by the single-flow theorem, so the continuous half closes onto v425; both halves of the preregistered check are now executed)
TFPT — Introduction and reading guide
Original identifier and classification
FTR.CRDISC.01Identity [E] + typed boundary [C] (exact symbolic identities on compiler kernels; the continuous-solver half open)
No authored topic assignment in this snapshot.
Read the statement, conditions and evidence=150 2026-07-31 (XVII) (the interacting RP route of the alignment bit, executed: EXT-SOURCE COUPLING SEPARATES THE 81-TWINS DIRECTIONALLY IN THE UNIT BOX ( v584 promoted) — exact rational flip thresholds with the v572 pencil factors as numerators; positive coupling [formula in source] heals exactly the compiler twin, the alt twin is rigid; response pole on the golden polynomial)
TFPT — Introduction and reading guide
Original identifier and classification
DIAMOND.BIT.RPFORM.01Identity [E] (exact integral/spectral computations; honest negative on the kinematic selection; RP-slot open)
No authored topic assignment in this snapshot.
Read the statement, conditions and evidence=150 2026-08-01 (IV) (the sheet involution exists unconditionally ( v590 promoted): the integral [formula in source] -commuting involutions are exactly [formula in source] (rigidity, both twins); the v574 type theorem [formula in source] seam reversal [formula in source] zero-mode fixing single out the explicit [formula in source] with exact [formula in source] -signature uniquely — GATE.QGEO.01's involution-existence input relocates to DERIVED)
TFPT — Introduction and reading guide
Original identifier and classification
QGEO.WINDING.SELF.01Identity [E] + typed gate [C] (rank theorem symbolic; enumerations at declared bound; the remaining gate named)
No authored topic assignment in this snapshot.
Read the statement, conditions and evidence=150 2026-07-31 (XI) (the continuous half of the cross-ratio check executed and closed: UNIFLOW-DEGENERATE ( v575 promoted) — the native exports are forced degenerate by the single-flow theorem, so the continuous half closes onto v425; both halves of the preregistered check are now executed)
TFPT — Introduction and reading guide
Original identifier and classification
FTR.CRCONT.01Identity [E] + typed closure [C] (exports recomputed; degeneracy theorem exact; the closure onto v425 typed)
No authored topic assignment in this snapshot.
Read the statement, conditions and evidenceResearch contracts
Research contracts
Original identifier and classification
FTR.JETS.01Identity [E] + typed closure [C] (exact trajectories and Schwarzians; the joint test external)
No authored topic assignment in this snapshot.
Read the statement, conditions and evidenceGroup-theoretic audits (optional)
E8 audit and bootstrap
Original identifier and classification
DIAMOND.BIT.EXTSOURCE.01Exact [E] + typed consistency [C] (thresholds closed rational; verified numerically; response level only)
No authored topic assignment in this snapshot.
Read the statement, conditions and evidenceGroup-theoretic audits (optional)
E8 audit and bootstrap
Original identifier and classification
QGEO.INVOL.01Exact [E] + typed relocation [C] (exact sympy; demands declared; continuum derivation open)
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Read the statement, conditions and evidenceGroup-theoretic audits (optional)
E8 audit and bootstrap
Original identifier and classification
QGEO.COVER.01Exact [E] fingerprints + typed candidate [C] (Burau convention validated; Q-identification open)
No authored topic assignment in this snapshot.
Read the statement, conditions and evidenceGroup-theoretic audits (optional)
E8 audit and bootstrap
Original identifier and classification
QGEO.DICT.01Exact [E] entries + quantified negatives (numeric prefilter, symbolic confirmation)
No authored topic assignment in this snapshot.
Read the statement, conditions and evidenceGroup-theoretic audits (optional)
E8 audit and bootstrap
Original identifier and classification
QGEO.REAL.01Exact [E] existence/uniqueness/char identities + [X] quantified joint negative + [C] the TFPT readings (exact sympy; numeric prefilter with symbolic confirmation for the scan)
No authored topic assignment in this snapshot.
Read the statement, conditions and evidenceGroup-theoretic audits (optional)
E8 audit and bootstrap
Original identifier and classification
QGEO.EMBED.01Exact [E] existence realization (integrality, conjugation, saturation index all exact sympy) + typed open canonicity [O]; NO marker moves
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Read the statement, conditions and evidenceGroup-theoretic audits (optional)
E8 audit and bootstrap
Original identifier and classification
QGEO.CANON.01Exact [E] equivariance/duality/Klein identities + [C] typed opens (exact sympy; one numeric inertia count of an exact hermitian matrix)
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Read the statement, conditions and evidenceGroup-theoretic audits (optional)
E8 audit and bootstrap
Original identifier and classification
QGEO.DUALFORMS.01Exact [E] duality/dictionary/positivity identities + [X/O] quantified negatives and typed opens (exact sympy; two numeric inertia counts of exact matrices) + Lean certificate FORM.QGEO.04
No authored topic assignment in this snapshot.
Read the statement, conditions and evidenceGroup-theoretic audits (optional)
E8 audit and bootstrap
Original identifier and classification
QGEO.SEAMMARKS.01Exact [E] seam/infinity/witness identities + [X] quantified translator negatives + [C] typed per-mark framing (exact sympy)
No authored topic assignment in this snapshot.
Read the statement, conditions and evidenceGroup-theoretic audits (optional)
E8 audit and bootstrap
Original identifier and classification
QGEO.EQORDER.01Exact [E] anti-isometry/order/localization identities + [C] typed localization reading + [X] quantified translator negatives (exact sympy; Smith normal forms over Z)
No authored topic assignment in this snapshot.
Read the statement, conditions and evidence=150 2026-08-01 (XXVI) (the translator factorization lands ( v609 promoted): the geometric identity of [formula in source] is CLOSED — the mirror intertwiner [formula in source] ( [formula in source] ) is unique, unimodular ( [formula in source] ), [formula in source] -integral and [formula in source] -involutive ( [formula in source] exactly), and the v605 element factorizes exactly as [formula in source] with [formula in source] : [formula in source] — all three v605 residuals are now resolved (seam reversal v603, zero-mode rule v607, [formula in source] -identity v609))
TFPT — Introduction and reading guide
Original identifier and classification
QGEO.TRANSLATOR.01Exact [E] translator/bridge/chain/duality identities + [C] typed opens (exact sympy; Smith transforms over Z; Lean addendum green)
No authored topic assignment in this snapshot.
Read the statement, conditions and evidence=150 2026-08-01 (XXVI) (the translator factorization lands ( v609 promoted): the geometric identity of [formula in source] is CLOSED — the mirror intertwiner [formula in source] ( [formula in source] ) is unique, unimodular ( [formula in source] ), [formula in source] -integral and [formula in source] -involutive ( [formula in source] exactly), and the v605 element factorizes exactly as [formula in source] with [formula in source] : [formula in source] — all three v605 residuals are now resolved (seam reversal v603, zero-mode rule v607, [formula in source] -identity v609))
TFPT — Introduction and reading guide
Original identifier and classification
QGEO.MODESEP.01Exact [E] torsion/separation identities + [C] typed frame caveat + [X] honest arithmetic negative (exact sympy; Smith transforms over Z)
No authored topic assignment in this snapshot.
Read the statement, conditions and evidence=150 2026-08-01 (XXIV) (the selection rule lands ( v607 promoted): the infinity torsion is a genuine [formula in source] space, the deck rotation acts with char [formula in source] mod [formula in source] — EXACTLY ONE projective eigenline, and it IS the top mode; the three modes carry mutually exclusive canonical labels (seam [formula in source] [formula in source] -real, top [formula in source] deck-eigen, zero [formula in source] the only unlabeled) and [formula in source] flips exactly the labeled pair: BOTH v590 demands expressed through cover structure (typed reading; the gate residual is the continuum derivation))
TFPT — Introduction and reading guide
Original identifier and classification
QGEO.SELRULE.01Exact [E] F_3/rigidity/labeling identities + [C] typed selection reading (exact sympy / F_3 arithmetic; Smith transforms over Z)
No authored topic assignment in this snapshot.
Read the statement, conditions and evidence=150 2026-08-01 (XXXII) (the interacting gamma slice lands at toy level ( v615 promoted): the gamma battery executed ON the RP-surviving interaction class (the alignment bit [formula in source] , positive coupling, v534) — THE INTERACTING MIRROR FLIP: at the forced twist [formula in source] the mirror state's odd sector is STRICTLY NEGATIVE DEFINITE on every cut and every coupling [formula in source] (bounded away from zero: kill test (3) cannot fire on the surviving class — v608 upgraded from [formula in source] to the full grid); the mark transport exists interacting (kill test (7) does not fire); the odd transfer spectrum stays multiplicity-free; and the dead member has no RP home — the dynamical bit selection and the chirality data CO-LOCATE on the same member)
TFPT — Introduction and reading guide
Original identifier and classification
WOIT.GAMMA.FREE.01Exact [E] sector/spectrum/incidence statements on the explicit v524 net + [C] the gamma reading (free slice; A_hol untouched)
No authored topic assignment in this snapshot.
Read the statement, conditions and evidence