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 2026-08-01 (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.CFACTOR.01Exact [E] uniqueness/unimodularity/integrality/involutivity/factorization identities + [C] the closed-identity reading (exact sympy)
No authored topic assignment in this snapshot.
Read the statement, conditions and evidence=150 2026-08-01 (XXVIII) (the periods round lands ( v611 promoted): the analytic layer of the cover is CLASSICAL — all five basic period integrals are exact Beta values with Gamma denominators on the [formula in source] grid ( [formula in source] ); the [formula in source] rotation acts on periods with the exact characters [formula in source] ; [formula in source] exactly; and the cross-factor period ratio admits no low-degree integer relation (PSLQ null) — the two CM factors are period-independent, as the v610 splitting demands)
TFPT — Introduction and reading guide
Original identifier and classification
QGEO.LANDSCAPE.01Exact [E] characters/point-counts/census + [C] CM-theory reading and named resources (deterministic integer computations; no floats beyond the census prefilter)
No authored topic assignment in this snapshot.
Read the statement, conditions and evidence=150 2026-08-01 (XXX) (the canonical period normalization lands ( v613 promoted) — THE ANALYTIC BRIDGE CLOSES: the quarter rotation acts DECK-FREE on the four branch segments (all [formula in source] wrap factors exactly [formula in source] ), and the exact dictionary is [formula in source] — [formula in source] EXACTLY, explaining [formula in source] structurally, with the deck power unique; the period rows (hol [formula in source] , hol [formula in source] , antihol [formula in source] ) realize the rotation eigenframe; the Hodge weights are explicit Gamma monomials ( [formula in source] , complex Beta formula); and [formula in source] PER CHARACTER: the compiler polarization is MINUS the analytic Hodge form — Riemann–Hodge positivity realized, v612's named step B5 executed)
TFPT — Introduction and reading guide
Original identifier and classification
QGEO.PERIODS.01Exact [E] symbolic Beta identities + 40-digit certificates + PSLQ-null consistency + [C] the period-dictionary reading
No authored topic assignment in this snapshot.
Read the statement, conditions and evidence=150 2026-08-01 (XXX) (the canonical period normalization lands ( v613 promoted) — THE ANALYTIC BRIDGE CLOSES: the quarter rotation acts DECK-FREE on the four branch segments (all [formula in source] wrap factors exactly [formula in source] ), and the exact dictionary is [formula in source] — [formula in source] EXACTLY, explaining [formula in source] structurally, with the deck power unique; the period rows (hol [formula in source] , hol [formula in source] , antihol [formula in source] ) realize the rotation eigenframe; the Hodge weights are explicit Gamma monomials ( [formula in source] , complex Beta formula); and [formula in source] PER CHARACTER: the compiler polarization is MINUS the analytic Hodge form — Riemann–Hodge positivity realized, v612's named step B5 executed)
TFPT — Introduction and reading guide
Original identifier and classification
QGEO.POLFRAME.01Exact [E] spectrum/diagonalization/signature identities + [C] the bridge reading (exact sympy)
No authored topic assignment in this snapshot.
Read the statement, conditions and evidence=150 2026-08-01 (XXXI) (the Gauss–Manin transport round lands ( v614 promoted) — THE DECK STEP IS THE BOUNDARY MONODROMY: transporting the segment cycles along the rigid quarter-rotation loop, the discriminant [formula in source] winds ONCE around [formula in source] and the transported periods factorize EXACTLY, [formula in source] ; at [formula in source] the deck factor is [formula in source] on EVERY sheet (the exponent [formula in source] forced by the puncture count); the canonical transport matrix in the segment basis is EXACTLY [formula in source] — the v613 dictionary [formula in source] is CANONICAL, no conjugator freedom left, and [formula in source] re-derives [formula in source] ; v613's residue F1 closed at the transport level)
TFPT — Introduction and reading guide
Original identifier and classification
QGEO.PERNORM.01Exact [E] dictionary/uniqueness identities + 40-digit certificates + Gamma-monomial closed forms + [C] the fork-basis residue (sympy + mpmath)
No authored topic assignment in this snapshot.
Read the statement, conditions and evidence=150 2026-08-01 (XXXI) (the Gauss–Manin transport round lands ( v614 promoted) — THE DECK STEP IS THE BOUNDARY MONODROMY: transporting the segment cycles along the rigid quarter-rotation loop, the discriminant [formula in source] winds ONCE around [formula in source] and the transported periods factorize EXACTLY, [formula in source] ; at [formula in source] the deck factor is [formula in source] on EVERY sheet (the exponent [formula in source] forced by the puncture count); the canonical transport matrix in the segment basis is EXACTLY [formula in source] — the v613 dictionary [formula in source] is CANONICAL, no conjugator freedom left, and [formula in source] re-derives [formula in source] ; v613's residue F1 closed at the transport level)
TFPT — Introduction and reading guide
Original identifier and classification
QGEO.TRANSPORT.01Exact [E] factorization/deck/uniqueness identities + 25-digit transport certificates + [C] the boundary-monodromy reading (sympy + mpmath)
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.TOY.01Float-track certificates (tolerances declared) + exact combinatorics + [C] toy fence (numpy/sympy)
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
WOIT.SU2.KIN.01Exact [E] operator identities (sympy) + [C] the kinematic fence
No authored topic assignment in this snapshot.
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 evidenceGroup-theoretic audits (optional)
input 5 tfpt 3 e8 audit bootstrap
Original identifier and classification
WOIT.GAMMA.SEMI.01Float-track certificates (declared tolerances) + exact Clifford combinatorics + [C] toy fence
No authored topic assignment in this snapshot.
Read the statement, conditions and evidence=150 2026-08-01 (XXXVI) (the covered seam lands ( v623 promoted) — the lattice skeleton of the covering-level identification: the seam lifted to the [formula in source] -cover is ONE 48-site NS circle for the uniform weights (the alternating pair DISCONNECTS it — a new independent kill), the lifted clock has EXACT ORDER 12 with [formula in source] deck ( [formula in source] as lattice combinatorics), the v622 kernel identity generalizes verbatim to [formula in source] , and the deck-character mode grid is the 12-grid ( [formula in source] ) with the untwisted sector equal to the base seam VERBATIM and the twisted pair carrying [formula in source] on bilinears (the [formula in source] sheets); the fermionic deck lift satisfies [formula in source] (the spin double))
TFPT — Introduction and reading guide
Original identifier and classification
QGEO.SEAMID.01Exact [E] mode-sum/dictionary identities (sympy) + must-fail control + [C] the covering residue typing
No authored topic assignment in this snapshot.
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 evidenceGroup-theoretic audits (optional)
input 5 tfpt 3 e8 audit bootstrap
Original identifier and classification
EXTREV.LATTICE.01Exact [E] closure/bytecode/congruence identities + [X] the ill-posed retype + [C] conditional typing (sympy; citations web-verified)
No authored topic assignment in this snapshot.
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 evidenceGroup-theoretic audits (optional)
input 5 tfpt 3 e8 audit bootstrap
Original identifier and classification
QGEO.ORBCAS.01Exact [E] closed forms and expansions (sympy exact; 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
E8.INCIDENCE.01Exact [E] census (Fraction combinatorics) + honest kill + [C] typed observations (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
FTR.PGL2.01Exact [E] PGL2/intertwining identities + [C] typed reading (sympy exact; 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
E8.ZIQUOTIENT.01Exact [E] quotient/lattice identities + [E, KILL] typed cascade negative (Python-only per GATE.WOLFRAM.02).
No authored topic assignment in this snapshot.
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 evidence