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.
Search the complete foundation register
783 matching active claims. Showing at most 20 per page. Original statement text and long numerical details open within each claim.
The 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
FLAV.NU.TEXTURE.MECHANISM.01Open (research contract; both structural nulls are binding constraints; NUSCALE.05/.06 unmoved) | Round-3 v1024 provides a finite parent-internal witness [E/N]; the physical texture/scale remains Open [O].
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
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
GRAV.WEINBERG.WITTEN.01Open (research contract; binding firewall before any spin-2 marker move; no script)
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 evidenceTEL-B reduction (2026-09-04)
Research contracts
Original identifier and classification
SEAM.MMST.TELB.C1C2A.01Proven subclaims [E]: C1 native interval certificate plus analytic axis bound; C2a analytic all-even-N theorem plus outward constant certificate. Parent contracts remain Open [O].
No authored topic assignment in this snapshot.
Read the statement, conditions and evidenceTEL-B reduction (2026-09-04)
Research contracts
Original identifier and classification
SEAM.MMST.TELB.ROUND3.01Mixed: TV interval-certified [E]; C2b scalar reduction is analytic proof plus Arb arithmetic [E]; old ALG2 implication refuted [X]; CF/DG, ALG-EXH, MMST and TOE remain Open [O].
No authored topic assignment in this snapshot.
Read the statement, conditions and evidenceResearch Contract — CHIRAL4D.MIRROR.DET16.01 (DET16 rank-one projector, finite cluster)
Research contracts
Original identifier and classification
CHIRAL4D.MIRROR.DFILTER.BLOCK.01Proven finite block identity [E]; GW/gauge reading conditional [C]; DET16 [C], NOMIRROR [O], T4 and TOE [O] unchanged.
No authored topic assignment in this snapshot.
Read the statement, conditions and evidenceNeutrinos
Standard Model and flavor structure
Original identifier and classification
FLAV.NU.PARENT.INTERTWINER.01Proven finite witness [E/N]; physical neutrino texture and scale remain Open [O].
No authored topic assignment in this snapshot.
Read the statement, conditions and evidenceResearch Contract — GRAV.SPIN2.EMERGENCE.01 (massless transversal spin-2 from the same spectral determinant)
Research contracts
Original identifier and classification
GRAV.PARENT.GAP.NO_GO.01Proven finite no-go/boundary [E]; massless spin-2 emergence, Ward identities and universal coupling remain Open [O].
No authored topic assignment in this snapshot.
Read the statement, conditions and evidenceResearch Contract — FTRANSFER.SK.RHO0.01 (Schwinger–Keldysh completion: cosmological transfers need [formula in source] )
Research contracts
Original identifier and classification
FTRANSFER.PARENT.Z5CAP.01Finite candidate and exact algebraic boundaries [E/N]; global rho_0, Gauss-projected Weyl realization and unique SK functional remain Open [O].
No authored topic assignment in this snapshot.
Read the statement, conditions and evidenceT2: uniform relaxed TEL-B theorem.
Research contracts
Original identifier and classification
SEAM.MMST.TELB.NORM.01Identity (analytic theorem with native interval certificate; fixed regulator)
No authored topic assignment in this snapshot.
Read the statement, conditions and evidenceT3/T4: canonical DET excitations and the signed wall.
Research contracts
Original identifier and classification
CHIRAL4D.MIRROR.SIGNED.CAR.01Identity (conditional Hamiltonian-class and exact finite regression)
No authored topic assignment in this snapshot.
Read the statement, conditions and evidenceT6/T8: full Gauss counts, internal cap and selection rules.
Research contracts
Original identifier and classification
PARENT.GAUSS.D4.ROUND4.01Identity (exact finite projected counts and conditional symmetry obstructions)
No authored topic assignment in this snapshot.
Read the statement, conditions and evidenceT7: local constraints and zero-mode removal.
Research contracts
Original identifier and classification
GRAV.SPIN2.LOCAL.CONSTRAINT.01Identity (quadratic target only; global zero-mode prescription required)
No authored topic assignment in this snapshot.
Read the statement, conditions and evidenceALG2: sector generation and conditional uniform section.
Research contracts
Original identifier and classification
SEAM.MMST.ALG2.FRAME.01Identity (conditional finite-algebra and uniform-frame bridge)
No authored topic assignment in this snapshot.
Read the statement, conditions and evidenceThe specified free curvature field target
Frontier and open physical interfaces
Original identifier and classification
GRAV.FREE.CURVATURE.FOCK.01Identity in declared zero-mean free target [E]; TFPT identification [O]
Topic connection recorded by an authored Atlas relation.
Read the statement, conditions and evidencePositive transverse curvature on the null cone
Frontier and open physical interfaces
Original identifier and classification
GRAV.FREE.CURVATURE.COVARIANT.01Identity in declared free continuum target [E]; TFPT identification [O]
Topic connection recorded by an authored Atlas relation.
Read the statement, conditions and evidence