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 assumptions needed for geometric modular flow
Research contracts
Original identifier and classification
GRAV.NONCIRCULAR.01Firewall (standing discipline rule, in force; audit census recorded)
Topic connection recorded by an authored Atlas relation.
Read the statement, conditions and evidenceFrom internal structure to an observable response
Research contracts
Original identifier and classification
OBS.TRANSDUCTION.01Contract (principle registered; finite W[J] transduction shadow executed; per-bundle proofs stay Open)
Topic connection recorded by an authored Atlas relation.
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 — WOIT.OS.TWISTOR.01 (the Osterwalder–Schrader twistor bridge)
Research contracts
Original identifier and classification
SEAM.INT.ODDSPLIT.01Measured/Exact [E] (toy level; JP sufficient-only; v529 fence inherited); no marker moves
No authored topic assignment in this snapshot.
Read the statement, conditions and evidenceResearch Contract — WOIT.OS.TWISTOR.01 (the Osterwalder–Schrader twistor bridge)
Research contracts
Original identifier and classification
SEAM.INT.OSAVOID.01Measured [E] (toy level; v529 fence inherited); 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
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 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 contracts
Research contracts
Original identifier and classification
DIMENSION.SELECTOR.4D.01Conditional [C] (exact selector under the named axiom set A1-A4; axiom provenance from the compiler open)
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 evidenceFull quantum gravity — induced from the boundary kernel
Frontier and open physical interfaces
Original identifier and classification
TFPT4D.LATTICE.ACTION.01Open (research contract; T1-T7 harness + Euclidean T2 kill + Hamiltonian-route T2 clearance executed at toy level; no gate closed)
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 lattice fundamental interpretation
Frontier and open physical interfaces
Original identifier and classification
QFT4D.LATTICE.FUNDAMENTAL.01Decision (registered route/typing; no [E] claim, no marker move; QFT4D.OS.RECON.01 unchanged as the math program)
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 common source contract for spin two
TFPT — Introduction and reading guide
Original identifier and classification
GRAV.SPIN2.EMERGENCE.01Open (research contract; quadratic witnesses [E] + quadratic Hamiltonian half executed; content pinned on the untruncated form factor; Einstein eq stays a downstream/conditional readout) | Round-3 v1024 supplies finite gap/TT locality no-gos [E]; spin-2 emergence remains Open [O].
Topic connection recorded by an authored Atlas relation.
Read the statement, conditions and evidenceThe physical initial state contract
TFPT — Introduction and reading guide
Original identifier and classification
FTRANSFER.SK.RHO0.01Open (research contract; mechanism executed [N]/[C]; FTRANSFER.GENERATING.01 covers equilibrium only) | Round-3 v1024 gives a finite internal candidate and algebraic boundaries [E/N]; global rho_0 and SK uniqueness remain Open [O].
Topic connection recorded by an authored Atlas relation.
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 evidenceNeutrinos
Standard Model and flavor structure
Original identifier and classification
FLAV.NUSCALE.06Candidate [C]/[N] + mechanism [O] (pentagon-class misalignment; no seesaw closure; FLAV.NUSCALE.05 unmoved)
No authored topic assignment in this snapshot.
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 evidence