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.
Quantum and boundary structure
32 authored claim references in the foundation record. The membership comes from explicit Atlas authoring relations.
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32 matching active claims. Showing at most 20 per page. Original statement text and long numerical details open within each claim.
The explicit D₅ and A₃ lattice construction of E₈
Architecture, E8 and the electromagnetic fixed point
Original identifier and classification
E8.GLU.01Lattice
Topic connection recorded by an authored Atlas relation.
Read the statement, conditions and evidenceThe ambient gravitational measure problem
TFPT — Introduction and reading guide
Original identifier and classification
QG.AMB.01Open (decoupled general QG; non-TFPT)
Topic connection recorded by an authored Atlas relation.
Read the statement, conditions and evidenceThe conditional entanglement route to linearized gravity
Research contracts
Original identifier and classification
GRAV.ENTROPY.EQUILIBRIUM.01Entanglement-equilibrium gravity [E]/[C]/[O] (parameter-free linearised Einstein 8pi=1/c3; thermo=geo coincidence via |mu4|=|Z2|chi; J3 assembled; entropy density atom-fixed; residual = nonlinear + v_geo)
Topic connection recorded by an authored Atlas relation.
Read the statement, conditions and evidenceThe seam and horizon correspondence
Origin Theory
Original identifier and classification
SEAM.THEOREM.01Identity [I] + open theorem [A]
Topic connection recorded by an authored Atlas relation.
Read the statement, conditions and evidenceThe dimensionless seam area coefficient
Origin Theory
Original identifier and classification
SEAM.KHALF.01Identity [I] + Lattice/topology [L] (coefficient) + [A] (absolute scale only)
Topic connection recorded by an authored Atlas relation.
Read the statement, conditions and evidenceRealizing the seam as a physical boundary
Origin Theory
Original identifier and classification
QGEO.REALIZE.01Physical [C] (seam-side identification) + [O] (open realisation)
Topic connection recorded by an authored Atlas relation.
Read the statement, conditions and evidenceThe Coxeter clock and its quarter action
Origin Theory
Original identifier and classification
COX.CLOCK.01Identity (exact)
Topic connection recorded by an authored Atlas relation.
Read the statement, conditions and evidenceThe modular spectral closure assembly
Research contracts
Original identifier and classification
QFT.MSC.01Numerical (assembly certificate) [E]/[C]/[O]
Topic connection recorded by an authored Atlas relation.
Read the statement, conditions and evidenceThe seam realization contract
TFPT — Introduction and reading guide
Original identifier and classification
SEAM.EQUIV.01Contract [E] (typing + firewall + taxonomy) + [O] (the named theorem)
Topic connection recorded by an authored Atlas relation.
Read the statement, conditions and evidenceWhen modular flow has a geometric interpretation
Origin Theory
Original identifier and classification
QGEO.BW.01Reduction [E]/[C]/[O] (BW geometric modular flow)
Topic connection recorded by an authored Atlas relation.
Read the statement, conditions and evidenceThe formally encoded scalar spectral gap
Origin Theory
Original identifier and classification
FORM.SPECTRALGAP.01Formal [F] (Lean kernel; no extra axioms) -- the scalar core + the finite-dimensional diagonalisable case of the spectral-gap meta-theorem (v383): gap => unique attractor + geometric decay => parameter-free
Topic connection recorded by an authored Atlas relation.
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 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 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 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 evidenceWhat the code interpretation preserves and loses
input 5 tfpt 3 e8 audit bootstrap
Original identifier and classification
E8.CODESEM.01Exact [E] code/dictionary identities + [E, kill] the 30-census control (exact arithmetic; Python-only per GATE.WOLFRAM.02).
Topic connection recorded by an authored Atlas relation.
Read the statement, conditions and evidenceThe Gaussian code and four bit information space
Architecture, E8 and the electromagnetic fixed point
Original identifier and classification
E8.GAUSSCODE.01Exact [E] SNF/census/semantics identities + [E, kill] three must-fail controls (exact arithmetic; Python-only per GATE.WOLFRAM.02).
Topic connection recorded by an authored Atlas relation.
Read the statement, conditions and evidenceThe 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 evidenceThe finite two qubit stabilizer identification
input 5 tfpt 3 e8 audit bootstrap
Original identifier and classification
E8.CLIFFORD2Q.01Exact [E] finite group/lattice identification (H1-H3) with the H4 layer honestly PARTIAL (the index bit identified as the sqrt2/Hadamard Galois bit, not J <-> -J); no marker move (Python-only per GATE.WOLFRAM.02).
Topic connection recorded by an authored Atlas relation.
Read the statement, conditions and evidence