Engine 1 — discrete closure
From the five-slot carrier: the D₅ half-spinor, the family geometry A₃ = ℙ¹∖μ₄, the μ₄ glue to E₈, and the Standard-Model packet — N_fam = 3, Ω_adm = 48, b₁ = 41/10, and the residue matrix R with det 8.
Introduction · Reading guide
TFPT in one map.
Two axioms, one discrete compiler, the Standard Model.
The entry document for the TFPT 5.1 set. It does not introduce new physics — it is the reading guide. Its purpose is to state what TFPT claims, what it does not claim, how the compiler closure is organized, and where each load-bearing argument is isolated in the document set — every claim graded and resolving to a single machine-checked ledger.
The compiler closure (one-line claim)
Front-box: inputs, contribution, exclusions, falsification surface
Inputs
The two axioms {c₃ = 1/(8π), g_car = 5}. Everything else — the gauge group, the constants, the scale grammar — is a consequence.
Contribution
The compiler closure, the two-engine picture, the dependency DAG, the proof ledger, and the live experimental tests — stated in one place.
Not introduced here
No new physics. The load-bearing derivations — the E₈ glue, the SM packet, the masses, the gravity sector — live in the companion documents.
Falsification or audit surface
Fails as a guide if it misstates the dependency order, if a status marker disagrees with the ledger, or if a claim is promoted past the grade its companion document carries.
What TFPT claims
One compiler, not a list of fits
The introduction makes two things explicit: what TFPT does claim at the compiler level, and what it explicitly does not promote past its grade. The split is what makes the falsification surface auditable.
Claimed at the primitive level
- TFPT is a discrete compiler with two inputs: the seam constant c₃ = 1/(8π) and the five-slot carrier g_car = 5. Nothing else is inserted by hand.
- The carrier gives D₅, the family geometry gives A₃, and the μ₄ glue closes E₈ = (D₅ ⊕ A₃) + μ₄ as a lattice theorem — 240 = 16·5·3, 248 = 240 + 8 are carrier traces.
- α⁻¹ = 137.0359992168 is the unique root of a parameter-free cubic (existence + uniqueness proved), and the flavor matrix, masses and θ₁₂ = 1/3 − φ₀/2 follow from one φ₀-ladder.
- The bootstrap loop re-derives the inputs: g_car = 5 is forced three ways and the 8 in c₃ equals rank E₈ — the discrete core is overdetermined, with only π irreducible.
Not claimed at this level
- E₈ is the unimodular audit/compiler hull, not an unbroken physical gauge group — so the no-go results against literal E₈ world-formulas do not apply.
- The dimensionful EW/QCD masses (m_W, m_Z, m_H, sin²θ_W, α_s) sit on the RG scheme layer; the absolute quark amplitude scale reduces to the U_point anchor.
- The frontier items — η_B, m_p/m_e, Koide, dark matter, full quantum gravity — are honest handles, not forced compiler powers.
- No strict physical TOE is certified: the ambient quantum-gravity measure (G6) remains the open completion target.
The two axioms
Everything is generated from the seam constant and the five-slot carrier. They are not even independent: both are elementary symmetric polynomials of the single anchor a = (1,1,2), so the inputs collapse to the anchor plus the lone continuous primitive π.
P1 — seam constant
P2 — five-slot carrier
The two engines
Discrete closure, boundary dressing, bootstrap
Read from the two axioms, the theory factorises into exactly two engines — a discrete closure from g_car and a boundary dressing from c₃ — and the bootstrap loop that feeds the E₈ closure back to fix the inputs.
Engine 2 — boundary dressing
From the seam constant: the seed u = φ₀, the electromagnetic fixed point α⁻¹, the Einstein normaliser ξ, and the exponential scale grammar 1 : 5 : 10 that gives v_EW, H₀ and Λ. Gravity is this engine's geometry channel.
The bootstrap loop
The E₈ closure feeds back as an internal consistency check: g_car = 5 is forced three ways (rank-fill, Coxeter-match, integer-glue), and the 8 in c₃ equals rank E₈ = h(D₅) = φ(30) — recovered independently. The bootstrap overdetermines the discrete core; only π stays irreducible.
Status discipline
The status matrix
Every layer of the dependency DAG carries its own grade — exact identity, lattice theorem, numerical fixed point, conditional, or open. The single source of truth is the machine-checked status ledger; if the text and the ledger ever disagree, the ledger wins.
LayerStatus languageToneWhere handled
- Two axioms {c₃, g_car}Declared inputs — c₃ Gauss–Bonnet-hardenable, P2 algebra Lean-formalised[O]Doc 1
- E₈ glue D₅ ⊕ A₃ + μ₄Lattice theorem — common discriminant ℤ₄, glue norms 5/4 + 3/4 = 2[E]Doc 1
- Carrier traces 240, 248, b₁, det RExact identities read off the carrier and the residue matrix[E]Docs 1–2
- EM fixed point & flavor anglesNumerical fixed points — α⁻¹ = 137.0359992, sin²θ₁₂, sin²θ₁₃[E]Docs 1–2
- Masses, inflation, baryonsConditional — the φ₀-ladder, the R² scalaron, Ω_b and η_B[C]Docs 2, 4
- Frontier itemsHonest handles — Koide, m_p/m_e, dark matter, full quantum gravity[C]Doc 4
- Open interfaces v_geo, G_net, F_transferNumbered research contracts — the scale anchor, the metric inclusion, and the transfer functor[O]Doc 7
Document map
Four core documents plus three companions
The reviewer path is the architecture and the two axioms (Doc 1), the E₈ glue and the α fixed point (Doc 1), the Standard Model (Doc 2), the E₈ audit and bootstrap (Doc 3), and the honest frontier (Doc 4). Appendix H (horizon), the Origin Theory synthesis, and the research contracts sit alongside.
Doc 1Compiler core
Architecture and the E₈ Compiler
The two axioms, the derivation map, and the D₅ × A₃ → E₈ construction
Doc 2Compiler core
The Standard Model from the Compiler
The φ₀-ladder, flavor from parabolic transport, and the worked closures
Doc 3E8 audit & bootstrap
E₈ Audit, Cascade Bridge and Bootstrap
The seven E₈ slices as an audit raster, the cascade spine, and the Möbius loop
Doc 4Honest frontier
Frontier Items
η_B, m_p/m_e, Koide, dark matter and quantum gravity — honest status
Doc 5Adversarial audit
Red Team — The Adversarial Audit
Targets A–E: attacking the five load-bearing reductions at their weakest transitions
Doc 6Appendix H — reframe
Appendix H — The Horizon Unit System
One seam constant c₃ = 1/(8π) as the universal horizon thermal code
Doc 7Origin synthesis
Origin Theory
The seam as a horizon, the cyclic compiler hull, and the parameter-free attractor
Doc 8Open research gates
Research Contracts for the Remaining Interfaces
v_geo · G_net · F_transfer — the live residual as numbered contracts
Reading order
Two paths through the same set
The dependency order of the four core documents is rigid (1 → 2 → 3 → 4). The recommended reading order starts from the introduction and adds the three companions — Appendix H, the Origin Theory synthesis, and the research contracts — without breaking the chain.
Recommended public order
- 0Doc 0 — IntroductionReading guide & status assessment
- 1Doc 1 — Architecture & E₈Two axioms, the glue, α⁻¹
- 2Doc 2 — Standard ModelThe φ₀-ladder & flavor matrix
- 3Doc 3 — E₈ audit & bootstrapAudit raster, the loop
- 4Doc 4 — FrontierHonest open items
- 6Doc 6 — Origin TheoryWhy no free number remains
- 7Doc 7 — Research contractsThe open interfaces v_geo, G_net, F_transfer
Mathematical dependency order
- 1Doc 1 — Architecture: the two axioms, D₅ × A₃ → E₈, α⁻¹
- 2Doc 2 — Standard Model: the φ₀-ladder, flavor matrix, θ₁₂
- 3Doc 3 — E₈ audit raster, cascade bridge, Möbius bootstrap
- 4Doc 4 — Frontier: η_B, m_p/m_e, Koide, dark matter, QG
- 5Doc 5 — Appendix H — horizon unit system (reframe)
- 6Doc 6 — Origin Theory — the gapped unique attractor
Read the full reading guide.
The introduction is the entry document of the TFPT 5.1 set. It states the compiler closure, the two-engine picture, the dependency DAG, the proof ledger, and the live experimental tests — with every claim graded and resolving to the ledger.
- · Stefan Hamann
- · Alessandro Rizzo
- · TFPT 5.1 document set