Two numbers go in — a boundary number 1/(8π) and a five-slot carrier — and the discrete Standard-Model core, the dimensionless constants and several scale readouts come out. The dashed loop is the point: the machine reproduces the very two numbers it started from, so the discrete core is overdetermined rather than fitted.

Read from the two axioms, the theory factorises into exactly two engines: a discrete closure (from g_car = 5) that builds E₈ and the SM packet, and a boundary dressing (from c₃) that produces the seed, α⁻¹ and the scale grammar. Gravity is not a third block — it is the geometry channel of Engine 2.

TFPT 5.4 closes the discrete compiler, the algebraic SM readout, the EM fixed point, the admissible gapped IR sector and the R + R² spectral-action shadow. It does not yet certify a strict physical TOE end-to-end (the seam keystone is closed only modulo a cited published theorem). The live residual is three named interfaces: one dimensionful scale anchor v_geo [O], the metric-sector inclusion G_net (route split 2026-07-22: MMST route SEAM.EQUIV.MMST.01 [C] closed modulo cited theorems, twistor route SEAM.EQUIV.TWISTOR.01 [O], parent SEAM.EQUIV.01 [O] as an unconditional claim), and the typed runnable transfer suite F_transfer (v371–v375). The keystone's 128-spinor extension leg is now re-founded on the peer-reviewed crossed-product package (v469, Longo–Rehren/Böckenhauer/KLM), with the realisation input reduced to invariant level — SEAM.EQUIV.01 stays [O]. The historical labels (U_wall)/(G_metric)/(F_frontier) are kept only for ledger continuity.

The two axioms are not even independent: they are the elementary symmetric polynomials of the single parabolic anchor a = (1,1,2), and its power sums generate the big Lie data directly. The inputs collapse to the anchor plus the lone continuous primitive π. And a is itself half-forced: three positive integers summing to 4 admit exactly one partition, {1,1,2}, so g_car = e₂ = 5 and |Z₂| = e₃ = 2 are arithmetic corollaries of the four marks given the weight typing — machine-checked with all negative controls (v491, sharpening v53); the residual is the weight-typing postulate, and P2 stays the declared axiom. The typing itself is now hardened (v499): given the four marks, rank 3, the cusp class and unitarity (U), the Deligne canonical extension of the flavor connection has deg E = −4 (residue traces) and Mehta–Seshadri stability forces h⁰(E) = 0, so integrality (Birkhoff–Grothendieck), positivity and the sum 4 are theorems — the residual shrinks to the module identification plus (U), both [C]; and that module-identification rest is now ONE residual with the QGEO modulus rest (the order-4 clock = the Coxeter/cusp-class carrier datum; v503, QGEO.EMERGE.LIGHT.01, no marker moves). That common residual is itself reduced to ONE alignment bit — the collar deck central in the mark-D₄; the clock's ORDER is fermionically forced, U² = (−1)^F exactly (v506, SEAM.CLOCK.RIGIDITY.01, markers unchanged) — and the bit is no tautology: the deck's CLASS is derived (every mark-free collar deck is a half-period translation of the seam double), only its POSITION stays the [C] input (v507, SEAM.BIT.ORIGIN.01, markers unchanged). The freedom theorems (v510, SEAM.BIT.FREEDOM.01) type that position half as TOPOLOGY — the covering deck is free on the seam circle, the edge class is excluded — so the bit reduces to the square-modulus datum τ = i alone; and the flag-transitivity web (v512, SEAM.TAU.FLAG.01) gives that datum its sharp DISCRETE form: bare mark-transitivity is automatic for every free-circle configuration (the pair-exchanging V₄; no local jet sees the side bit), while FLAG transitivity (marks AND their two sides indistinguishable, V₄ → D₄) ⟺ τ = i — a 13-fold exact equivalence web whose negation is concretely measurable (odd-doublet split (2/π)ln cot(δ/2) ≠ 0); free OS positivity is since documented as the EIGHTH side-blind test (v521): the bit is not derivable from free RP/Θ existence and remains genuine discrete input. The bit has since survived TEN side-blind derivation attacks on that scoreboard — free RP/Θ (the eighth, v521), the exhausted Wick-computable free-plus-twist state class (the ninth, v525) and the first genuinely interacting seam toy (the tenth, v529) — and is now physically DEFINED as the twist-class choice: facets #14/#15 extend the web to 15 exact equivalences (both directions each), the flip-axis fraction is a gauge-robust order parameter (O = 1/2 at m = 4, 0 elsewhere), and its η holonomy is in principle interferometrically readable (v528, SEAM.BIT.TWISTCLASS.01; the bit remains formal input — a definition replaces no derivation, no marker moves). Since the straddle round there is also the first POSITIVE selection datum (v534, SEAM.STRADDLE.CONE.01): reflection positivity, imposed on the interacting mark family, keeps exactly ONE member alive — δ = π/2 with positive coupling, the same member that carries the twist-class order parameter (toy-level evidence for a dynamical origin, not a derivation, no marker moves). The consolidated reduction state (2026-07-23): the compiler's dimensionless inputs reduce to four marks (derived from P1-side topology), one discrete symmetry-lift bit — the twist-class choice (flag transitivity ⟺ τ = i; equivalently the clock / the CM-fixed half-period / the non-split extension class on the free seam circle) — and π — a reduction state, not an abolition of the axiom.

The compiler framing sits in the Zuse–Schmidhuber–Wolfram lineage — physics as the output of a short computation. TFPT shares three instincts with it: minimal description length as the selection principle (no load-bearing free number, only π), deterministic resource-bounded generation (a chain of exact identities in about a second, not a search over models — the spirit of Schmidhuber's Speed Prior), and compressibility as the aesthetic (choosing E₈ is choosing the icosahedron, the shortest-to-describe object). It diverges on three points: TFPT forces one program instead of a measure over all universes, its description language is algebraic (Lie/lattice/VOA) rather than Turing bit-strings, and — the load-bearing difference — it is falsifiable, freezing dated kill-tested predictions where the algorithmic-TOE lineage stays metaphysics. This is positioning, not a new claim: it moves no status marker.