The published foundations of TFPT

AX.P1.01Axiom (declared input; reduces to the anchor a=(1,1,2)+pi)

AX.P2.01Axiom (declared input; over-determined bootstrap fixed point, Lean-forced)

SEAM.EQUIV.CONTINUUM.02Sharpening [E]/[O] (the order-4 clock + Coxeter-match pin E8 over SO(16); the residual is purely the chiral-edge existence)

SEAM.EQUIV.CONTINUUM.03Continuum chain assembly [C]/[E]/[O] (edge-existence reduced via anomaly inflow; residual = lattice realization tied to seam one-sidedness; B already closed by v40)

SEAM.MMST.INCLASS.01SEAM.EQUIV.01 reduced to the single S3 lattice-realisation input; MMST in-class verified for the collar [E]/[C]/[O]

SEAM.S3.LATTICE.01S3 realised as an explicit gapped chiral-Majorana lattice model (numerical Chern |C|=1, c_-=8, det K 4->1) [E]/[C]/[O]

SEAM.S3.E8CHARACTER.01the chiral c=8 content is (E8)_1 (248 currents, 1 primary) via the exact character + mu4/GSO promotion [E]

SEAM.EQUIV.BOOTSTRAP.01Correction [E]/[O] (inputs are bootstrap-forced fixed points; g_car=5 IS the icosahedral 5 of h(E8)=30; golden emergent from the mu4-glue; residual = the physical continuum realisation)

SEAM.EQUIV.RIGID.01Route B / reduction [E]/[O] (rigidity + the icosian-ring identity reduce L2 to one question: does the raw seam carry the golden ratio?; NOT closed)

SEAM.EQUIV.CLOSURE.01Analysis/roadmap [E]/[O] (the flat->spherical base locus; four closure modes; no free theorem; only rigidity B or axiom P3; NOT closed)

SEAM.EQUIV.GEOM.01Capstone/roadmap [E]/[O] (5 of 6 links theorems; the group forced by the icosahedral atoms; the keystone reduced to the single orbifold-realisation arrow L2 = SEAM.EQUIV.01)

GATE.WOLFRAM.02Numerical (second path, extension verified 623/623)

FR.KOIDE.07Identity [I] (exact operator factor + negative control) + Physical [C] (the transfer mechanism)

HOR.TRISECT.01Identity [I] (uniformization, normal form, curvature, slope) + Physical [P] (clock bridge)

HOR.CLOCK.01Identity [I] (static pin, tower, clock spectrum, rate) + Physical [P] (quantum clock)

SYNTH.INVENTORY.01Identity [I] (inventory + relocation arithmetic) + typing contract (gap completeness)

HOR.CLOCK.02Identity [I] (tower, cross-link, target arithmetic, coupling) + Physical [P] (identification)

ARCH.TRIAD.01Identity [I] (exact arithmetic/matrix identities; audit typing for the 121 lemma)

SYNTH.INVENTORY.02Identity [I] (machine bookkeeping + typing contract)

SYNTH.INVENTORY.03Identity [I] (machine bookkeeping + typing contract; ledger-row membership)