The published foundations of TFPT

DUAL.FRAME.01Identity (exact) [E]/[C]

FLAV.TH13.01Numerical/identity (flavor readout) [E]/[C]/[O]

FLAV.NUSCALE.01Bookkeeping [E] + window [N]/[C] + [O] absolute scale + [X] kill

QFT4D.EG.ALLORDER.01All-order EG/BRST contract [C] (imported EG causal factorisation + BRST renormalisation on the TFPT finite dim-4 gauge+matter class + the seam gap); prerequisites power-counting/BRST-nilpotency/gap [E]

DYNAMICS.UNIVERSAL.01Universal synthesis [E]/[C] (every sector = a gapped operator with a unique attractor + spectral gap => parameter-free; extends v303 theory-wide; 3 gaps computed, the cross-sector identification [C])

CORRECTIONS.GAP.01Correction calculus [E]/[C] (each sector's gap sets its first-correction size; (2/3)^6 family vs golden family; the harvest of v383)

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

E8.CMDUAL.01E8 character CM-duality [E]/[C] (chi_E8(i)=12 vs chi_E8(omega)=0: the (E8)_1 character maximal at the seam tau=i, zero at the family tau=omega; the two are the only elliptic points so the values are forced) -- the seam/flavor rigidity duality, extends v282

SEAM.EQUIV.02Dual keystone at tau=omega [E]/[C]/[O] (the family/flavor sector as the order-3 Eisenstein/A2 face: chi_E8(omega)=0, A2 Cartan det 3=N_fam reads R in E6xA2 with det R=8=dim A2, delta=the tau=omega CM phase, cusp weights=the order-3 deck; dual to the seam=(E8)_1 at tau=i). A named contract, NOT a closure

FLAV.PMNS.CLOSE.01PMNS closed modulo the keystone [E]/[C]/[O] (CP-phase origin = the tau=omega CM phase v405; angles [E]; J=-0.0297 derived; absolute scale = one seesaw ratio = v_geo; zero free flavor dials beyond v_geo). Resolves v270's open phase + scale

ARITH.TRICHOTOMY.01Atom trichotomy [E]/[C]: {2,3,5} ram/inert/split in Z[i] (2 ram, 3 inert, 5 split) vs Z[omega] (3 ram, 2,5 inert); the ramified prime of each ring = its atom; each atom is the unique ramified prime of one facet of Q(i,sqrt-3,sqrt5), product 30=h(E8); seam/flavor/golden reading [C]

DIAMOND.EISEN.01Eisenstein/CP operator [E]/[C]: the family rotation P realises the hex norm 7=N_omega(3+2omega) via (3I+2P)(3I+2P^2)={7,7,25} (dual of v415's {13,13,9}); the CP clock W=-P^2 (W^2=P, W^3=-I, Spec {-1,zeta6,zeta6^-1}) gives delta_CKM=pi/3, delta_PMNS=4pi/3; all flavor clocks are zeta30-powers, the seam mu4 the Galois side phi(30)=8=rank E8; the carrier mu5 has no 3x3 operator [C]

ARITH.NORMTRIPLE.01Cyclotomic norm triple [E]/[C]: the carrier split (3,2) over the three atom-rings Z[omega],Z[i],Z[zeta5] gives det(3I+2 Comp(Phi_{3,4,5}))=(7,13,55)=(scalaron,Delta_Q,quark numerator); the carrier-5 clock is the 4x4 Phi5-companion C5 (golden in its 2cos values, N(3+2 zeta5)=55=quark numerator); NEG control anchor (5,4)->(21,41,461) fails in the carrier ring; (3,2) FORCED (v14) not unique, but the UNIQUE CROSS-SECTOR seed -- only (3,2)->(7,13,55) spans gravity/flavor/masses while (2,1)->(3,5,11) is all-core [C]

SEAM.GALOIS.01Seam mu4 = carrier's Galois group [E]/[C]: 30 squarefree => no order-4 cyclic, so the seam mu4 is the Galois side (Z/30)^x=mu4 x Z2; the mu4 factor IS (Z/5)^x=Gal(Q(zeta5)) (carrier), the Z2 IS (Z/3)^x (family/CP); the Frobenius zeta5->zeta5^2 is the explicit order-4 operator G with G C5 G^-1=C5^2, G^4=I; resolves the v409 asymmetry (seam = automorphism, not a hand) [C]

FR.POLE.QED.01F_pole external [E]/[C]/[O]: the Koide source->pole transfer is a one-loop EM effect; Koide is rescaling-invariant (Q(c*m)=Q(m)) so the shift is flavor-split; the tree->pole gap 0.0022 is one-loop-EM-sized (=phi0/24 to 0.6%, =alpha/pi to ~5%), pole at 2/3 (IR attractor); a 1-loop QED per-lepton-log estimate shifts Koide by EM-loop order toward 2/3; the exact flow time t~2.84 is scheme-dependent external QED, only sized; F_pole stays [C], firewalled (v187) -- rate forced (v327/v82), flow external

FLAV.THIRDGEN.PATTERN.01Numerical [N]/[C]/[O] (candidate pattern; record of v84 untouched)

FLAV.DM2RATIO.01Numerical [N]/[C]/[O] (candidate relation; informal pi phi0 table heuristic superseded as comparator)

FLAV.NUSCALE.02Candidate [P]/[N]/[X]/[C]/[O] (carrier normalisation collapses the trade-off; window bracketing; integer rung declined at 1-loop; decision computation named)

FLAV.NUSCALE.04Enumeration/decision [E]/[O] (the 3/5 Clebsch door closed; negative result; window candidate stands)

FLAV.NUSCALE.05Candidate [C]/[N] + mechanism [O] (structured point inside the v481 window; scalaron-trace hypothesis typed, not derived; no seesaw closure)