The published foundations of TFPT

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

FLAV.SELECTOR.CLOSE.01R4' selector folds into the keystone [E]/[C]/[O] (the (d,n) pairings {2,8,121}={|Z2|, rank E8=dim A2=det R, ||Pl(K)||_1^2} are the tau=omega family-slice atoms; n.a=8=dim A2 reads R in E6xA2; deriving (d,n) folds into SEAM.EQUIV.02; residue = why 11)

SHEET.GEN.BINARY.01Sheet generator V is a binary compiler [E]/[C]: V^n closed form + V^n.1 binary spine + four bilinear families (6,7,9,11; 13,27,55,56); spine FORCED by Spec(V)={0,1,2}, Lie/theta readings audit-typed [C]

FLAV.UD.VPOWER.01u/d ratio as a V-power readout [E]/[C]: c_u/c_d=(1.V^4.1)/((a.V.1)(1.V^2.1))=55/117, identical to 5*11/(9*13); exact re-encoding, value stays [C]

DIAMOND.SHEET.SOURCE.J.01Sheet source corner J=M(1,-2) on the Z2 wall [E]/[C]: chi_J=(6,3,2), a.J.a=30=h(E8), det(I+J)=12, det(2I+J)=40; readings audit-typed

DIAMOND.SHEET.CALCULUS.01Sheet axis = characteristic-difference calculator [E]/[C]: Delta e1=3, Delta^2 e2=4, Delta^2 e3=8; anchor energy 52+11t (30->41->52->63); readings audit-typed

DIAMOND.CENTER.RESOLVENT.01Center C resolvent portal [E]/[C]: det C=14=dim G2, det(I+C)=52=dim F4, det(2I+C)=120=|R^+(E8)| (G2->F4->E8^+); reading audit-typed

DIAMOND.GAUSS.01Gaussian operator [E]/[C]: J=[U,V]/3 is the mu4 quarter-turn (J^2=-I), 3+2i/5+4i are eigenvalues of 3I+2J/5I+4J (norms 13=Delta_Q/41=10 b1), the norms become operator identities, intrinsic order-4 deck D=-I+J-J^2 with chi2=ker[U,V]=a-1; geometric-deck match sharpens (not closes) the v140 Z3 residue [C]

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]

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

SEAM.GALOIS.NET.01Galois<->Net bridge / four-fold mu4 identity [E]/[C]: the seam mu4=Gal(Q(zeta5))=(Z/5)^x is the SAME cyclic Z/4 as the (E8)_1 glue <(1,1)> AND the discriminant disc(A3)=disc(D5)=Z/4 (D5 cyclic because rank 5 odd; D8 even=Klein control); only the carrier prime 5 gives (Z/p)^x=Z/4; glue order 4 => 16/4^2=1=E8 (vs Klein/order-2 => D8 det 4); cyclic Z/4 selects E8, Klein excluded -- the v419 Galois gearbox IS the holomorphic net's glue, a direct Galois->G_net bridge. Deck/divisor=Galois=discriminant=simple-current is a compression per v428 (one object read four ways), not four witnesses [C]

QGAMB.NODEP.01No-Ambient-Dependency [E]/[C]: no frozen readout is computed from QG.AMB.01 -- it is a certification SINK (every dependent is a gravity-gate/QG row, no prediction), not a value source (script '-'; predictions computed by v3/v7/v9/v268, never an ambient-measure script), and its only predictive link is theta13's architectural 4D-QFT contract edge (coherence, not numerical); the gap margin Delta_eff~1.648>0 decouples its back-reaction (v337). v369 prose -> machine-checked DAG/script fact [E]; verdict [C], does NOT prove SEAM.EQUIV.01

SEAM.EQUIV.LTORP.01(LTO-RP) keystone reduction [E]/[C]: SEAM.EQUIV.01's intrinsic-BW lemma reduced to the cited NPW26 commuting-projector theorem, mapping corrected -- (LTO-RP)=u_Theta=J=intrinsic BW (theta K theta=-K), NOT omega o rho=omega; the mu4 clock is a modular symmetry [rho,K]=0 (sigma^psi=rho type-wrong); A-and-NOT-B refutes clock-invariance => (LTO-RP). Make-or-break: NPW26 prove (LTO-RP) for topologically-ordered models (trace/anyonic), the seam is invertible (|det E8|=1) + beta=1 KMS (not a trace), in neither bucket. REDUCTION not closure; two open sub-steps (Z/2-reflection commuting-projector LTO realisation; invertible-KMS (LTO-RP)). SEAM.EQUIV.01 stays [O]

DYN.TRANSFER.UNIVERSAL.01Single-flow reduction [E]/[C]: the four F_transfer flows are the ONE v238 recovery semigroup restricted to sectors (native gap 6 ln(3/2), native rates e^{-Delta}=(2/3)^6, b3=-7); F_pole=v99 generator at q=2, F_Boltzmann washout=that contraction (CP 4pi/3 native), F_QCD rate native -- only the ANCHORS (v_geo/C_p/M_R) external; F_relic's cosmological IC theta_i the one wall. Reduction not internalisation, firewall-clean; extends v383 static->dynamic

SEAM.EQUIV.LTORP.KMS.01Invertible beta=1-KMS (LTO-RP) [E]/[C]: the corner NPW26 leave open (they do topologically-ordered; the seam is invertible + KMS, not a trace) is constructively satisfiable -- a gapped reflection-symmetric mu4-even collar has Theta K Theta=-K (u_Theta=J) and [rho,K]=0, so (LTO-RP) holds by direct Tomita-Takesaki; |det E8|=1 (no anyons), state not a trace; neg controls have teeth. Advances v424 sub-step (ii); SEAM.EQUIV.01 stays [O] (continuum sub-step (i) remains), finite-dim witness not continuum theorem

OVERDET.WITNESS.MAP.01Witness map [E]/[C]: disjoint grammars multiply, same-generator projections compress; the seven arithmetic witnesses are refined by v428 to COMPRESSION (facets of one (2,3,5)/E8 object, v236). The genuine multiplication is the multiply-forced inputs + foreign witnesses (alpha^-1~137); coincidence is expensive for the discrete core; does not by itself establish physics

OVERDET.WITNESS.RECLASS.01Witness re-classification [E]/[C]: v427's seven arithmetic witnesses are facets of ONE (2,3,5)/E8 object (v236) => compression, not seven multiplications. The genuine multiplication is the '8' forced four independent ways (rank E8, h(D5), phi(30), Milnor) + the foreign alpha^-1~137. Honest correction of v427 (consistent with v305/v236/v313)