Original claim records.

Original ledger status

FR.CLOCK.PROBE.01

FR.CLOCK.PROBE.01

A FALSIFIABLE probe of how external the 'external physics' really is (2026-06-24): do the frontier scheme-numbers land on the {2,3,5} clock (= the anchor atoms |Z2|,N_fam,g_car, v394) or not? Strict No-Free-Pattern discipline (v100): 'on the clock' means an EXACT match to a ratio/power of {2,3,5}/golden, NOT a wide-band fit. [E] eta_B DECUPLE: A_Lambda=10=|Z2|*g_car=2*5=p3(anchor) ON CLOCK (v212). [E] KOIDE RATE: the F_pole Moebius multiplier (2/3)^6=(|Z2|/N_fam)^6 ON CLOCK (v303/v82). [E] AXION SPINE ANGLE: the robust DM branch theta_i=pi*N_fam/g_car=3pi/5=108deg ON CLOCK (v211/v373). [E] PROTON C_p~2.83+-0.15 is NOT a discriminating clock value: within its +-5.3% band multiple distinct simple values fit (2^{3/2}=2.828, 17/6=2.833, 14/5=2.800), so a clock match is non-unique => by No-Free-Pattern C_p is EXTERNAL (firewall v187/v374 correct), NOT assigned a clock value. [C] VERDICT: 3 of the 4 frontier scheme-numbers land EXACTLY on the {2,3,5}/golden clock; the IRREDUCIBLE external residue shrinks to essentially the proton's QCD number C_p (pure non-perturbative QCD) -- 'external physics' was OVERSTATED.

Recorded status: Clock probe of the frontier [E]/[C] (3 of 4 'external' scheme-numbers -- A_Lambda, Koide rate, axion spine -- land EXACTLY on the {2,3,5} clock; only the proton C_p is genuinely external; a falsifiable anti-numerology test)

Original ledger status

SEAM.RIGIDITY.01

SEAM.RIGIDITY.01

THE SEAM STATE RIGIDITY THEOREM AS ONE NAMED TARGET (2026-06-24, Paper A / the G_net closure contract): consolidates the scattered state-invariance reductions (v177/v198/v199/v308/v309/v335) into a single citable theorem and HARDENS the finite-block evidence to a multi-mode sweep. Does NOT close SEAM.EQUIV.01 (the continuum scaling-limit existence stays the cited MMST/Adamo step, v336/v392). [E] RP-DEFINABILITY HINGE: OS reconstruction gives a canonical transfer operator T=e^{-H} from the RP state + reflection alone (v54) on a quasi-free state (v155), so Lambda_Sigma is RP-definable WITHOUT importing the mu4 normal form (non-circular). [E] GROUND-STATE REDUCTION: for a quasi-free RP state C=1/2(1+sgn H_1), so omega o rho=omega <=> [rho,H_1]=0 <=> H_1 block-diagonal in the four mu4-character classes. [E] BAND-LIMITED CORE (the hardening): [rho,|k|]=0 exactly and a character-block-diagonal sub-principal symbol commutes with rho while a single off-character entry breaks it, swept N=4..64 (beyond the 3-dim H^1 of v177/v199). [E] HOLOMORPHY=>(E8)_1: c=g_car+N_fam=8, |det Cartan(E8)|=1 (one primary) vs |det Cartan(D8)|=4, index 4=|mu4|, gap 6 ln(3/2)>0 -- the unique even-unimodular rank-8 lattice net (v83/v154/v308). [O] THE ONE RESIDUAL: [rho,Lambda_Sigma]=0 on the FULL L^2 <=> intrinsic Bisognano-Wichmann modular geometricity, the same [O] as v199/v309, now stated as the single theorem residual.

Recorded status: Seam State Rigidity contract+evidence [E]/[O] (Paper A: the G_net keystone as one named theorem -- RP-definability hinge + band-limited mu4-character core swept N=4..64 + holomorphy=>(E8)_1; the one residual = full-L^2 / intrinsic BW). NOT a closure of SEAM.EQUIV.01

Original ledger status

GRAVITY.COMPLETE.01

GRAVITY.COMPLETE.01

GRAVITY-COMPLETE = BOUNDARY-COMPLETE + AMBIENT-REDUNDANCY (2026-06-24, Paper B / the gravity closure accounting): the explicit verdict combining the parameter-free LOCAL field equation (v358/v359) and the ambient REDUNDANCY (v369). Does NOT construct the ambient measure and does NOT close SEAM.EQUIV.01. [E] LOCAL EQUATION PARAMETER-FREE: G_ab+Lambda g_ab=(1/c3)T_ab with 1/c3=8pi (the four c3-roles consistent: Unruh 1/(2pi)=4c3, EH 1/(16pi)=c3/2, Einstein 8pi=1/c3, Bekenstein 1/4=1/|mu4|), Lambda prefactor (8pi)^2*48 c3^4=3/(4pi^2). [E] REDUNDANCY DISCRIMINATORS: holomorphic (E8)_1 => DHR=Vec (|det Cartan|=1 vs 4) + torus GSD=1, Petz recovery (2/3)^6, gap margin Delta_eff=6 ln(3/2)-31/(4pi^2)~1.648>0. [E] O_phys SUBSET A_Sigma: the five physically reachable gravitational readout classes (Newton 8pi, Lambda 3/(4pi^2), scalaron c3^7, horizon density 1/4=1/|mu4|, BH recovery (2/3)^6) are all boundary/seam/gap readouts -- the bulk ambient measure adds none. [C] THE VERDICT: Gravity-complete (TFPT sense) = Boundary-complete + Ambient-redundancy. [O] RESIDUAL (no new gate): SEAM.EQUIV.01 + intrinsic Bisognano-Wichmann (v369/v329).

Recorded status: Gravity-completeness accounting [E]/[C]/[O] (Paper B: the explicit verdict = local parameter-free equation + ambient redundancy; O_phys subset A_Sigma over 5 readout classes; residual = SEAM.EQUIV.01 + intrinsic BW, no new gate)

Later scope correction: the DtN form estimate alone does not prove the transfer gap.

Original ledger status

GRAV.NONLOCAL.01

GRAV.NONLOCAL.01

THE NONLOCAL SPECTRAL-GRAVITY ACTION; LOCAL R+R^2 IS ITS IR PROJECTION (2026-06-24, Paper C / the 4D gravity-action contract): consolidates v304/v370/v380/v386 and adds the IR-matching check. Does NOT prove the entire-analyticity of the resummed form factor (stays the cited heat-kernel resummation, the [O] of v304/v380); PERTURBATIVE only. [E] ENTIRE FORM FACTOR -> ONE POLE: the dressed spin-2 propagator 1/(p^2 a) with a(u)=e^u has its ONLY pole at p^2=0 (residue a(0)^{-1}=1>0, one healthy massless graviton, no Stelle ghost). [E] EVERY TRUNCATION CARRIES THE GHOST: T_1=1+u has the Stelle zero u=-1, and the nearest-zero modulus grows monotonically with order -> infinity, so 'entire'='do not truncate' (v380). [E] IR PROJECTION = R+R^2: a(u)=1+u+u^2/2+... reproduces the spectral-action R+R^2 structure (v28/v36) with the FIXED scale M_scal^2/Mbar^2=c3^7 (exponent 7=g_car+N_fam-1). [E] THE SCALE IS AN ATOM: M=M_scal=c3^{7/2}Mbar, the exponent 7 and half-power 7/2 carrier atoms (v253), determined not fitted. [O] RESIDUAL: (i) a(Box)=e^{Box/M^2}=the EXACT off-shell curved-space Hessian is the cited heat-kernel resummation (analyticity assumption); (ii) PERTURBATIVE graviton unitarity, NOT the nonperturbative ambient measure (QG.AMB.01, [C] redundancy v369).

Recorded status: Nonlocal-gravity action contract [E]/[O] (Paper C: the entire form factor gives a ghost-free one-pole propagator whose IR projection is exactly the atom-scaled R+R^2; the entire-a assumption + perturbative-only stay [O]). Consolidates v304/v370/v380/v386, adds the IR-matching check

Original ledger status

METROLOGY.CLOSURE.01

METROLOGY.CLOSURE.01

THE FINAL INPUT SET {a, pi, v_geo} CERTIFIED (2026-06-24, Paper D / the scale-modulus closure): 0 dimensionless dials + 1 dimensionful unit, consolidating v153 (No-Unit), v274 (over-determined anchor), v364 (gravity adds no unit), v384 (v_geo is theorem-forbidden, type B). Does NOT 'solve' v_geo (a dimensionless compiler provably cannot output a scale); it CERTIFIES the single declared unit. [E] INPUT SET: a=(1,1,2) -> elem-sym (e1,e2,e3)=(4,5,2)=(|mu4|,g_car,|Z2|), c3=1/(2 e1 pi)=1/(8 pi); the one dimensionful input is v_geo, NO dimensionless dial. [E] DIMENSIONAL BOOKKEEPING (No-Unit, v153): mass~v_geo^1, 1/G~v_geo^2, Lambda~v_geo^4, U_point~v_geo^1, m/mu=e^{3/4}~v_geo^0; under L->lambda L a dimensionless datum is invariant while v_geo^d scales as lambda^{-d}, so a scale cannot be a function of scale-invariants -- v_geo is a forced INPUT. [E] GRAVITY ADDS NO UNIT (v364): 1/c3=8pi and (8pi)^2*48 c3^4=3/(4pi^2) are dimensionless. [N] OVER-DETERMINATION (v274): gravity route (8 pi G)^{-1/2}=2.4353e18 GeV vs cosmology route 2.438e18 GeV agree to 0.11% (conditional on the Lambda-branch). [O] v_geo THEOREM-FORBIDDEN: TOE_strict = TOE_dimensionless + [v_geo], not 'derive the metre' (v384 type B). [2026-08-03 LIII: sharpened to torsor language by v725 (VGEO.TORSOR.01): the input set {a, pi, v_geo} is the calibration point of a rank-1 R+ scale torsor; the bookkeeping table of this row is the machine-verified export table there; no status move.]

Recorded status: Metrology closure [E]/[N]/[O] (Paper D: the final input set {a,pi,v_geo} -- 0 dimensionless dials + 1 unit; dimensional bookkeeping over all dimensionful observables; G-vs-Lambda over-determination 0.11%; v_geo theorem-forbidden). A metrology end-cap, no new derivation

Original ledger status

FTRANSFER.SUITE.01

FTRANSFER.SUITE.01

THE F_transfer FUNCTOR CERTIFICATE (2026-06-24, Paper E / the physical-interface contract): the four frontier sectors are ONE functor F_transfer = F_observable o F_threshold o F_RG, consolidating the typed solvers (FR.POLE.SOLVE.01, FR.BOLTZMANN.SOLVE.01, FR.RELIC.SOLVE.01, FR.QCD.BUDGET.01). Does NOT re-press any frontier observable into the compiler (forbidden by the frontier firewall, v187); it certifies the composition law and the kill-test coverage. [E] COMPOSITION LAW: every frontier observable factors as source -> threshold/matching -> standard RG -> observable (verified structurally for all four). [E] EXACT ATOM SOURCES: Koide Q_src (phi0-ladder, v93); leptogenesis A_Lambda=2 g_car=10 and delta_CP=4pi/3 (v9/v212); axion f_a=M_scal/128 (v185/v211); m_p/m_e carrier beta b3=-(11-2 n_f/3)=-7 (v164/v262). [E] KILL-TEST COVERAGE: each sector carries a committed falsifier (Koide wrong-sign QED; eta_B outside [obs/3,3obs]; axion outside [0.08,0.16]; m_p/m_e C_p band excluding 1836.15). [C] THE FIREWALL: the PHYSICAL prediction of each sector stays [C]/[O] (threshold/RG/solver dependent); only the algebraic SOURCE is [E] -- no frontier observable is a primitive compiler output. [E] NO FREE DIAL: external inputs declared with propagated error budgets, algorithmic and versioned.

Recorded status: F_transfer functor certificate [E]/[C] (Paper E: the four frontier sectors as one F_observable o F_threshold o F_RG with exact atom sources + kill-test coverage + the firewall; physical predictions stay conditional). A consolidation, no new number

Original ledger status

ARITH.HULL.01

ARITH.HULL.01

The three number-field facets COMPOSE to a degree-8 = rank(E8) abelian field (2026-06-24): K=Q(i,sqrt-3,sqrt5), the arithmetic hull dual to the E8 lattice hull, composing the v390/v394 facets that were only ever used one at a time. [E] INDEPENDENCE: the squarefree parts -1,-3,5 are multiplicatively independent in Q*/(Q*)^2 (no nonempty subset product is a square), so the three quadratics are linearly disjoint and [K:Q]=2^3. [E] DEGREE = rank E8: [K:Q]=2^3=8=rank(E8)=g_car+N_fam, Galois group (Z/2)^3 of order 8; the relation 2^omega(h)=rank is E8-special (the E7 control h=18, omega=2, 2^2=4!=7). [E] SEVEN SUBFIELDS: exactly 7 quadratic subfields {-1,-3,5,3,-5,-15,15}. [E] 4+3 SPLIT = |mu4|+N_fam: exactly 4 imaginary (-1,-3,-5,-15)=|mu4| (CM/dynamic) + 3 real (3,5,15)=N_fam (RM/static). [E] RAMIFIED ONLY AT THE ATOMS: every quadratic subfield ramifies only over {2,3,5}=the atoms=the primes of h(E8)=30. [E] CM/RM=DYNAMIC/STATIC: 2,3 imaginary-quadratic (disc -4,-3) carry the {2,3}-arithmetic dynamic rates (v394), 5 real-quadratic (disc +5) carries the static golden carrier (no independent prime-5 rate). [C] K is the abelian (Z/2)^3 'arithmetic hull' dual to the E8 lattice hull; the 7 quadratic subfields are a candidate for the 7 E8 audit slices.

Recorded status: Arithmetic hull [E]/[C] (the three facet fields compose to K=Q(i,sqrt-3,sqrt5): degree 2^3=8=rank E8, Galois (Z/2)^3, 7 subfields = 4 imaginary (|mu4|) + 3 real (N_fam), ramified only at {2,3,5}; 2^omega(h)=rank is E8-special) -- a synthesis, no new number

Original ledger status

E8.CMDUAL.01

E8.CMDUAL.01

The (E8)_1 vacuum character at the two CM points (2026-06-24): chi_E8 = E4/eta^8 = j^{1/3} equals 12 at the seam CM point tau=i and 0 at the family CM point tau=omega, extending v282 (chi_E8(i)=12) to the second elliptic point. [E] chi_E8^3=j (q-series). [E] SEAM tau=i (Q(i), order 4): cross-ratio 2 => j=1728 => chi_E8(i)=1728^{1/3}=12 (E8 present, v282/v214). [E] FAMILY tau=omega (Q(sqrt-3), order 6): the equianharmonic lambda (lambda^2-lambda+1=0) => j=0 => chi_E8(omega)=0 (E4 vanishes, v220/v267). [E] DUALITY: the SAME function chi_E8 takes its two CM values {12,0} at the two atoms' CM points -- maximal at the seam, zero at the family. [E] tau=i (order 4) and tau=omega (order 3/6) are the ONLY elliptic points of PSL(2,Z), so chi^3=j forces chi(i)=12 and chi(omega)=0 (not chosen). [C] STRUCTURAL READING: the seam is rigid where E8 is present (chi=12, SEAM.EQUIV.01 closes) while the flavor/CP sector is the soft residual where E8 degenerates (chi=0, the U_wall amplitude / v_geo / the CP texture). [C] DUAL-KEYSTONE CANDIDATE: the flavor sector = the j=0 degeneration of (E8)_1 at tau=omega, dual to the seam = (E8)_1 at tau=i.

Recorded status: E8 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

Original ledger status

SEAM.EQUIV.02

SEAM.EQUIV.02

The dual keystone at tau=omega (2026-06-24): the family/flavor sector as the order-3 Eisenstein/A2 face of E8, dual to the seam=(E8)_1 at tau=i (SEAM.EQUIV.01/v404). A NAMED CONTRACT (genre of v286/v398), NOT a closure. [E] chi_E8(omega)=j(omega)^{1/3}=0 (E4 vanishes at tau=omega, v404) vs chi_E8(i)=12 -- the family sits where the holomorphic (E8)_1 structure degenerates. [E] A2 is the tau=omega Eisenstein/hexagonal lattice: Cartan det=3=N_fam, h(A2)=3=N_fam, automorphism mu6=mu3(triality) x mu2(sheet, v233). [E] the flavor matrix R lives in the E6 x A2 slice: 248=||R||_F^2+det R+2(1^T R a)N_fam=78+8+2*27*3, ||R||_F^2=78=dim E6, det R=8=dim A2=rank E8. [E] the CP phase delta_PMNS=4pi/3 (delta_CKM,lead=pi/3=arg zeta6) is the hexagonal Eisenstein CM phase at tau=omega (v220/v231/v233). [E] the cusp weights {0,1/3,2/3} are the order-3 deck = N_fam = det Q = cusp-class order (v72), fixing Spec(Q+)=(1,2,3)=A3 exponents (v69/v137). [C] the dual keystone: the raw cusp/family transport IS the order-3 Eisenstein/A2 deck at tau=omega; the two keystones sit at the only two elliptic points of PSL(2,Z). [O] residual (parallel to SEAM.EQUIV.01's continuum existence): the canonical Z3 deck identification (v140) + the absolute scale = one v_geo-class UV input (No-Unit, v153).

Recorded status: Dual 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

Original ledger status

FLAV.PMNS.CLOSE.01

FLAV.PMNS.CLOSE.01

The PMNS dynamics closed modulo the tau=omega keystone (2026-06-24): the CP-phase ORIGIN is the family CM point (v405) and the absolute scale is one v_geo-class unit, so PMNS has zero free flavor dials beyond v_geo. Resolves the two [O]'s v270 left open (the assembled phase + the open scale). [E] the three angles sin^2 th12=1/3-phi0/2 (v9), th23=45 (v9), sin^2 th13=phi0 e^{-5/6} (v268) assemble to one exactly-unitary U_PMNS (v270). [C] CP-PHASE ORIGIN: delta_PMNS=4pi/3 is the tau=omega hexagonal CM phase (v405/v220/v233), arg zeta6=pi/3, mu6=mu3 x mu2 -- so under SEAM.EQUIV.02 the phase has an operator home, upgrading v270's [O] assembled input to a keystone consequence. [C] J_PMNS=s12 c12 s23 c23 s13 c13^2 sin(delta)=-0.0297, a derived CP strength (no free phase once delta is the keystone value), matching NuFIT ~ -0.026. [E] the absolute scale = one seesaw ratio m3=(y_nu v_EW)^2/M_R (v272) -- one v_geo-class UV input the No-Unit theorem (v153) forbids deriving, NOT a flavor gap. [C] net: PMNS = three angles[E] + delta[tau=omega keystone] + J[derived] + absolute scale[one v_geo unit]; zero free flavor dials. [O] residual: the seesaw operator realisation (M_R not a clean Mbar power, v272/v184) + the normal-ordering Sigma m_nu floor 0.0586 eV kill test (v272).

Recorded status: PMNS 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

Original ledger status

FLAV.SELECTOR.CLOSE.01

FLAV.SELECTOR.CLOSE.01

The R4' selector residue folds into the tau=omega keystone (2026-06-24): the three (d,n) selector pairings ARE the tau=omega family-slice atoms, so deriving the selector pair reduces to the family sector being the E6 x A2 (tau=omega) object (v405). [E] the frame (1,a,sigma) is a Z^3 basis with det(1|a|sigma)=11=||Pl(K)||_1, and n=(5,-9,6) is the unique covector with n.1=2, n.a=8, n.sigma=121=11^2 -> (d,n)=>R columnwise (v136/v139). [E] n.a=8=rank E8=dim A2=det R -- the anchor-pairing equals the A2 (tau=omega Eisenstein) block dimension that reads R in the E6 x A2 slice (||R||_F^2=78=dim E6; v405). [E] the three pairing values {2,8,121}={|Z2|, rank E8=dim A2=det R, ||Pl(K)||_1^2} = the tau=omega family-slice atoms (the mu2 sheet of mu6, the A2 block, the Plucker frame volume). [E] the square selects the point (v139): sigma-pairing=11(11+t), a perfect square only at t=0. [C] the reduction: deriving (d,n) (R4') folds into SEAM.EQUIV.02 -- d=(3/2)a-2*1 is anchor-derived (v139), the three pairings are the family-slice atoms. [O] residue: the lone non-atomic value is 11=||Pl(K)||_1 (the quark Plucker constant, flagged v42/FLAV.RIGID); why 11 is the sharpened R4' residue.

Recorded status: R4' 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)

Original ledger status

SHEET.GEN.BINARY.01

SHEET.GEN.BINARY.01

The sheet generator V is a binary internal compiler (2026-06-24): the rank-2 sheet axis V=Q diag(0,1,1) of the centered cross (v95/v218) has powers that print the binary carrier spine. [E] CLOSED FORM (induction F(n)*V=F(n+1)): V^n={{0,2^(n-1),0},{0,2^n,0},{0,2^(n+1)-2,1}}, so V^n.1=(2^(n-1),2^n,2^(n+1)-1)=(1,2,3),(2,4,7),(4,8,15),(8,16,31),... [E] BILINEAR FAMILIES (exact in n, 1=(1,1,1), a=(1,1,2)): 1.V^n.1=7*2^(n-1)-1, 1.V^n.a=7*2^(n-1), a.V^n.a=11*2^(n-1), a.V^n.1=11*2^(n-1)-2; at n=1 = (6,7,9,11). [E] readouts 1.V^2.1=13=Delta_Q, 1.V^3.1=27=1.R.a, 1.V^4.1=55=quark numerator, 1.V^4.a=56=dim 56_E7; 11=a.V.a the anchor amplitude. [C] SPINE READING (audit, NOT promoted): the spine {2^(k-1),2^k,2^(k+1)-1} is FORCED by Spec(V)={0,1,2}; the matches (1,2,3)=A3 exponents, (2,4,7)=(|Z2|,|mu4|,7), (4,8,15)=(|mu4|,rank E8,dim A3), (8,16,31)=(rank E8,dim S+,2^g_car-1=248/8) are audit Lie/dimension matches (v95 typing). [C] THETA CROSS-LINK (audit raster): sigma3(2)=9=a.V.1=N_fam^2, sigma3(3)=28=1.V^3.a=det(I+R), sigma3(5)=126 = local E7 root shell (tfpt_3).

Recorded status: Sheet 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]

Original ledger status

FLAV.UD.VPOWER.01

FLAV.UD.VPOWER.01

The quark u/d ratio is a pure V-power readout (2026-06-24): the established c_u/c_d=g_car*||Pl(K)||_1/(N_fam^2 Delta_Q)=55/117 (v94) re-expresses EXACTLY via the sheet generator V (v410). [E] c_u/c_d=(1.V^4.1)/((a.V.1)(1.V^2.1))=55/(9*13)=55/117, with 55=1.V^4.1, 9=a.V.1=N_fam^2, 13=1.V^2.1=Delta_Q. [E] IDENTITY: same number as 5*11/(9*13); the V-power numerator repackages g_car*11=55=1.V^4.1. [C] HONEST TYPING: an exact RE-ENCODING, no new physical input -- the value 55/117 and the u/d identification stay [C], coupled to the U_wall readout rigidity; the gain is that numerator and denominator both iterate ONE operator.

Recorded status: u/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]

Original ledger status

DIAMOND.SHEET.SOURCE.J.01

DIAMOND.SHEET.SOURCE.J.01

The sheet source corner J (2026-06-24): the determinant surface has two s-independent iso-volume walls (v135) t=-1 (det=4=|mu4|, carries K) and t=-2 (det=2=|Z2|); the operator on the Z2 wall, J:=M(1,-2)=C-2V=((4,1,0),(4,1,2),(5,1,1)), was unnamed and completes the sheet axis J,K,C,F=M(1,-2..1). [E] CLEAN CHAR POLY: chi_J=lam^3-6lam^2+3lam-2 => (tr,e2,det)=(6,3,2)=(|R^+(A3)|,N_fam,|Z2|). [E] RESOLVENT/ANCHOR: a.J.a=30=h(E8), det(I+J)=12=dim g_SM=chi_E8(i), det(2I+J)=40=|R(D5)|. [C] the Lie readings are audit-typed like the G2/F4 shadows of v95/v218.

Recorded status: Sheet 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

Original ledger status

DIAMOND.SHEET.CALCULUS.01

DIAMOND.SHEET.CALCULUS.01

The sheet axis is a discrete characteristic-difference calculator (2026-06-24): on M_t=C+tV (v95/v218) the elementary-symmetric coefficients encode atoms as DIFFERENCE ORDERS. [E] e1(t)=3t+12, e2(t)=2t^2+15t+25, e3(t)=det M_t=4t^2+14t+14 => Delta e1=3=N_fam, Delta^2 e2=4=|mu4|, Delta^2 e3=8=rank E8 (the e3 curvature cross-cited to v218/v224; the full (e1,e2,e3) ladder is new). [E] ANCHOR-ENERGY LADDER: a.M_t.a=52+11t (step 11=a.V.a, v410); 30->41->52->63=(h(E8),10 b1,dim F4,7 N_fam^2). [E] FOUR-ROW AXIS J,K,C,F: (tr,e2,det)/a.M.a=(6,3,2)/30,(9,12,4)/41,(12,25,14)/52,(15,42,32)/63. [C] atom/Lie readings audit-typed.

Recorded status: Sheet 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

Original ledger status

DIAMOND.CENTER.RESOLVENT.01

DIAMOND.CENTER.RESOLVENT.01

The center C is a resolvent portal G2 -> F4 -> E8 (2026-06-24): the center C=M(1,0) (v95) is the t=0 evaluation of V; its shifted determinants climb the exceptional ladder. [E] CENTER INVARIANTS (v95): tr C=12=dim g_SM=chi_E8(i), det C=14=dim G2, sum C=31=2^g_car-1=248/8. [E] RESOLVENT LADDER: det(C)=14=dim G2, det(I+C)=52=dim F4, det(2I+C)=120=|R^+(E8)| -- the exceptional shell ladder G2->F4->E8^+ as det(C+kI), k=0,1,2 (the resolvent ladder is the new content; reading [C], audit-typed).

Recorded status: Center 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

Original ledger status

DIAMOND.GAUSS.01

DIAMOND.GAUSS.01

The square CM-norm dictionary is operator-realised and the mu4 deck is intrinsic (2026-06-25): the Gaussian arithmetic of v222/v230 lifted from numbers to OPERATORS via J=[U,V]/3, the complex structure born from the commutator of the binary V and ternary U compilers (v410/v95). [E] J=((-1,1,0),(-2,1,0),(-3,1,0)) integer, Spec(J)={i,-i,0}, J^2=-I on the rank-2 image, J^3+J=0 (a mu4 quarter-turn). [E] 3I+2J has spectrum {3+2i,3-2i,3} and 5I+4J has {5+4i,5-4i,5}: the Gaussian integers 3+2i (norm 13=Delta_Q) and 5+4i (norm 41=10 b1) are LITERAL operator eigenvalues. [E] (3I+2J)(3I-2J)=9I-4J^2 has Spec {13,13,9} and (5I+4J)(5I-4J)=25I-16J^2 has Spec {41,41,25} -- the v222/v230 norms as operator identities (kernel slot = real part^2: 9=N_fam^2, 25=g_car^2). [E] the intrinsic deck D=-I+J-J^2=((-1,1,0),(-2,1,0),(-4,3,-1)): D^4=I, chi_D=(x+1)(x^2+1), Spec {i,-1,-i}; the chi2 line is canonically ker[U,V]=(0,0,1)=a-1=the V-fixed line. [C] the geometric-deck identification: D shares chi with the seam deck delta (v146), the diamond fixes chi2=a-1 internally, sharpening the v140 Z3 residue to one concrete identification (NOT closed). An operator lift of v222/v230 + an intrinsic-deck construction; reuses existing data; no new number.

Recorded status: Gaussian 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]

Original ledger status

ARITH.TRICHOTOMY.01

ARITH.TRICHOTOMY.01

The atom trichotomy (2026-06-25): {2,3,5} are ramified/inert/split in the two exceptional CM rings, and each atom is the unique ramified prime of one quadratic facet of K=Q(i,sqrt-3,sqrt5) (v403). Sharpens v222/v230 (atoms read only as CM norms) and v390/v394/v403 (the three facets) into one prime-splitting table. [E] Z[i] (square/seam, tau=i): 2=|Z2| RAMIFIES (2=-i(1+i)^2), 3=N_fam INERT (3 mod 4, norm 9=N_fam^2), 5=g_car SPLITS ((2+i)(2-i), 1 mod 4) -- the carrier rank g_car=5 FACTORS on the seam. [E] Z[omega] (hex/flavor, tau=omega): 3=N_fam RAMIFIES (N(1-omega)=3), 2=|Z2| INERT (norm 4), 5=g_car INERT (norm 25=g_car^2). [E] the ramified prime of each ring IS its atom: Z[i] ramifies at 2 (sheet/seam), Z[omega] at 3 (family/flavor). [E] the three facets Q(i)/Q(sqrt-3)/Q(sqrt5) (disc -4,-3,5) ramify over exactly one atom each (2,3,5), product 2*3*5=30=h(E8); 2 imaginary (CM/dynamic) + 1 real (RM/static) = the v403 reading at the prime level. [C] the seam/flavor/golden reading. Exact number theory composing existing facts; no new number.

Recorded status: Atom 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]

Original ledger status

DIAMOND.EISEN.01

DIAMOND.EISEN.01

The Eisenstein/CP operator -- the hexagonal dual of the Gaussian seam operator v415 (2026-06-25): where v415 put the SQUARE seam (tau=i, mu4) on operators via J=[U,V]/3, this puts the HEX/flavor side (tau=omega, mu3/mu6) on operators and unifies both with the seam into ONE order-30 Coxeter clock. [E] EISENSTEIN DECK: the family rotation P=(1 2 3) has P^3=I, chi_P=x^3-1, P^2+P+I=ONES, so on the plane perp to (1,1,1) it satisfies omega^2+omega+1=0 -- the order-3 dual of J^2=-I. [E] HEX NORM 7 AS OPERATOR: (3I+2P)(3I+2P^2)=7I+6 ONES, Spec {7,7,25} -- 7=N_Z[omega](3+2omega)=scalaron on the omega-plane, 25=g_car^2 on (1,1,1); the dual of v415's (3I+2J)(3I-2J)->{13,13,9}; NEG control (5I+4P)(5I+4P^2)->{21,21,81}, N_omega(5,4)=21!=41 (v222 rigidity). [E] CP CLOCK W=-P^2 (=omega^2*(-1)=rho v233), order 6: W^3=-I, W^2=P, chi_W=x^3+1, Spec {-1,zeta6,zeta6^-1}; delta_CKM,lead=arg(zeta6)=pi/3 (eigenvalue of W), delta_PMNS=arg(zeta6^4)=4pi/3 (eigenvalue of W^4=P^2), W^3=-I the Z2 sheet flip rho^3=-1 (v231/v233/v316/v320); mu6=mu3 x mu2 in one operator. [E] ONE ORDER-30 CLOCK: all flavor-side clocks are powers of zeta30 (h(E8)=30=2*3*5=|Z2|*N_fam*g_car): zeta30^15=-1 (mu2), zeta30^10=omega (mu3), zeta30^6=zeta5 (mu5), zeta30^5=zeta6 (mu6); the SEAM mu4 (i) is NOT a power (4 nmid 30) -- the Galois side (Z/30)^x of order phi(30)=8=rank E8=mu4 x Z2 (totatives {7,13,17,23} order 4); Q(zeta30) carries BOTH E8 invariants (cyclic h=30 flavor hands + Galois rank=8 seam). [C] REALISATIONS + HONEST GAP: J(mu4)/P(mu3)/W=-P^2(mu6)/sigma(mu2) are 3x3 operators, but the CARRIER mu5 (zeta5) has none (needs dim>=4; the golden phi=2cos(pi/5) shows up only as an output-side trace, v313/v349); honest negatives: no U,V-diamond operator carries x^2-x+1 (only -P does), the seam and family clocks do NOT combine ([D,P]!=0, no mu12), and N(3+2 zeta6)=19!=7 (the clean 7 is the omega-norm). An operator lift + synthesis tying v222/v230/v233/v315/v316/v404/v415; no new number.

Recorded status: Eisenstein/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]

Original ledger status

ARITH.NORMTRIPLE.01

ARITH.NORMTRIPLE.01

The cyclotomic norm triple (2026-06-25): the carrier split (3,2) read in the three atom-rings gives (7,13,55)=(scalaron, Delta_Q, quark numerator), and the missing CARRIER-5 clock of v417 is found as the 4x4 Phi5-companion C5 (Z[zeta5], rank phi(5)=4). [E] CARRIER-5 CLOCK: C5 has chi=x^4+x^3+x^2+x+1, C5^5=I, tr=-1 (the four primitive 5th roots); the GOLDEN ratio is its real-part data zeta5+zeta5^4=2cos(72)=(sqrt5-1)/2=1/phi, zeta5^2+zeta5^3=2cos(144)=-(sqrt5+1)/2=-phi (output-side golden, v313/v349; dim 4 -- refines v417's gap from 'no operator' to 'no 3x3 operator, but a clean 4x4 one'). [E] CARRIER NORM = QUARK NUMERATOR: N_Z[zeta5](3+2 zeta5)=det(3I+2 C5)=55=5*11=g_car*||Pl(K)||_1=1^T V^4 1 (v410/v411), the c_u/c_d numerator. [E] THE TRIPLE: det(3I+2 Comp(Phi_n))=(7,13,55) for n=(3,4,5)=(scalaron, Delta_Q, quark numerator) over Z[omega],Z[i],Z[zeta5] (atoms 3,2,5, v416) -- the SAME carrier split (3,2) in three rings, ties v222/v415/v417. [E] NEG CONTROL: the anchor (5,4)->(21,41,461); 21=N_omega(5,4) and 41=10 b1 are named (v222) but the CARRIER ring gives 461 (prime, un-named), so the anchor does NOT reach a named carrier number -- the Phi5/carrier ring separates (3,2)->55 from (5,4)->461. [C] HONEST: (3,2) is FORCED (b+s=5, b^2+s^2=13, v14) not UNIQUE -- a scan over (a>b>=1, a+b<=9) against the named-constant set finds exactly {(2,1)->(3,5,11)=(N_fam,g_car,||Pl(K)||_1), (3,2)->(7,13,55)}, a small ladder; (3,2) is the forced rung carrying the load-bearing triple, NOT the unique clean split. [C] SHARPER (CROSS-SECTOR) DISCRIMINATOR: of the two clean splits ONLY (3,2)->(7,13,55) spans three DIFFERENT physics sectors (gravity=scalaron, flavor=Delta_Q, masses=quark numerator), while (2,1)->(3,5,11) is all-core (N_fam,g_car,Plucker) -- so (3,2) is the UNIQUE cross-sector seed; the ladder reads input (2,1)->output (3,2), difference 4*(1,2,11)=(4,8,44). Exact number theory composing v415/v416/v417/v222; no new physical number.

Recorded status: Cyclotomic 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]