Original claim records.

Original ledger status

QGEO.MODHAM.01

QGEO.MODHAM.01

BEDROCK omega o rho = omega VIA AN EXPLICIT MODULAR HAMILTONIAN (2026-06-21, TOE attack point 2): the next concrete step on the open bedrock QGEO.SYM.01. [E] NON-CIRCULAR upstream: marks=2 chi(S^2)=4 (Gauss-Bonnet, v216) and the order-4 clock z->iz from cross-ratio 2 / j=1728 (v214/v267), so mu4 is DERIVED, not assumed (rho^4=I). [E] for the thermal quasi-free covariance C=1/(1+e^{H1}) the one-particle modular Hamiltonian K=log((1-C)/C) recovered from C round-trips to the seam operator H1 (machine precision). [E] rho C rho^dag=C AND [rho,K]=0 <=> omega o rho = omega, because mu4 curvature couples only modes n-n' in 4Z (i^{n-n'}=1). [E] NEG: a non-mu4 (period-2/Z2) curvature breaks the invariance. [O] residual: the RAW RP-collar C is intrinsically this clock-invariant thermal quasi-free state (Bisognano-Wichmann intrinsicality). Sharpens v198/v210; does NOT close QGEO.SYM.01.

Recorded status: Reduction [E]/[O] (modular bedrock)

Original ledger status

CAR.SM.ANOM.01

CAR.SM.ANOM.01

THE CARRIER HALF-SPINOR IS ONE ANOMALY-FREE SM GENERATION + THE SM RG (2026-06-21, TOE attack point 3): connects the discrete compiler to constructive 4D QFT, closing the spectrum+anomaly+beta sub-question exactly. [E] 16=Lambda^even(C^5)=1+10+5; SU(5) c SO(10): 10+5bar+1 = one SM generation (Q,u^c,d^c,L,e^c,nu^c), 16 Weyl states. [E] ANOMALY-FREE: sum Y=0, sum Y^3=0, [SU2]^2U1=0, [SU3]^2U1=0 (exact Fraction arithmetic). [E] one-loop RG from the carrier content (3 gen + 1 Higgs): (b1,b2,b3)=(41/10,-19/6,-7); b1 numerator 41 = the EM-budget integer (v3/v159), b3=-(11-2 n_f/3) with n_f=2 N_fam. [E] NEG: dropping nu^c leaves an incomplete 15!=16 multiplet; a 4th family shifts b1 off 41/10 (N_fam=3 pins the RG). [C]/[O] the full Epstein-Glaser interacting S-matrix (v269/v271/v273) and the Yukawa sector stay open. Closes the spectrum/anomaly/beta layer; not the interacting S-matrix.

Recorded status: Identity [E] (spectrum+anomaly+RG) + [C]/[O] (S-matrix)

Original ledger status

QGAMB.CLUSTER.01

QGAMB.CLUSTER.01

THE PHYSICAL QG MEASURE AS A GAP-DECOUPLED, CLUSTERING OBJECT (2026-06-21, TOE attack point 4): the honest statement in place of an over-claimed 4D measure for QG.AMB.01/G_metric. [E] the seam transfer spectrum {1,(2/3)^6,(1/3)^6} gives geometric clustering of the connected correlator at rate (2/3)^6, correlation length xi=1/Delta=1/(6 ln(3/2)). [E] finite susceptibility sum (2/3)^{6n}=1/(1-(2/3)^6)=729/665<inf => a well-defined admissible-sector thermodynamic limit (unique vacuum). [E] gap-decoupling (v76): Delta-31/(4pi^2)~1.648>0, the gap survives metric dressing so the physical sector is DECOUPLED from the un-built ambient. [E] NEG: an ungapped transfer (2nd eig->1) sends xi,chi->inf (no clustering). [C] spectral-action dictionary a2=EH, a4=R^2/72 (v36) + KMS beta=1 (v259). [O] the FULL ambient measure QG.AMB.01 is not built -- gap-decoupled and inert, so the physical sector does not need it.

Recorded status: Reduction [E]/[C]/[O] (gap-decoupled measure)

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

Original ledger status

HYP.INJECT.01

HYP.INJECT.01

THE HYPERGRAPH SUBSTRATE SHARPENED -- WHAT A REWRITE MUST INJECT (2026-06-21, TOE attack point 5): turns the open rewrite-to-full-structure question into a precise list. [E] the affine-E8 Kac marks (1,2,3,4,5,6,4,2,3) are the Perron eigenvector (A.marks=2 marks, top eigenvalue 2) -- the Coxeter skeleton is graph-spectral (v298/v299). [E] the subleading eigenvalue is exactly 2cos(pi/5)=golden ratio phi (the icosahedral (2,3,5)/5-fold signature; spectrum {+-2,+-phi,+-1,+-1/phi,0}). [E] HONEST NEGATIVE: the recovery rate (2/3)^6 is NOT any eigenvalue of A (the lazy-update rate (phi+2)/4=0.9045 != 2/3), so the family-recovery dynamics (gap 6 ln(3/2)) is carried by the cusp weights {0,1/3,2/3}, NOT the adjacency. [E] HONEST NEGATIVE: phi0=1/(6pi)+48c3^4 is analytic, not a rational edge fraction (v298). [O] CONCLUSION: a full-structure rewrite must inject exactly two non-graph-spectral data -- the cusp weight 2/3=|Z2|/N_fam and the analytic seed phi0; the open question is precisely delimited, not closed (NOT a derivation of P1/P2).

Recorded status: Reduction [E]/[O] (substrate sharpening)

Original ledger status

GOLD.ATOMS.01

GOLD.ATOMS.01

THE GOLDEN RATIO IS THE g_car=5 SIGNATURE -- THE (2,3,5) ATOMS ARE THE NETWORK SPECTRAL ANGLES (2026-06-21, v312 follow-up made exact). [E] EXACT: the affine-E8 adjacency charpoly factors x(x^2-4)(x^2-1)(x^2-x-1)(x^2+x-1); the golden minimal polynomial x^2-x-1 divides it, so phi=2cos(pi/5)=(1+sqrt5)/2 is an EXACT algebraic eigenvalue (not a numerical near-value). [E] ATOMS = SPECTRAL ANGLES: the non-trivial eigenvalues are 2cos(pi/k) for exactly k in {2,3,5}={|Z2|,N_fam,g_car}: 2cos(pi/2)=0, 2cos(pi/3)=1, 2cos(pi/5)=phi, plus the second 5-fold harmonic 2cos(2pi/5)=1/phi -- the golden ratio is SPECIFICALLY the g_car=5 (5-fold) signature. [E] NEW WITNESS for g_car=5: the 5-fold spectral angle pi/5, structurally distinct from Pascal (v2)/RR (v228)/reverse glue (raises the v305 multiplicity). [E] ICOSAHEDRAL SELECTION: 1/|Z2|+1/N_fam+1/g_car=31/30>1 (spherical => finite 2I => E8); numerator 31=2^g_car-1=248/8=1+h(E8) (the v63/v76 gap-margin numerator), denominator 30=h(E8)=|Z2|*N_fam*g_car. HONEST anti-numerology (v305): the four readings of 31 are ONE anchor-derived quantity, a unification/compression NOT new independent evidence. [E] HONEST NULL: phi is NOT a TFPT phenomenological readout (structural lattice/network quantity, kept out of the data grammar). [C] DIRECTION: phi=2cos(pi/5) is the E8-quasicrystal (Elser-Sloane cut-and-project) ratio -> a candidate aperiodic substrate for the v312 question.

Recorded status: Identity/Lattice [E] (spectral) + [C] (quasicrystal direction)

Original ledger status

COX.COUPLE.01

COX.COUPLE.01

COUPLE OR FACTORIZE? THE ORDER-30 COXETER SECTORS COUPLE AS A CYCLOTOMIC FIELD (2026-06-21, v314 follow-up). The v314 question -- does 30=g_car*(2 N_fam)=5*6 couple the carrier (5-fold, golden, Q(sqrt5)) and family (6=2*3, rational) sectors, or just factorize? [E] GROUP FACTORIZES: gcd(5,6)=1 => Z/30 = Z/5 x Z/6 (CRT, direct product); order-5 subgroup <c^6>, order-6 <c^5> -- group-level decoupled (consistent with the v314 field obstruction). [E] EXPONENTS FACTOR: the E8 exponents = totatives(30) split as totatives(5) x totatives(6); phi(30)=phi(5)phi(6)=4*2=8=rank E8; (m mod5, m mod6) is a bijection onto {1,2,3,4}x{1,5}. [E] FIELD COUPLES: [Q(zeta30):Q]=phi(30)=8=rank E8; Q(zeta30) is the COMPOSITUM of the carrier field Q(zeta5) (contains the golden sqrt5) and the family field Q(zeta6)=Q(zeta3) (contains zeta3). [E] GALOIS = mu4 x Z2: (Z/30)^x=(Z/5)^x x (Z/3)^x=Z/4 x Z/2 (order 8, max element order 4, NOT cyclic Z/8); mu4=(Z/5)^x is the CARRIER Galois, Z2=(Z/3)^x the FAMILY Galois -- so the P2 seam clock mu4 IS the Galois group of the carrier's golden field (refines v223). [E] CARRIER GENERATOR: sqrt5=phi+1/phi=2 phi-1 (the sum of the two golden network eigenvalues) = the quadratic Gauss sum zeta5-zeta5^2-zeta5^3+zeta5^4 in Q(zeta5), g^2=5. [C] VERDICT: 30=5*6 does NOT dynamically entangle the sectors (direct product + the v314 field obstruction) -- it couples them as the cyclotomic compositum Q(zeta30), Galois mu4 x Z2, degree rank E8; the carrier (sqrt5) and family (zeta3) are conjugate sub-data of ONE cyclotomic field, bridged by GALOIS not by a dynamical map.

Recorded status: Identity/Lattice [E] (cyclotomic Galois) + [C] (verdict)

Original ledger status

GALOIS.READOUT.01

GALOIS.READOUT.01

DOES THE GALOIS mu4 x Z2 (v315) ORGANIZE THE PHYSICAL READOUTS? YES -- THE CP PHASES (2026-06-21, v315 follow-up to phenomenology). [E] FAMILY FACTOR: the hexagonal CP unit rho=zeta_6=zeta_30^5 is the order-6=2 N_fam factor c^5 of v315 (5=30/6); the carrier is zeta_5=zeta_30^6 (order 5=g_car, c^6) -- the CP phase lives in the FAMILY factor, not the carrier. [C] CP PHASES (inherits v231/v233): delta_CKM,lead=pi/3=arg(zeta_6), delta_PMNS=4pi/3=arg(zeta_6^4) (the power 4=|mu4|, the seam clock). [E] SHEET FLIP: zeta_6^4=-zeta_6 (rho^3=-1), so delta_PMNS=delta_CKM+pi (the |Z2| sheet); mu6=mu3 x mu2 (family x sheet), zeta_6=-zeta_3^2. [E] GALOIS Z2 = CP CONJUGATION: Gal(Q(zeta_6)/Q)=(Z/6)^x={1,5}=Z2, sigma: zeta_6->zeta_6^5=conj(zeta_6) (delta->-delta) -- the FAMILY Galois factor of mu4 x Z2 IS the physical CP-conjugation symmetry. [E] CARRIER STATIC: zeta_5=zeta_30^6 (the golden sqrt5) carries NO phase readout -- mu4=(Z/5)^x organizes the lattice/spectrum, not a CP phase. [E] HONEST SEPARATION: the magnitudes (sin^2 theta12=1/3-phi0/2, phi0=1/(6pi)+48c3^4 transcendental) are NOT in any Q(zeta_n) -- Galois organizes PHASES (cyclotomic), the magnitudes are the analytic seed. [C] VERDICT: the v315 Galois coupling reaches SM phenomenology through the FAMILY (order-6) factor -- the CP phases are its cyclotomic data (rho=zeta_6=zeta_30^5, mu6=mu3 x mu2, Gal Z2=CP conjugation); the carrier (mu4/golden) factor is static; the magnitudes are the analytic seed (v314 field split).

Recorded status: Identity/Lattice [E] (cyclotomic CP) + [C] (physical identification)

Original ledger status

GALOIS.FAMILY.01

GALOIS.FAMILY.01

ARE THE 3 GENERATIONS A mu3/GALOIS ORBIT? YES (mu3), REFINED 1+2 BY GALOIS (2026-06-21, v316 follow-up to the generation structure). [E] GENERATIONS = CUBE ROOTS: the 3 cusp weights {0,1/3,2/3} (Spec(Q+)=3a+1={1,2,3}=A3 exponents) map under w->e^{2 pi i w} to the 3rd roots of unity {1,zeta_3,zeta_3^2}. [E] mu3 ORBIT (transitive): the cyclic family symmetry w->w+1/3 mod 1 permutes them cyclically -- ONE transitive Z/3=mu3 orbit (the family IS the cube-root orbit). [E] RECOVERY: the transfer eigenvalues (1-w)^6={1,(2/3)^6,(1/3)^6} attach to the weights; the attractor (eigenvalue 1, the stationary law, v56) is the w=0 weight. [E] GALOIS REFINEMENT 1+2: Gal(Q(zeta3)/Q)=Z2, sigma: zeta_3->zeta_3^2 acts on weights by w->2w mod 1, FIXING w=0 (rational) and SWAPPING w=1/3<->w=2/3 -- so the Galois orbit is 1 (fixed) + 2 (pair), NOT transitive. [E] FIXED = ATTRACTOR: the Galois-fixed w=0 <-> transfer eigenvalue 1 (the law); the Galois-conjugate pair w=1/3,2/3 <-> the decaying modes (2/3)^6,(1/3)^6 (the hierarchy) -- selection = the rational generation. [E] SAME Z2 AS CP CONJUGATION (v316): sigma: zeta_3->zeta_3^2=conj(zeta_3). [E] COUNTS: N_fam=3=|mu3|=#weights=|Spec(Q+)| (A3 exponents {1,2,3}). [C] VERDICT: the 3 generations ARE a single mu3 (cyclic family) orbit {1,zeta_3,zeta_3^2}; the Galois group refines it to 1 (rational=the recovery attractor) + 2 (conjugate pair=the hierarchy), that Z2 = the v316 CP conjugation; the family STRUCTURE is arithmetic, the mass MAGNITUDES stay the analytic seed (NOT derived).

Recorded status: Identity/Lattice [E] (mu3+Galois orbit) + [C] (verdict)

Original ledger status

ARITH.CAPSTONE.01

ARITH.CAPSTONE.01

THE CAPSTONE: THE SM STRUCTURAL SECTOR IS Q(zeta30) + GALOIS mu4 x Z2, COMPLETE INPUT {a, pi, v_geo} (2026-06-21, synthesis of the v313-v317 arc). [E] ARITHMETIC SKELETON: the SM STRUCTURAL sector (3 generations, 2 CP phases, the orbit/hierarchy ordering) lives in the cyclotomic field Q(zeta30): [Q(zeta30):Q]=phi(30)=8=rank E8, 30=|Z2|*N_fam*g_car=h(E8), Galois (Z/30)^x=mu4 x Z2 (order 8) -- carrier mu4=(Z/5)^x (golden sqrt5, v313/v315), family/sheet Z2=(Z/3)^x (zeta3=CP conjugation, v316); the 3 generations = the mu3 cube-root orbit (v317), the 2 CP phases = the zeta6 family-factor data (v316). [E] RIGIDITY: forced by the anchor atoms {|Z2|,N_fam,g_car}={2,3,5}=elementary-symmetric data of a=(1,1,2); 30=2*3*5 -- no freedom in the skeleton. [E] MAGNITUDE REDUCTION: the seed phi0=(|mu4|/N_fam)c3+Omega_adm c3^4=(4/3)c3+48 c3^4 (c3=1/(8pi)) is a PURE function of pi (no free parameters), coefficients anchor-derived (4/3=|mu4|/N_fam, 48=Omega_adm=N_fam*dim_Splus); so the magnitudes (sin^2 theta12=1/3-phi0/2) are {a,pi}-determined, transcendental (NOT cyclotomic) but NOT free. [E] FREE INVENTORY: dimensionless free parameters = 0 (everything is {a,pi}); pi the unique transcendental primitive (ARCH.CORE.01/v53); v_geo the unique dimensionful input (No-Unit Theorem v153/v78) -- complete input = {a, pi, v_geo}. [O] HONEST RESIDUAL: this rigidity holds GIVEN the axioms; it does NOT prove the raw seam REALIZES the structure -- the open bedrock QGEO.SYM.01/SEAM.EQUIV.01 stays [O]. VERDICT: SM structural sector = Q(zeta30)+Galois mu4 x Z2 (rigid, anchor-forced, degree=rank E8); magnitudes = {a,pi}-transcendental (phi0); the only genuinely free datum is v_geo; dimensionless free parameters: 0.

Recorded status: Synthesis/inventory [E] (arithmetic + {a;pi} reduction) + [O] (seam realisation)

Original ledger status

RATE.TRANSLATE.01

RATE.TRANSLATE.01

DO THE DISCRETE-KERNEL AND DYNAMIC RATES TRANSLATE? AN EXACT NUMBER-FIELD SPLIT (2026-06-21, v312/v313 follow-up). [E] FIELD SPLIT: the affine-E8 adjacency spectrum is the rational part {0,+-1,+-2} in Q plus the golden part {+-phi,+-1/phi} in Q(sqrt5) (min poly x^2-x-1, discriminant 5); the dynamic transfer spectrum {1,(2/3)^6,(1/3)^6} is ENTIRELY rational (in Q). [E] TRANSLATION (the (2,3)-fold/family sector): the rational discrete angles 2cos(pi/2)=0 (|Z2|=2) and 2cos(pi/3)=1 (N_fam=3) are the SAME atoms that build the recovery rate (2/3)^6=(|Z2|/N_fam)^(2 N_fam) in Q -- same field, same atoms, so the family/sheet rates DO translate. [E] NO-TRANSLATION (the 5-fold/carrier sector): phi in Q(sqrt5) minus Q has NO rational dynamic image (2/3 is neither an adjacency nor a lazy-update eigenvalue; heat-kernel t=Delta/(2-phi)~6.37 not clean) -- the carrier 5-fold is STATIC-only (builds the lattice/spectrum, not a dynamic rate). [E] SHARED CLOCK: both are facets of the order-30 Coxeter element, 30=h(E8)=g_car*(2 N_fam)=5*6; the golden in the order-5 factor, the recovery exponent 6=2 N_fam=30/g_car in the order-6=2*3 factor. [E] QUASICRYSTAL: E8=H4+phi H4 (240=2*120, 120=|2I|=|R+(E8)|), so the phi cut-and-project carries the 5-fold carrier (Q(sqrt5)) but the cusp weights {0,1/3,2/3} are RATIONAL (3-fold), a separate parabolic datum -- the substrate carries the carrier, NOT the family dynamics (confirms v313/v312). [C]/[O] VERDICT: a static<->dynamic translation functor exists ONLY on the rational (2,3-fold/family) sector; the carrier 5-fold is field-obstructed (static-only), the bridge holding both is the order-30 Coxeter element.

Recorded status: Identity/Lattice [E] (number-field split) + [C]/[O] (functor verdict)

Original ledger status

TRANSLATE.CLOCK.01

TRANSLATE.CLOCK.01

THE TRANSLATION CLOCK: THE DISCRETE<->DYNAMIC BRIDGE IS THE ORDER-30 COXETER ELEMENT, A CLOCK WITH TWO COPRIME HANDS 5 x 6 (2026-06-22, synthesis of the v313-v318 arc + v124/v55, answering 'is the static<->dynamic translation a clock running 0,1,2,3,4,5 or 1,2,3,4,5?'). [E] TRANSLATION IS A CLOCK: the only object holding both the static carrier (Q(sqrt5)) and the dynamic family (rational) data is the order-30 Coxeter element (v314); 30=h(E8)=g_car*(2 N_fam)=5*6, gcd(5,6)=1 => Z/30=Z/5 x Z/6 (two coprime hands, v315). [E] DYNAMIC HAND RUNS 0..5: the dynamic factor is Z/6=2 N_fam (ticks {0,1,2,3,4,5}); the recovery exponent is EXACTLY 6=|Z/6|=2 N_fam, rate (2/3)^6=(|Z2|/N_fam)^(2 N_fam); the order-6 generator is c^5 (zeta_6=zeta_30^5, the hexagonal CP unit, v316). [E] POSITION 0=THE CONSERVED LAW, 1..=THE LIVE PHASES: the resummed translation clock rate(n)=-p2 ln(1-n/N_fam) (v124) has rate(0)=0 (the attractor/stationary law, eigenvalue 1, v56) and live modes rate(1)=6 ln(3/2), spectrum {1,(2/3)^6,(1/3)^6}; the E8 live phases (Coxeter exponents=totatives of 30) start at 1 ({1,7,...,29}), the 0 phase is NOT a totative -- so '0,1,2,3,4,5' is the law-inclusive labelling, '1,2,3,4,5' the live-only labelling. [E] STATIC HAND RUNS 1..5: the static factor is Z/5=g_car (ticks {1,2,3,4,5}); golden field Q(sqrt5) (phi=2cos(pi/5), min poly x^2-x-1, disc 5), field-obstructed (no rational dynamic image, v314) -- static-only; zeta_5=zeta_30^6 carries no phase (v316). [E] ONE FULL TURN=30: lcm(5,6)=30=h(E8)=the full Coxeter period; rank E8=8=phi(30)=#live phases pairing m+(30-m)=30 into |mu4|=4 invariant planes (v55). [C] VERDICT: the discrete->dynamic translation IS the order-30 clock = (static 5-ring) x (dynamic 6-ring); the dynamic hand {0,...,5} carries the rate (exponent 6=2 N_fam), the static hand {1,...,5} the golden carrier (no rate); '0 vs 1' = law-inclusive vs live-only.

Recorded status: Synthesis/Identity [E] (clock factorization + hand arithmetic) + [C] (one-clock reading)

Original ledger status

GALOIS.CP.PREDICT.01

GALOIS.CP.PREDICT.01

A NEW FALSIFIABLE PREDICTION FROM THE GALOIS STRUCTURE: THE TWO CP PHASES ARE LOCKED, delta_PMNS = delta_CKM,lead + pi (2026-06-22, the v316 follow-up turned testable). [E] ONE UNIT TWO POWERS: both CP phases are powers of one hexagonal unit rho=zeta_6 in the family Galois factor (v316): delta_CKM,lead=arg(rho)=pi/3 (60 deg), delta_PMNS=arg(rho^4)=4pi/3 (240 deg), rho^4=-rho. [E] FORCED RELATION: delta_PMNS-delta_CKM,lead=pi exactly (the Z2 sheet flip rho^3=-1), equivalently delta_PMNS=4*delta_CKM,lead -- the quark and lepton leading CP phases are NOT independent (one is fixed by the other). [C] PREDICTION OF RECORD: delta_PMNS,lead=240 deg, forced from delta_CKM,lead=60 deg + the sheet flip (180 deg) -- upgrades delta_PMNS from an assigned texture to a Galois-forced relation to the measured quark phase. [N] CURRENTLY COMPATIBLE: 240 deg lies within the broad current global-fit range for the PMNS Dirac phase (NuFIT 6.0, normal ordering); decisive test = DUNE/Hyper-K/JUNO. [X] KILL TEST: a measured delta_PMNS robustly incompatible with delta_CKM,lead+pi=240 deg (beyond the sub-leading budget, at >3 sigma) falsifies the Galois-CP organization (v316/v317). A genuine NEW falsifiable cross-prediction from the v313-v319 arithmetic arc; the leading-order/holonomy reading is [C] like delta_CKM, the relation itself [E], the kill test [X]; does NOT derive the magnitudes.

Recorded status: Identity [E] (Galois relation) + [C] (prediction) + [X] (kill test)

Original ledger status

KILL.BOARD.01

KILL.BOARD.01

THE FORWARD KILL-TEST BOARD: THE DECISIVE UPCOMING MEASUREMENTS, RANKED (2026-06-22, forward companion to v307's current-data board). [N] assembles the decisive NEXT measurements, each LOCKED to a freeze_file.csv kill row (so the test and the frozen signal cannot drift apart): #1 JUNO sin^2 theta12=0.306747 (fastest, sub-percent), #2 CMB-S4/LiteBIRD r in [0.0033,0.0048] (kill robust r>0.01), #3 DESI/Euclid w=-1 (kill robust w!=-1), #4 DUNE/Hyper-K delta_PMNS=240deg=delta_CKM,lead+pi (the NEW v320 Galois-CP relation; kill if away from 240 deg at >3 sigma), #5 DUNE/LEGEND/nEXO normal ordering + small m_betabeta, #6 PSI n2EDM theta_eff=0, #7 JUNO sin^2 theta13=0.0231 (now ~2 sigma), #8 LiteBIRD/Simons beta=0.2424 deg. [N] COVERAGE: every entry backed by a freeze_file kill row; the v320 CP relation is on the board; JUNO theta12 rank 1; >=7 decisive tests each with a concrete kill threshold. A forward decision ledger (timelines/reach are the publicly-stated experimental targets, not TFPT outputs); complements v307; no new physics.

Recorded status: Numerical/data [N] (forward decision ledger)

Original ledger status

GALOIS.CP.SHARPEN.01

GALOIS.CP.SHARPEN.01

THE v320 CP-LOCK PREDICTION SHARPENED INTO A QUANTITATIVE PRE-REGISTERED KILL TEST (2026-06-22). [E] DISCRETE LADDER: the leading CP phase sits on the six hexagonal nodes arg(rho^k)=k*60 deg; delta_CKM,lead=60 (node 1), delta_PMNS,lead=240 (node 4). [E] MULTIPLIER = DECK ORDER: delta_PMNS,lead=|mu4|*delta_CKM,lead=4*(pi/3)=4pi/3=delta_CKM,lead+pi (rho^4=-rho) -- the node selector IS the seam clock order |mu4|=4. [C] SUB-LEADING BUDGET: delta_CKM,full=pi/3+3 lambda^2 (~68.7 deg); the lepton sub-leading is a SEPARATE open holonomy term bounded by ~3 lambda^2~8.7 deg => band 240 +- ~9 deg. [N] CURRENT TENSION: vs NuFIT 6.0 NO (delta_CP=212 +26/-41 deg) the leading 240 deg sits at +1.08 sigma, band lower edge ~231 deg at +0.74 sigma -- compatible today. [X] SHARPENED KILL: the nearest wrong node (180/300) is 60 deg away, far beyond the budget; DUNE/Hyper-K at ~5-15 deg discriminate the node, >3 sigma outside kills the lock. [E] DISCRIMINATION POWER: an anarchic delta_CP hits the band with p~5% and node 4 (not 1/3/5) 1-in-6. Sharpens v320; no magnitudes derived.

Recorded status: Identity [E] (node+multiplier) + [C] (budget) + [N] (tension) + [X] (kill test)

Original ledger status

QGEO.BW.01

QGEO.BW.01

THE KEYSTONE PUSHED ONE STEP -- BISOGNANO-WICHMANN MAKES THE SEAM MODULAR FLOW GEOMETRIC (2026-06-22): the mu4 deck invariance is NOT an independent axiom. [E] CLOCK = GEOMETRIC ROTATION: rho=diag(i^n)=exp(i(pi/2)L), L=diag(n) the seam rotation generator; rho^4=exp(i2pi L)=I -- mu4 in U(1)_rot (quarter turns). [E] BW: a rotation-covariant covariance C=f(L) gives K=log((1-C)/C)=g(L), so [K,L]=0 (the modular flow commutes with all rotations) AND [rho,K]=[rho,C]=0 -- the mu4 clock is a modular symmetry FOR FREE (no fine-tuned curvature, unlike v309). [E] DISCRIMINATOR vs v309: a period-4 curvature preserves the clock ([rho,K]=0) but its modular flow is NOT geometric ([K,L]!=0) -- BW is strictly stronger (pins the whole rotation group, not just mu4). [E] NEG: a non-rotation-covariant C breaks [rho,K]!=0. [C] LINKED BEDROCK: GIVEN the seam is the (E8)_1 chiral net (v308/SEAM.EQUIV.01), Bisognano-Wichmann/Hislop-Longo make the vacuum modular flow geometric => QGEO.SYM.01 (omega o rho=omega) is DOWNSTREAM of SEAM.EQUIV.01 + a rotation-invariant vacuum, NOT an independent axiom (two open items collapse toward one). [O] residual: the raw collar vacuum is rotation-invariant (cleaner than v309's bespoke thermal state, shared with v308). Sharpens v309/v198; does NOT close QGEO.SYM.01.

Recorded status: Reduction [E]/[C]/[O] (BW geometric modular flow)

Original ledger status

HYP.FIBER.01

HYP.FIBER.01

THE MINIMAL HYPERGRAPH SUBSTRATE THAT WORKS -- A (2,3,5)-NETWORK FIBERED BY A 3-FOLD CUSP CHANNEL (2026-06-22, the constructive v312 follow-up): reproduces BOTH the E8 skeleton AND the recovery gap. [E] NETWORK FACTOR (carrier/5-fold): T_net=(A+2I)/4 fixes the Kac marks (eigenvalue 1 = E8 skeleton), subleading (phi+2)/4 (golden); (2/3)^6 NOT in its spectrum (the v312 negative). [E] CUSP FIBER (family/3-fold): T_cusp=diag((1-w)^{2N_fam}), w in {0,1/3,2/3} (N_fam=3, v317), spectrum {1,(2/3)^6,(1/3)^6}, recovery gap at w=1/3 (v76/v221). [E] FIBERED SUBSTRATE CARRIES BOTH: T=T_net (x) T_cusp has top eigenvalue 1 (eigenvector marks (x) w=0 = E8 skeleton x democratic cusp) AND (2/3)^6 as a genuine eigenvalue (network attractor x cusp subleading). [E] HONEST INJECTION (v312): without the fiber (T_net (x) I_3) there is NO (2/3)^6 -- the cusp datum is injected, not graph-spectral; substrate = network x cusp = the v315 split 30=g_car*(2 N_fam)=5*6, the gap living entirely in the family factor. [E] MINIMALITY: the smallest fiber is the 3-node cusp (=N_fam); a 2-node fiber cannot hold 3 weights -> minimal substrate = (2,3,5)-net x 3-cusp = order-30 (v319 clock). [C] VERDICT: a CONSISTENT fibered realization (carrier x family) matching the arithmetic 5x6 split, but the cusp weight stays injected (v312) -- not a derivation of 2/3 from a pure rewrite. Sharpens v312; the open rewrite question is unchanged.

Recorded status: Construction [E]/[C] (fibered substrate)

Original ledger status

FORM.SEAMEQUIV.01

FORM.SEAMEQUIV.01

LEAN: SEAM.EQUIV.01 COMPOSITION CHAIN (2026-06-22). Lean 4 formalisation (TfptCarrier/SeamEquivChain.lean) of the v308 closing chain: the four nodes GapPositive -> InvertibleSRE -> HolomorphicC8 -> SeamIsE8 assembled as a well-typed composition theorem seamEquivChain, with the three cited literature steps (Kitaev free-fermion invertibility; Mueger / Kawahigashi-Longo-Mueger holomorphy; Conway-Sloane E8 uniqueness) declared as named axioms and the carrier recovery gap (the OS step) as the single open input. #print axioms seamEquivChain confirms the residual is EXACTLY those named steps + recovery_gap (no hidden assumption). Plus a decide-proven discriminator: primariesE8=1 != primariesD8=4 (|det Cartan| distinguishes the holomorphic E8 from the same-central-charge rival D8=SO(16)). Built end-to-end (lake build, 3357 jobs) on Lean v4.29.1 + Mathlib. The VALUE is the machine-checked composition + the axiom audit (which pins the keystone residual to the named cited theorems + the one OS input), NOT a from-scratch proof of the cited steps -- so it does NOT close SEAM.EQUIV.01.

Recorded status: Formal

Original ledger status

QGEO.KEYSTONE.01

QGEO.KEYSTONE.01

THE SEAM KEYSTONE AS ONE CITABLE THEOREM (2026-06-22): the raw seam state is the flat tau=i pillowcase state, with EXACTLY ONE open lemma. Assembles the keystone pieces into one statement -- IF (raw RP-collar seam state = flat tau=i pillowcase / rotation-invariant state) THEN 4 square marks + mu4 deck + omega o rho=omega + holomorphic c=8 => (E8)_1, with the carrier recovery gap as input. [E] FOUR SQUARE MARKS: n=2chi(S^2)=4 (Gauss-Bonnet, v216); cross-ratio 2 => j=1728 (order-4 CM, v214/v267). [E] FLAT PILLOWCASE: S^2(2,2,2,2), chi_orb=2-4(1-1/2)=0 => flat tau=i (Troyanov). [E] MU4 FINGERPRINT: DtN sub-principal at m=0 mod 4 (v201/v280). [E] HOLOMORPHY SELECTOR: det Cartan(E8)=1 vs D8=4 (v83/v143/v308). [E] INPUT GAP: Delta=6 ln(3/2)>0 (v76/v302). [O] ONE OPEN LEMMA: the raw collar state IS the flat tau=i pillowcase / rotation-invariant state, SHARED by both bedrock IDs (QGEO.SYM.01, SEAM.EQUIV.01; v323), machine-pinned in Lean (FORM.SEAMEQUIV.01 + FORM.QGEO.BW.01). An assembly/reduction certificate (like v176/v261), NOT a closure.

Recorded status: Synthesis/reduction [E]/[O] (keystone-as-one-theorem)

Original ledger status

FR.SUITE.01

FR.SUITE.01

THE F_transfer SOLVER SUITE (2026-06-22): the four transfer readouts as ONE runnable harness, each a gapped relaxation to a unique attractor, with values + uncertainties + honest typing (productises FR.DYNAMICS.01/v303). [E] F_pole (Koide): Moebius contraction to Q*=2/3 with multiplier (2/3)^6 = the seam-clock subleading eigenvalue, unique attractor at the SEAM rate. [C] F_Boltzmann (eta_B): washout contraction to the balance 6.1e-11, monotone (H-theorem), external thermal rate. [C] F_relic (axion): the comoving number N=E/omega is the adiabatic invariant, the relic freezes (seed theta_i=3pi/5), cosmological rate. [I] F_QCD (m_p/m_e): 1-loop RG with carrier b0=7 flows to the Gaussian UV fixed point, Lambda_QCD generated; standard RG. [N] F_RareKaon (bridge): BR(K+)=9.45e-11 on NA62 2016-2024 (v202). [O] SHARED SHAPE: all 5 are gapped relaxations to a unique attractor; only F_pole has the seam rate (2/3)^6, the other 4 share the SHAPE with external rates honestly fenced (v187/v303) -- the suite makes the frontier measurable WITHOUT claiming the external rates.

Recorded status: Numerical/synthesis [E]/[C]/[I] (F_transfer solver suite)

Original ledger status

HYP.REWRITE.01

HYP.REWRITE.01

DERIVING THE CUSP WEIGHT 2/3 FROM A MINIMAL REWRITE (2026-06-22, sharpening HYP.FIBER.01/v324 + HYP.INJECT.01/v312). A minimal local rule -- a family channel with N_fam=3 slots, one absorbing attractor (w=0) and |Z2|=2 surviving (the Z2 pair) -- supplies the cusp fiber. [E] MINIMAL REWRITE: M=[[1,0,0],[0,1/3,1/3],[0,1/3,1/3]] has spectrum {1,2/3,0}; the recovery survival 2/3=(N_fam-1)/N_fam=|Z2|/N_fam EMERGES from the rule arity, not injected. [E] RECOVERY RATE DERIVED: over the order-6=2 N_fam dynamic hand the rate is (2/3)^6=64/729 = the recovery gap (v76/v324), derived not put in. [E] NON-GRAPH-SPECTRAL (proof, sharpening v312): 2/3 is NOT a root of the affine-E8 charpoly x(x^2-4)(x^2-1)(x^2-x-1)(x^2+x-1) (p(2/3)=-3520/19683 != 0), so the recovery rate cannot be an adjacency eigenvalue -- necessarily the branching channel. [E] ATTRACTOR: the absorbing state (eigenvalue 1) is the democratic w=0 law (v317). [O] HONEST RESIDUAL: the rewrite DERIVES 2/3 from the arity {|Z2|,N_fam}={2,3} (the anchor atoms, still the input P2/v23) -- v324's injected datum REDUCED to the anchor arity, not derived from nothing. UPDATE 2026-07-15 (v486/HYP.REWRITE.02): the uniform rule is the DEGENERATE case (spectrum {2/3, 0}); the unique lazy Z2-pair walk (stay 1/2, hop 1/6, leak 1/3) generates the FULL physical spectrum {1, (2/3)^6, (1/3)^6} over the same order-6 hand -- the (1/3)^6 mode now has a local-rule origin; superseded as full-spectrum generator, the 2/3 arity story unchanged.

Recorded status: Construction/proof [E]/[O] (cusp weight from a minimal rewrite)