Original claim records.

Original ledger status

TOPO.BRIESKORN.01

TOPO.BRIESKORN.01

BRIESKORN CAPSTONE (2026-06-17): the (2,3,5) Brieskorn singularity x^2+y^3+z^5 is the ONE generator of the discrete skeleton -- the capstone of the icosahedral round (v55/v219/v223/v232/v233). Its three exponents ARE the atoms (|Z2|,N_fam,g_car)=(2,3,5). (1) MILNOR NUMBER = the '8': mu=(2-1)(3-1)(5-1)=(|Z2|-1)(N_fam-1)(g_car-1)=1*2*4=8=rank E8=#exceptional P^1 = the '8' in c3=1/(8 pi), a FIFTH independent origin (after geometry=2|mu4|, lattice=rank E8, gravity=8pi, Coxeter=phi(30)). (2) MONODROMY = the order-30 Coxeter cycle: the Milnor monodromy eigenvalues lambda=zeta_2^j1 zeta_3^j2 zeta_5^j3 (1<=ji<=ai-1) are the eight primitive 30th roots e^{2pi i m/30}, m in {1,7,11,13,17,19,23,29} = the E8 exponents; characteristic polynomial = Phi_30 (degree phi(30)=8=mu), so the Milnor monodromy IS the E8 Coxeter element of order 30=h(E8) (v55). (3) BOTH CLOCKS are facets of this one monodromy: the monodromy GROUP <h>=Z/30=Z/2(sheet)xZ/3(family/triality)xZ/5(carrier) carries the mu3 triality (the CP phase omega, v233) as the order-3 power h^10; the GALOIS group Gal(Q(zeta_30)/Q)=(Z/30)^x=Z/2xZ/4 carries the order-4 element (x7) = the mu4 clock acting on the spectrum (v223). (4) Milnor lattice=E8 (the resolution intersection form, v232/v234), link=Poincare homology sphere S^3/2I. (5) SYNTHESIS: one singularity x^2+y^3+z^5 generates the atoms (exponents), the 8 (Milnor number), E8 (Milnor lattice), the order-30 cycle (monodromy), both clocks (mu3 in <h>, mu4 in Galois) and the seam (link) -- not many numbers sharing {2,3,5} but one icosahedral singularity read several ways. Unifies the icosahedral round; does NOT close a gate.

Recorded status: Lattice/Topology (exact) [E]/[I]

Original ledger status

CONTRACT.QFT4D.01

CONTRACT.QFT4D.01

4D LAGRANGIAN VIA THE SPECTRAL ACTION (2026-06-17): the honest CONTRACT for the Phase-3 structural gap (the 2d chiral seam net v156/v175 + its dynamics v238-v243 -> the physical 4d theory). The natural TFPT bridge is NOT a holographic guess but Connes' spectral action: a SINGLE Dirac operator whose spectral action Tr f(D/Lambda) yields gravity AND the matter (gauge+Higgs) Lagrangian. The gravity half is verified (v36: R+R^2); this types the matter half as a contract and checks the arithmetic pieces. (1) [E] carrier spinor = one generation: carrier D5(+)A3 = SO(10)xSO(6) (=SO(16) grading, v156); the SO(10) half-spinor = dim S^+ = 2^(g_car-1) = 16 = one SM generation (15 Weyl fermions + nu_R), N_fam = 3 -- the carrier carries the SM matter representation. (2) [E] SM gauge group inside the carrier: SU(3)xSU(2)xU(1) (rank 4, dim 12) in SU(5) (rank 4, dim 24) in SO(10)=D5 (rank 5, dim 45); color SU(3) also in A3=SU(4) (Pati-Salam, dim 15); rank(D5)+rank(A3)=8=rank E8. (3) [E] one Dirac operator -> gravity + matter: the Seeley-DeWitt expansion gives a2~R (Einstein-Hilbert) and a4~(R^2, Weyl^2, F_{mu nu}F^{mu nu} Yang-Mills, |D phi|^2 Higgs); gravity half machine-verified (v36), Yang-Mills a4 standard Gilkey. (4) [X] falsifiable hooks: spectral-action boundary relations g3=g2=sqrt(5/3)g1 and a Higgs-quartic relation (Chamseddine-Connes-Marcolli). (5) [O] CONTRACT.QFT4D.01 obligations: (i) the seam induces the SM Dirac operator D; (ii) the finite NCG geometry = the carrier algebra (FORM.P2.02); (iii) the spectral action of D reproduces the measured SM couplings under the v36 gravity normalisation -> then the 4d SM+gravity Lagrangian is an OUTPUT. The genuine Phase-3 target, NOT closed

Recorded status: Contract [O] (with [E] arithmetic + [X] hooks)

Original ledger status

PS.SPECACT.01

PS.SPECACT.01

SPECTRAL-ACTION HEAT-KERNEL EXPANSION (a0,a2,a4) + EXPLICIT kappa(f2/f0) (2026-06-17): closes the open obligation v252 #11 (spectral-action expansion) and makes the kappa-dependence on the cutoff moments explicit (v253 #5). The bosonic spectral action S = Tr f(D/Lambda) has the Seeley-DeWitt expansion S ~ 2 f4 Lambda^4 a0 + 2 f2 Lambda^2 a2 + f0 a4 (f4,f2 moments, f0=f(0)). (1) [E] expansion structure: a0=cosmological (N int sqrt g), a2=Einstein-Hilbert + Higgs mass, a4=Yang-Mills + Weyl^2 + R^2 + Higgs quartic + R|H|^2, with N=dim H_F=96 (Gilkey/Chamseddine-Connes). (2) [E] trace inputs a=Tr(Y+Y)=2.96, b=Tr((Y+Y)^2)=2.92, b/a^2=0.333=1/3 (top-Yukawa dominated, the Chamseddine-Connes value). (3) [E] gauge normalisation: the a4 Yang-Mills term fixes g3=g2=sqrt(5/3)g1, sin^2 thetaW=(sum T3^2)/(sum Q^2)=3/8 (cross-check v245). (4) [C] Higgs quartic: lambda(Lambda) ~ g^2 b/a^2 = g^2/3; with the sigma ingredient present (v254) this is the famous ~125 GeV (vs ~170 GeV without sigma) Higgs-mass prediction after RG running (m_H vs 125.25 GeV); exact coefficient + running cited. (5) [E] scalaron from R^2: the gravitational a4 carries a Weyl^2 + R^2 term with coefficient ~ f0 N; the R^2 spin-0 mode IS the Starobinsky scalaron, M_s its mass (R+R^2 gravity emerges from the spectral action). (6) [C] kappa made explicit: a2 carries f2 (Einstein-Hilbert), a4 carries f0 (R^2/scalaron + gauge), so kappa=M_PS/M_s=sqrt((f2/f0) c_PS/c_grav) is an explicit ratio of the two moments x traces over H_F; the RG value kappa~1.3 (v253) fixes f2/f0 to O(1). (7) [O] the exact kappa decimal and exact lambda(Lambda) need the cutoff function f fixed -- the last genuinely open input.

Recorded status: Numerical (spectral action) [E]/[C]/[O]

Original ledger status

SCALE.OVERDET.01

SCALE.OVERDET.01

THE SINGLE MASS ANCHOR IS OVER-DETERMINED; NO DERIVABLE ABSOLUTE SCALE IS A THEOREM (2026-06-18): sharpens the No-Unit theorem (v153). [E] one anchor: every dimensionful output is a pure number x M_bar^d (rho_Lambda/M_bar^4 = (3/4 pi^2) e^{-2 alpha^-1} = 7.13e-121 v60/v7, M_scal/M_bar = c3^{7/2} v7, the whole mass spectrum); the absolute neutrino scale (v272) and v_geo are the SAME anchor. [N] OVER-DETERMINATION: two independent routes to M_bar agree -- Route 1 (gravity) M_bar = (8 pi G)^{-1/2} = 2.4353e18 GeV; Route 2 (cosmology) invert the compiler prediction rho_Lambda/M_bar^4 with the measured rho_Lambda^{1/4} = 2.24 meV -> M_bar = 2.438e18 GeV, agreeing to 0.11%. [E] the anchor is the gravitational unit (G), the one measured dimensionful input of all physics (modern SI fixes hbar, c exactly). [E] THEOREM not gap: the seam is a conformal c=8 chiral CFT (v157/v158), scale-invariant by construction so provably no intrinsic scale; the scale is gravitational, entering only through the ambient measure (QG.AMB.01). [A] TFPT is scale-complete up to one over-determined anchor (the Planck mass) -- maximal predictivity for a dimensionless compiler, not a missing derivation.

Recorded status: Identity [E] + over-determination [N] + re-typing [A]

Original ledger status

REDTEAM.F.01

REDTEAM.F.01

RED TEAM Target F -- adversarial audit of the perturbative 4D-QFT + scale round (v269-v275), published in release 5.2. TWO attacks land and force a narrowing (now folded into v269/v274); the rest survive as typed. (1) GRAVITY S_pert NON-UNITARY: power-counting renormalizability is not unitarity -- the spectral-action R^2/Weyl^2 sector gives a 4-derivative propagator 1/(p^2(p^2+M^2)) whose massive spin-2 mode has a NEGATIVE residue (the Stelle ghost), so S_pert is unitary for the matter+gauge sector only; the gravity perturbative S-matrix carries the ghost, which is exactly why the nonperturbative QG.AMB.01 (asymptotic safety v207 / boundary (E8)_1 net) is the real frontier, not a new gap. (2) OVER-DETERMINATION CONDITIONAL: v274 Route-2 inverts rho_Lambda/M_bar^4=(3/4pi^2)e^{-2 alpha^-1} = LAMBDA.BRANCH.01 [C], so the 0.11% gravity-vs-cosmology agreement is conditional on the Lambda-branch (the gravity route is unconditional). Already-honest: J_PMNS (v270) inherits delta's [C] provenance (assembled mu6/triality phase, not an M_nu output); the nu-scale (v272) is [O] with the NO floor Sigma m_nu=0.0586 eV as the one kill test. FIREWALL HOLDS: no positive-claim doc carries an unscoped overclaim (the red-team paper itself is excluded as it quotes forbidden phrases to forbid them). Verdict: SURVIVES (narrowed).

Recorded status: Red-team [P] (survives, narrowed)

Original ledger status

QFT4D.SPERT.04

QFT4D.SPERT.04

S_pert -> S_phys LSZ BRIDGE + ONE-LOOP UNITARITY (2026-06-18): connects the EG perturbative S-matrix (v269/v271/v273) to the physical asymptotic S-matrix (S_phys = LSZ on the OS-reconstructed Wightman functions, v240); the three-layer S-matrix is now S_top (v243) | S_pert (v269) --LSZ--> S_phys (v240). [E] LSZ BRIDGE: S_phys matrix elements = (amputate external legs)(on-shell residue sqrt(Z)) of the connected time-ordered correlators, and the EG time-ordered products of S_pert ARE those correlators (the OS Wick-rotation of the seam Wightman functions), so the perturbative amplitudes feed S_phys. [C] MASS GAP: Delta=6log(3/2)>0 (v64/v240) gives isolated one-particle states, so Haag-Ruelle scattering theory constructs the in/out asymptotic states and LSZ is valid. [E] ONE-LOOP UNITARITY (optical theorem): the s-channel one-loop bubble B(s)=int_0^1 dx ln(m^2-x(1-x)s-i eps) has discontinuity Im B(s)/pi = x_+ - x_- = sqrt(1-4m^2/s) for s>4m^2 EXACTLY -- the two-body phase-space factor -- so 2 Im M = sum_int dPi |M|^2 (cutting rule) holds at one loop: S_pert is unitary order by order for the matter+gauge sector. [E] THRESHOLD: Im B=0 for s<4m^2, turning on exactly at the physical two-particle threshold s=4m^2 (no spurious thresholds). [O] GRAVITY CAVEAT (rt_F): the R^2/Weyl^2 gravity sector has a negative-residue massive spin-2 mode (the Stelle ghost), so the gravity perturbative S-matrix is NOT unitary -- S_phys for gravity is the nonperturbative QG.AMB.01 frontier. [C] FIELD-STRENGTH Z: the EG scheme gives finite Z so the LSZ reduction is well-defined.

Recorded status: Bridge [E] (LSZ structure + one-loop optical theorem) + [C] (gap/Z) + [O] (gravity ghost)

Original ledger status

QGAMB.IDG.01

QGAMB.IDG.01

INFINITE-DERIVATIVE / NONLOCAL READING OF THE GRAVITY SECTOR (2026-06-19): a CONDITIONAL narrowing of the red-team rt_F / v278 Stelle-ghost attack -- NOT a closure of QG.AMB.01 and NO new parameter (the cutoff is the v259 seam KMS weight). [E] STELLE GHOST = TRUNCATION ARTEFACT: the local R+R^2/Weyl^2 four-derivative propagator 1/(p^2(p^2+M^2)) = (1/M^2)[1/p^2 - 1/(p^2+M^2)] partial-fractions to a healthy massless graviton (residue +1/M^2 at p^2=0) and a massive spin-2 mode with NEGATIVE residue -1/M^2 at p^2=-M^2 (the ghost). [E] ENTIRE FORM FACTOR HAS NO EXTRA POLE: for an infinite-derivative kinetic operator p^2 a(p^2) with a(z)=e^{z/M^2} entire and nowhere zero (exp has no zeros), the dressed propagator 1/(p^2 a) has its ONLY pole at p^2=0 -- no new pole, no ghost (Tomboulis 1997; Biswas-Mazumdar-Siegel 2006; Biswas-Gerwick-Koivisto-Mazumdar 2012). [E] NEG CONTROL: a polynomial truncation a(z)=1+z/M^2 (the R+R^2 order) has a real zero at z=-M^2 = the ghost pole, so 'entire vs polynomial' is the discriminating property. [C] the spectral-action cutoff is the beta=1 seam KMS weight f(u)=e^{-u} (v259/PS.SPECACT.02), not a free scheme; truncating Tr e^{-D^2/Lambda^2} at the a_4 Seeley-DeWitt order is what produces the local R+R^2 and hence the Stelle ghost. [C] CONDITIONAL NARROWING: IF the resummed graviton form factor of the un-truncated KMS spectral action is an ENTIRE function of bounded type, THEN the perturbative graviton is ghost-free and the rt_F attack is a truncation artefact. [O] OPEN: (i) the trace regulator f in Tr f(D^2/Lambda^2) is NOT identical to the kinetic form factor a(Box) -- that the heat-kernel resummation yields an ENTIRE a(Box) is an unproven analyticity assumption; (ii) a ghost-free PERTURBATIVE graviton is not the NONPERTURBATIVE ambient measure QG.AMB.01 demands.

Recorded status: Open (conditional narrowing of the perturbative Stelle-ghost attack; NOT a QG.AMB.01 closure)

Original ledger status

FIRSTPRINCIPLES.BOUNDARY.01

FIRSTPRINCIPLES.BOUNDARY.01

THE HONEST FIRST-PRINCIPLES BOUNDARY, mapped precisely (2026-06-22): answers (a) can M_Planck/v_geo be computed from first principles? and (b) can F_transfer (Koide, m_p/m_e, eta_B, axion) be made a first-principles compiler output? BOTH NO -- with the exact reason for each residual, classified into FOUR honest kinds. [E] v_geo/M_Planck FORBIDDEN BY THEOREM (No-Unit, v153): a mass is dimension 1 while every TFPT datum is dimension 0, so no dimensionless map outputs a scale; M_Planck is NOT a pure number, but is OVER-DETERMINED (gravity = dark energy to 0.11%, v274); every dimensionless RATIO is derived, only the one unit is not. [E] m_p/m_e structure in place (v262): the carrier outputs b3=-(11-2 n_f/3)=-7 driving the QCD run + the closed electron lepton ladder; exactly 2 inputs stay external: alpha_s(M_Z) and the lattice C_p=m_p/Lambda3~2.83. [X] alpha_s(M_Z) external BECAUSE OF A TENSION: TFPT content = SM (no new states) and the SM does NOT unify -- the GUT-normalised 1-loop couplings at 2e16 GeV spread by ~8.8 (no common point, v246) -- so a unified coupling is NOT predicted and alpha_s is not derivable; the route that would give it is a falsifiable tension. [N] C_p parameter-free but lattice-only (m_p/Lambda_QCD~2.83=O(1), nonperturbative hadronization, the discrete<->continuous handoff v35). [C] eta_B/axion = cosmological initial conditions (M_1/washout v169/v184/v212; misalignment v211); Koide Q=2/3 structural [E], only pole<->running [C]. [A] FOUR honest kinds: forbidden-by-theorem (the unit, over-determined) / external-parameter-free (lattice C_p) / external-tensioned (alpha_s via failed unification) / cosmological initial conditions. A boundary audit; fabricates nothing, closes nothing. [2026-08-03 LIII: the two thermal-time routes for INTERNALIZING the F_transfer clocks are now machine-killed -- v723 (FTRANSFER.STT.01, STT-KILLED: the QCD 1-loop clock is parabolic and not diagonalizable, no constant-rescaled modular flow reaches it; the pole/Boltzmann pair confirmed internal per v425, multiplier (2/3)^6 exact) and v724 (FTRANSFER.COCYCLE.01, T3B-DEAD: conditioned modular flows of one internal mother state give loxodromic/complex classes, not the frozen v578/v632 solver classes; cocycle composition exact, one KMS scale). The external clock contract STANDS and sharpens to the typed anchor census {one unit (v_geo-class), one angle theta_i, one lattice O(1) C_p}: T3's clock wall == T1's unit wall, counted once (v723 P4). No status move.]

Recorded status: Boundary audit [E]/[X]/[C] (what is derived / external / tensioned / forbidden)

Original ledger status

AS.RECONCILE.01

AS.RECONCILE.01

A_s is predicted (not missing), is DIMENSIONLESS (so it does NOT define an absolute mass), and the apparent -11 sigma tension is a reheating-channel question -- reconciled with the archived old derivation (TFPT v4.5/v4.6, 2026-06-22). [E] A_s = N_star^2 (M_scal/Mbar)^2/(24 pi^2) = N_star^2 c3^7/(24 pi^2) (v86); M_scal/Mbar = c3^{7/2} = 1.2565e-5 is a PURE RATIO, so A_s carries NO absolute scale -- it pins N_star (the e-fold count), NOT M_bar => A_s does NOT define mass (No-Unit v153 stands; 'mass itself' is set by gravity M_bar = (8 pi G)^{-1/2}, the one dimensionful input). [N] the -11.4 sigma is the slow-vs-fast reheating dichotomy: slow Higgs channel N_star=51.44 -> A_s=1.764e-9 (-11.4 sigma vs Planck 2.105(30)e-9); the A_s-preferred N_star=56.2 (~ the instantaneous bound 55.6). [P] ARCHIVE COMPARISON: the old v4.5/v4.6 (07_cmb_operational_closure) used the ALGEBRAIC N_star=3/phi0-1=55.42 (+ alpha_R=(Omega_adm/4pi)e^{1/phi0}) and reported A_s=2.124e-9; at that N_star the current normalisation gives A_s=2.047e-9 (-1.9 sigma) -- consistent (~4% offset = alpha_R vs c3^7); the old clean A_s = N_star~55.4 (near-instantaneous), NOT the slow channel. [E] nothing lost: the current theory DERIVES N_star from reheating physics (more honest) and exposes that the A_s match REQUIRES fast reheating; record band N_star in [50,60] (v84). [X] decisive test: fast preheating (A_s ok, c3^{7/2} stands) OR slow reheating confirmed (exponent-7 fails).

Recorded status: Reconciliation [E]/[N]/[P]/[X] (A_s predicted+dimensionless; tension = reheating channel; archive comparison)

Original ledger status

QFT4D.EG.ALLORDER.01

QFT4D.EG.ALLORDER.01

The all-order Epstein-Glaser/BRST contract for the perturbative 4D S-matrix S_pert (2026-06-23, review Point 3): the 'all-order closing statement' for the 4D perturbative QFT leg, typing the standard causal-perturbation-theory closure for the TFPT finite interaction class -- NOT a 4D path integral and NOT a new mechanism. [E] POWER-COUNTING: every gauge+matter vertex (Yang-Mills + Dirac-Yukawa + Higgs + ghost) is a mass-dimension-4 marginal operator, so the Epstein-Glaser singular order omega<=4 and the renormalisation ambiguity is a FINITE-dimensional local space at every order (power-counting renormalisable). [E] BRST NILPOTENCY s^2=0: s c^a=-(1/2) f^{abc} c^b c^c is nilpotent iff Jacobi holds; verified EXACTLY for su(2) (residual 0) and su(3) (1e-16), the carrier weak+colour gauge content. [E] the seam gap Delta=6 ln(3/2)>0 (v302) gives the IR-safe adiabatic limit g->1 (Epstein-Glaser-Blanchard-Seneor for a mass gap). [C] IMPORTED: T_n exists to all orders by causal factorisation (Epstein-Glaser 1973 / Brunetti-Fredenhagen). [C] IMPORTED: all-order BRST invariance (Piguet-Sorella / Kugo-Ojima quantum action principle) => Slavnov-Taylor to all orders. [E] SCOPE FENCE: matter+gauge ONLY -- the R^2/Weyl^2 gravity sub-sector (Stelle ghost) is the entire-form-factor resummation v304/v370/v380, NOT a local EG vertex; S_pert is NOT the ambient non-perturbative QG measure (QG.AMB.01, a [C] redundancy v369). NET [C], prerequisites [E]; NOT [E]. Extends the S_pert skeleton v269/v271/v273 + LSZ v278 from 1-loop matter+gauge to an all-order contract.

Recorded status: All-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]

Original ledger status

DYNAMICS.UNIVERSAL.01

DYNAMICS.UNIVERSAL.01

The UNIVERSAL spectral-gap / Perron-Frobenius principle (2026-06-23, bird's-eye synthesis): every TFPT sector is the SAME structural object -- a gapped operator with a UNIQUE leading attractor (the physics) and a spectral gap (the reason there is no free parameter). Extends v303 (which named this only for F_transfer) to the sectors made parameter-free AFTER it. [E] FLAVOR (computed): cusp transfer spectrum {1,(2/3)^6,(1/3)^6}, simple Perron leading 1, gap 6 ln(3/2)>0 (v56/v82/v240). [E] DISCRETE COMPILER (computed): affine-E8 adjacency Perron 2 (Kac marks, v312/v313), subleading 2cos(pi/5)=phi, gap 2-phi=1/phi^2>0. [E] DECOUPLING MARGIN (computed): Delta_eff=6 ln(3/2)-31/(4 pi^2)~1.648>0 (v76/v337). [E] TWO NUMBER-FIELD FACETS (v314): golden phi in Q(sqrt5) (carrier-5, static) and (2/3)^6 in Q (family-3, dynamic) are the prime-5 and prime-3 facets of the order-30 Coxeter clock 30=2*3*5=h(E8) -- a factorisation, NOT a forced equality. [C] OTHER SECTORS = SAME STRUCTURE: gravity=deltaS=0 equilibrium (v358/v359), QG=Gaussian saddle (v365), QFT=stable holomorphic c=8 RG fixed point (v157/v158), all-order S-matrix=adiabatic limit (v381), recovery=Petz fixed point (2/3)^6 (v221), F_transfer (v303), tau=i (v333). [C] META-THEOREM: gapped => unique attractor => parameter-free, theory-wide -- 'parameter-freeness is a theorem' (v56) is ONE spectral-gap statement wearing many hats. Anti-numerology: no new number.

Recorded status: Universal 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])

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

Original ledger status

GRAV.AMPLITUDE.01

GRAV.AMPLITUDE.01

The entire-form-factor graviton-exchange AMPLITUDE is finite, UV-softened and tree-unitary (2026-06-24) -- perturbative gravity as an explicit scattering problem, extending v304/v370/v380 from the propagator to the amplitude. The dressed spin-2 propagator P(p^2)=e^{-p^2/M^2}/p^2=1/(p^2 a) with a(u)=e^u (u=p^2/M^2), M=M_scal. [E] ONE POLE, GHOST-FREE: a=e^u entire and nowhere zero (v380) => the only pole is p^2=0 with residue lim p^2 P=e^0=1>0 (one healthy massless graviton). [E] UV-SOFTENED: the dressed/GR ratio e^{-u} at u=1,5,10,20 = 0.37,6.7e-3,4.5e-5,2.1e-9 -- suppressed faster than any power (infinite-derivative improvement), monotone->0. [E] LOW-ENERGY = GR + CALCULABLE CORRECTION: e^{-u}=1-u+u^2/2-...; the leading deviation -u=-p^2/M^2 (M=M_scal=c3^{7/2}Mbar~3.06e13 GeV, v253). [C] TREE UNITARITY: a single positive-residue pole, no extra poles / negative-norm states (entire zero-free form factor) => Im A>=0, consistent with v370 (spin-2) + v380 (entire). [C] AMPLITUDE STRUCTURE: A=(kappa^2/2)(T.P2.T')e^{-p^2/M^2}/p^2, GR at low energy, softened in the UV (P2 = Barnes-Rivers spin-2 projector, v370); perturbative-only (QG.AMB.01 stays a [C] redundancy, v369).

Recorded status: Perturbative graviton amplitude [E]/[C] (entire-form-factor exchange: finite, ghost-free, UV-softened, tree-unitary; perturbative-only)

Original ledger status

GRAV.LOOP.FINITE.01

GRAV.LOOP.FINITE.01

The entire-form-factor graviton is UV-finite at the LOOP level by power counting (2026-06-24) -- the honest next step past v386 (which established the tree amplitude), extending v304/v370/v380/v386 from the propagator to the superficial degree of divergence of loop graphs. HONEST SCOPE: this is the standard infinite-derivative/nonlocal-gravity finiteness statement (Tomboulis; Biswas-Mazumdar-Siegel; Modesto); it is NOT a full proof of perturbative quantum gravity. [E] SUPER-POLYNOMIAL FALLOFF: for every polynomial degree k, p^k e^{-p^2/M^2}->0 as p->inf (k=2..20), so the dressed propagator cannot leave a power-counting divergence. [E] ONE DRESSED LINE KILLS A QUADRATIC DIVERGENCE: int_{p0}^Lambda p^3(e^{-p^2/M^2}/p^2)dp -> (M^2/2)e^{-p0^2/M^2} (converged at 10M/20M), while the GR int p^3/p^2 dp grows quadratically. [E] SUPERFICIAL DEGREE -> -infinity: GR has a fixed degree D=4L+2V-2I per L-loop graph; the entire form factor multiplies the integrand by e^{-(#internal)p^2/M^2}, so the effective degree is -infinity at every loop order L (dressed cutoff-ratio ->1 vs GR ->4). [E] the regulator is the SEAM scale M=M_scal=c3^{7/2}Mbar~3.06e13 GeV (v253) with the seam KMS form factor e^{-u} (v259), a derived scale, not a Pauli-Villars dial. [C]/[O] LOOP UNITARITY is the subtle OPEN point: tree unitarity holds (single positive-residue pole, v386), but unitarity of a nonlocal form factor at loop level (Lorentzian continuation/macro-causality, Pius-Sen/Briscese-Modesto) is genuinely subtle and still debated -- NOT claimed solved.

Recorded status: Perturbative graviton loop UV-finiteness [E] (power counting; super-polynomial falloff, degree -> -infinity at every loop order, seam-regulated) + loop unitarity [C]/[O] (the honest open point, not claimed solved)

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

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]

Original ledger status

QGAMB.NODEP.01

QGAMB.NODEP.01

The No-Ambient-Dependency certificate (2026-06-25): no frozen TFPT readout is COMPUTED from the ambient QG measure QG.AMB.01 -- sharpening the v369/v384 prose redundancy ('QG.AMB.01 is a [C] redundancy, not dynamics') into a machine-checked DAG+script fact, told HONESTLY. [E] GAP-DECOUPLING MARGIN: 2 dim(E8) c3^2 = 31/(4 pi^2) (31=2^g_car-1) ~ 0.785, Delta = 6 ln(3/2) ~ 2.433, so Delta_eff ~ 1.648 > 0 (v76/v337); chi = 1/(1-(2/3)^6) = 729/665 finite (negative control: gap->0 => chi->inf, the ambient re-enters). [E] CERTIFICATION SINK: every claim that lists QG.AMB.01 as a dependency is a gravity-gate/QG-certification row (GATE.METRIC.01, GRAVITY.COMPLETE.01, the QGAMB.* cluster, SEAM.S3.RP.01, ...), NONE a frozen physical prediction -- QG.AMB.01 has no predictive direct dependent. [E] NOT A VALUE SOURCE: QG.AMB.01 has no producing script (ledger script='-'); every frozen prediction of record is computed by a compiler script (alpha^-1<-v3, sin^2 th12<-v9, sin^2 th13<-v268, cosmology<-v7), none of which is an ambient-measure script (v76/v330/v332/v334/v335) -- so no readout VALUE is produced by the ambient measure. [E] ARCHITECTURAL-ONLY LINK (honest): of the frozen readouts only theta13 transitively references QG.AMB.01, and the path runs through the 4D-QFT CONTRACT spine (PS.DIRAC.02 -> CONTRACT.QFT4D.01 -> QG.G2.01 -> GATE.METRIC.01) -- the readout lives INSIDE the unified spectral-action construction, a coherence edge, not a numerical input (its value sin^2 th13 = phi0 e^{-5/6}, v268, takes no ambient-measure input); alpha, theta12 and all of cosmology have NO route to QG.AMB.01 at all. [C] VERDICT: QG.AMB.01 is a gap-decoupled certification object -- no readout VALUE is computed from it, its only predictive link is the architectural 4D-QFT contract, and the gap margin (1.648>0) suppresses its back-reaction -- v369 as a DAG/script fact. HONEST: this does NOT prove SEAM.EQUIV.01 (the readouts depend on the seam being the (E8)_1 net, the one open keystone); QG.AMB.01 specifically is dead.

Recorded status: No-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

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

Original ledger status

SEAM.EHMODEL.04

SEAM.EHMODEL.04

SEAM-HORIZON REPLICA CHAIN AT COLLAR LEVEL (the kernel-identification premise of SEAM.THEOREM.01, exercised numerically; SEAM.EHMODEL.03's residual list sharpens again, the gate stays OPEN): (1) REPLICA => EH FORM ON A REAL OPERATOR [I] - matched conical deficit G(gamma,m) = log det L(gamma,m) - (gamma/2pi) log det L(2pi,m) of the discretized gapped cone operator (finite-volume polar grid, geometric tip grading, identical stencil across geometries so extensive terms cancel exactly) is linear in ln m with slope 2C(gamma), verified on deficit cones gamma/2pi = 1/4, 1/2, 3/4 (rel. err 0.01-0.05%) AND on REAL replica sheets gamma/2pi = 2 (0.8%), 3 (1.5%) - beyond linearisation, the regime the replica trick uses; (2) COEFFICIENT FORCED, SCALE = ANCHOR [I] - the EH slope is stable under IR/size refinement (0.5% drift) while the intercept (zeta-scale mu_lat 146.9 -> 153.1) drifts with the discretization: the v152 anchor exhibited on data; NO canonical ln(m/mu) = 3/4 emerges (recorded honestly - the anchor stays declared, not derived); (3) BFK SPLIT MEASURED ON THE DISCRETIZED CALDERON KERNEL [I] - Schur identity log det L = log det(halves_D) + log det S exact (~1e-16); across three cut geometries the Calderon/Schur factor's deficit slope follows a PURE CUT-EDGE law E(1-q) with tip term 0 (power check: the same law fails on the full determinant), the halves carry the whole tip 2C_cone via Kac doubling (exact) - v151's 'conically clean' measured on the kernel itself, not inferred from corner constants; (4) THE SEAM'S OWN SPECTRUM [I] - the v302 transfer masses m2 = 6 ln(3/2), m3 = 6 ln 3 (bend ln3/ln(3/2), v124/v147) sit ON the calibrated EH line (<=0.05%): det'(collar) inherits the EH variation mode-wise; the Perron/attractor mode (m=0) is IR-DIVERGENT, running exactly as -2C ln(IR ratio) - THE RECOVERY GAP Delta = 6 ln(3/2) IS WHAT MAKES THE INDUCED-GRAVITY COEFFICIENT FINITE (the same gap that makes the attractor unique, v56, makes 1/G finite). RESIDUAL [A/O]: the kernel premise is now discharged at the finite/model level; what remains of SEAM.THEOREM.01 is the CONTINUUM scaling limit of this statement (the MMST class - the same single residual as SEAM.EQUIV.01, v336) plus the one dimensionful anchor (v152). NOT claimed: a continuum proof, or a derivation of ln(m/mu) = 3/4

Recorded status: Numerical [I] (lattice determinants vs exact conical constants) + [A/O] (continuum leg + anchor stay open)

Original ledger status

GRAV.ENTROPIC.ACTION.01

GRAV.ENTROPIC.ACTION.01

THE ENTROPIC-ACTION BRIDGE (2026-07-13) -- Bianconi's 'Gravity from entropy' (Phys. Rev. D 111, 066001 (2025); arXiv:2408.14391; DOI 10.1103/PhysRevD.111.066001) quantified as an EXTERNAL CANDIDATE for the local volume action behind TFPT's parameter-free Einstein equation; closes NOTHING, adds ZERO knobs. Context: v359 derives G_ab + Lambda g_ab = (1/c3) T_ab thermodynamically and is honestly typed 'equation of state, not a from-action quantisation' [O]; Bianconi's S_B = -Tr_F ln(G~ g~^-1) (quantum relative entropy between the spacetime metric and the matter-induced metric; Araki-related via Delta^{1/2} = G~ g~^-1, her Appendix C) is a local covariant action whose variation yields Einstein + emergent nonnegative Lambda at low coupling -- exactly the missing variational layer IF the bridge identities hold. [E] CARRIER HODGE COUNT: her Omega^{0,1,2} matter fiber, placed on the five-slot carrier C^5 (NOT on 4d spacetime, where the fiber is 1+4+6 = 11), counts 1+5+10 = 16 = 2^(g_car-1) = dim S+_{D5}, Hodge-star folded (L^1 ~= L^4) onto L^even C^5 -- the carrier half-spinor's own Pascal row (v2/v44); vector-space identity ONLY. [E] COEFFICIENT MATCH (the one quantitative pin): her weak-coupling Lagrangian L = 3 beta R - alpha L_matter (her Eq. (45); the 3 = the three form blocks) matched to the TFPT EH normalisation 1/(16 pi G) = c3/(2G) fixes her free constant EXACTLY: beta'_B = c3/6 = 1/(48 pi); the 6 = 3 blocks x 2 (EH 1/2) = p2 = |R+(A3)| is recorded as a structural echo, NOT a proof. [E] ENTROPY POTENTIAL = QUADRATIC LAMBDA: Lambda_G = (1/2 beta) Tr_F(G - I - ln G) with s(x) = x - 1 - ln x >= 0, s''(1) = 1 (exact series) -- Lambda nonnegative and QUADRATIC around the entropic fixed point; with the TFPT displacement eps_* = e^{-1/alpha} Q this reproduces the closed v60 branch rho_Lambda/Mbar^4 = (3/4 pi^2) e^{-2/alpha}, and the prefactor match (beta' = c3/6, l_P^2 Mbar^2 = c3) yields the EXACT normalisation target Tr_F Q^2 = 32 c3^4 = 1/(128 pi^4) = (2/3) delta_top -- a closed algebraic target for the two-form (pair) block (binom(5,2) = 10), [C] until an explicit Q is constructed. [E] FRULLANI: -ln A = int_0^inf dt/t (e^{-tA} - e^{-t}) -- her log action is an all-scale-integrated heat-kernel action, the correct genre to compare with the TFPT relative spectral action S_rel,chi (KMS cutoff). [E] R^2 KILL TEST QUANTIFIED (pre-registered): the raw log expansion carries a curvature-squared coefficient of order (c3/6)^2; the TFPT Starobinsky sector needs Mbar^2/(12 M_scal^2) = 1/(12 c3^7) (M_scal^2 = c3^7 Mbar^2, v36); the EXACT mismatch is 3 c3^{-9} = 3 (8 pi)^9 ~ 1.20e13 -- THIRTEEN orders: a direct identification of the raw entropic action with the TFPT R^2 sector is FALSE without a mechanism (scalaron = light trace mode of her G-field generating c3^{-9}, or KMS-spectral renormalisation of the log action). [C] COMPRESSION CONJECTURE (the bridge proper, recorded not proven): P_Sigma (G~ g~^-1) P_Sigma = Delta_Sigma^{1/2} -- the physical Calderon compression of her relative metric operator equals the TFPT seam modular operator; if proven, S_B is a local volume representation of the TFPT relative spectral action; open together with the operator-level Hodge items (Clifford action, Dirac intertwining, leaf involution, Calderon polarisation). Lorentzian positivity of G~ g~^-1 is NOT automatic (timelike gradients); TFPT's OS/reflection-positive route is the sturdier construction. [O] NOT CLOSED: the v359 equation-of-state status stays [O]; adopting S_B would close it ONLY after the compression conjecture AND an R^2 mechanism; no status marker moves anywhere

Recorded status: Formal/Numerical [E] (five exact identities + quantified gap) + [C] (compression conjecture, Q-target) + [O] (variational completion open)