Original claim records.

Original ledger status

COSMO.LAM.01

COSMO.LAM.01

rho_Lambda/Mbar^4 = (3/4pi^2) e^{-2 a^-1} = 7.125e-121 (dark-energy scale 2.2375 meV)

Recorded status: Numerical

Original ledger status

COSMO.INF.01

COSMO.INF.01

Starobinsky A_s; n_s=1-2/N*; r=12/N*^2

Recorded status: Numerical

Original ledger status

COSMO.OMB.01

COSMO.OMB.01

Omega_b = (1-1/4pi) phi0 = 0.04894

Recorded status: Numerical

Original ledger status

FOUR.ROUTES.01

FOUR.ROUTES.01

THE FOUR BLACK-HOLE-BIRTH SOLUTION ROUTES INVESTIGATED (2026-06-22): direct answer to 'which closes ALL problems and is 100% provable' -- NONE individually; they CONVERGE on the same two irreducible residuals as v335 (SEAM.EQUIV.01 + the decoupled QG contour), reached now from the cosmological side. [E] ROUTE A (finite causal diamond) REFRAMES QG.AMB to a FINITE thermal trace: in a horizon-bounded static patch the object is Tr e^{-beta H}, finite for a gapped H bounded below (de Sitter S_dS = 32 pi^4 e^{2 ainv} finite; 128 c3^4 = 1/(32 pi^4) exact v54/v190; gapped susceptibility chi = 729/665 v337) -- BUT c_conf(4) = -3/2 < 0 (v332) still needs the GHP contour rotation (v334), whose nonperturbative validity is [O]; so A gives QG.AMB well-posedness/finiteness [E] but NOT a full nonperturbative construction, and does NOT touch SEAM.EQUIV.01. [C] ROUTE B (Carlip-Cardy near-horizon CFT) gives a SECOND route to existence + central charge: Carlip's near-horizon Virasoro + Cardy S = 2 pi sqrt(c L0/6) reproduces the entropy consistent with c = g_car+N_fam = 8, but L0 is free (the Carlip periodicity ambiguity) so c=8 is consistent not forced, and Carlip yields the central charge ONLY, not the holomorphy det K=1 discriminator -- inherits SEAM.EQUIV.01. [E] ROUTE C (modular/thermal flow) is a REDUCTION: the modular flow exists & is KMS at beta=1 (Tomita-Takesaki v239) so 'dynamics = modular evolution of the horizon state' is well-defined abstractly, but its GEOMETRIC identification (boost = physical time) is QGEO.SYM.01 = a corollary of SEAM.EQUIV.01 (v335). [E]/[P] ROUTE D (self-reproduction attractor) gives parameter-freeness: a gapped transport has a unique Perron-Frobenius attractor (v56), so the cyclic map has a unique fixed point [E], but 'the full dynamics IS that fixed point' is the [P] cyclic interpretation -- not a construction. [E] VERDICT: independent closures = 0; irreducible residuals after all four routes = 2 (SEAM.EQUIV.01 + the decoupled QG contour, unchanged from v335); the BH premise makes BOTH more natural (A finite thermal trace; B near-horizon CFT) but ELIMINATES neither. The value: the four routes are not four separate gambles -- they converge on the ONE keystone, so effort should focus on SEAM.EQUIV.01.

Recorded status: Analysis/roadmap [E]/[C]/[O] (none closes all or is 100% provable; all four converge on SEAM.EQUIV.01 + the decoupled QG contour)

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

Original ledger status

SEAM.ATTRACTOR.01

SEAM.ATTRACTOR.01

Unique attractor: a gapped boundary transport selects ONE fixed point [I]/[L]. The boundary transport spectrum {1,(2/3)^6,(1/3)^6} has spectral gap Delta=-log(2/3)^6=6 log(3/2)=2.4328>0. By Perron-Frobenius a primitive gapped operator has a UNIQUE dominant eigenvector and iteration converges to it geometrically at rate lambda2/lambda1=(2/3)^6, independent of initial state (demonstrated: two different starts -> same fixed direction, cos=1). This is the dynamical-systems content of 'parameter-free via fixed point' - the realized state is an ATTRACTOR, not a tuning; the convergence rate is the SAME (2/3)^6 of flavor+horizon (v54). Coxeter rotation lives in |mu4|=4 invariant planes (exponents pair m+(30-m)=30); sum exps=120=|R+(E8)|; #roots=rank*h=240. Entropy reset = the gap: T^n/lambda1^n -> rank-1 projector (only boundary law survives). Cyclic-cosmology reading is [P], not included

Recorded status: Identity/Lie [I]/[L]

Original ledger status

SEAM.CYCLE.01

SEAM.CYCLE.01

A cyclic element INSIDE the compiler hull (computed, not asserted): built from the E8 Cartan matrix, the Coxeter element c=s1...s8 has order EXACTLY h(E8)=30=|Z2|*N_fam*g_car=2*3*5 (verified by matrix powers, v55), and its eigenvalues are primitive 30th roots exp(2pi i m/30) with m the E8 exponents {1,7,11,13,17,19,23,29} = EXACTLY the phi(30)=8 totatives of 30. Hence rank E8=8=phi(30)=#exponents=#live phases of the order-30 cycle => the 8 in c3=1/(8pi) is the live-phase count of a primitive order-30 cyclic rotation of the hull, period 30=|Z2|*N_fam*g_car. PLUS one-alpha cross-sector: S_dS*rho_Lambda=1/(128 c3^4)=32 pi^4 (de Sitter Gibbons-Hawking entropy ~ 1/Lambda), so the SAME EM fixed point alpha^-1=137.036 sets the cosmic horizon entropy and Lambda smallness ~10^-122=e^(-2 alpha^-1). FURTHER: S_dS=2^g_car*pi^|mu4|*e^(2 alpha^-1) - the entropy prefactor 32 pi^4 = (Dirac spinor dim of D5=SO(10): S+ + S- =16+16=2^g_car) x pi^|mu4|, with 128=2^7 (7=scalaron exponent g+n-1): cosmic horizon entropy = carrier Clifford dim x pi^glue x EM fixed point. [I]/[L]; cyclic-cosmology reading is [P], not included

Recorded status: Identity/Lie [I]/[L]

Original ledger status

SEAM.HORIZON.01

SEAM.HORIZON.01

Seam=horizon [I] keystones (pure identities, NO cosmological narrative): (1) the integer 8 in c3=1/(8pi) is OVERDETERMINED and gravitationally aligned: geometry 8=2|mu4| (8pi=|mu4|*2pi seam winding), lattice 8=rank E8=g+n=h(D5)=phi(30)=det R, gravity 8pi=Hawking/Einstein coeff (G_uv=8pi T_uv) => if seam=horizon, c3 is gravitationally forced and the gravitational 8 MUST equal the lattice/geometry 8 (it does). Both pi-coeffs are 2pi*integer: phi_tree=1/(6pi),6=2 N_fam (Gauss-Bonnet); c3=1/(8pi),8=2|mu4|; phi_tree=(|mu4|/N_fam)c3=(4/3)c3. (2) ONE transfer operator for BOTH sectors: boundary transport spec {1,(2/3)^6,(1/3)^6}; lambda2=(2/3)^6 = SM flavor gap eigenvalue (Delta=-log(2/3)^6=6 log 3/2=2.4328, tfpt_2) = horizon Page recovery rate (I_n~lambda2^n, Appendix H). Cusp weights {0,1/3,2/3} at 4 mu4-punctures = boundary data. Supporting: S_BH=A/|mu4|, 128 c3^4=1/(32 pi^4), T_dS coeff 16=|mu4|^2. The cyclic self-reproduction reading is [P] interpretation NOT included here

Recorded status: Identity [I]

Original ledger status

ANCHOR.VGEO.01

ANCHOR.VGEO.01

v_geo = CLOSED METROLOGY STRUCTURE (R_+ unit torsor; one dimensionful calibration necessary by dimensional analysis -- the No-Unit theorem v153/v725; honest reframe, not a derived mass and not an open physics gap): no pure number can be dimensionful => one calibration is forced by LOGIC (every theory carries >=1 dimensionful input). ALL TFPT scales are dimensionless ratios times ONE M_bar: rho_Lambda/M_bar^4=(3/4pi^2)e^{-2 ainv} (v60), M_scal/M_bar=c3^{7/2} (v7), masses = (pi/sqrt2)c_f phi0^{k_f} v_geo. Cosmological pinning S_dS*rho_Lambda=1/(128 c3^4)=32 pi^4 (v55) => one measurement sets the unit. The flavor U_point reduces to the SAME v_geo (v75) => one scale shared by flavor+gravity. Theory at the minimum: one scale v_geo + one primitive pi

Recorded status: Identity [I] (ratios) + [A]/[O] (closed metrology: R_+ unit torsor; one calibration by dimensional analysis)

Original ledger status

COSMO.NSTAR.01

COSMO.NSTAR.01

N_star band -> POINT [P] (the announced 'future derivation from a reheating model' executed; demotion of N_star as a compiler output STANDS): the only compiler input is M_scal=c3^{7/2}Mbar=3.0600e13 GeV [I] (v28/v36/v80); everything downstream is imported standard physics - scalaron width Gamma=N_eff M^3/(48pi Mbar^2) with N_eff=4 (SM Higgs doublet; Starobinsky/Vilenkin/Gorbunov-Panin), reheating at H=Gamma => T_reh=(30 rho/(pi^2 g*))^{1/4}=9.55e9 GeV (g*=106.75), pivot matching with w=0 scalaron oscillations + entropy conservation on the EXACT Starobinsky potential V=(3/4)M^2 Mbar^2(1-e^{-sqrt(2/3)phi})^2. RESULT: N_star(k=0.05/Mpc)=51.44 => n_s=1-2/N_star=0.9611, r=12/N_star^2=0.00454. CROSS-CHECK: k=0.002/Mpc gives N_star=54.7 = the known R^2-reheating literature value (~54). ROBUSTNESS: channel ambiguity N_eff=1..100 moves N_star by <0.8 e-folds (log sensitivity); instantaneous-reheating upper bound N_star<=55.7. FREEZE DISCIPLINE: 51.4 lies inside the frozen registry band [50,60]; predictions_frozen.json NOT modified (v84 lock intact). HONEST TENSIONS RECORDED: (1) n_s=0.9611 is +0.90 sigma below Planck 2018 (0.9649+-0.0042) and increases the DESI-combined tension; (2) A_s COHERENCE is sharper: with M_scal fixed A_s=N^2 c3^7/(24pi^2) is also predicted, A_s(51.44)=1.764e-9 = -11.4 sigma vs Planck 2.105(30)e-9; the A_s-preferred N_star=56.20 exceeds even the instantaneous-reheating bound 55.61 by 0.59 e-folds (instantaneous gives 2.06e-9 = -1.5 sigma, compatible) => within standard physics the measured A_s REQUIRES near-instantaneous reheating and the slow Higgs-channel point is A_s-disfavoured. The [P] point is CONDITIONAL on the decay channel; the frozen band [50,60] remains the prediction surface of record. Kill criteria: robust n_s>=0.967 falsifies the reheating chain (not the [I]/[L] core); A_s already arbitrates between fast and slow reheating

Recorded status: Physical [P] (conditional on M_Star=M_scal + standard reheating)

Original ledger status

FR.DM.03

FR.DM.03

AXION RELIC HONEST MISALIGNMENT ESTIMATE (external-review proposal 2026-06-14; the determinant-line axion can be all DM but stays a [C] scenario): (1) SCALES [I]: f_a = M_scal/(2 dim S+ |mu4|) = M_scal/128 ~ 2.39e11 GeV (M_scal = c3^{7/2} Mbar ~ 3.06e13 GeV), QCD axion m_a ~ 5.7 ueV (1e12/f_a) ~ 23.8 ueV (FR.DM.02). (2) HARMONIC MISALIGNMENT UNDER-PRODUCES [N]: Omega_a h^2 ~ 0.12 (f_a/9e11)^{7/6} <theta^2> gives prefactor ~0.026 per theta^2 at this f_a, so theta_i ~ O(1) makes only ~21% of Omega_DM; reaching Omega_DM h^2 = 0.12 needs theta_eff^2 ~ 4.7, i.e. the large-angle (anharmonic) enhancement. (3) HILLTOP REQUIRED -> SCENARIO [C]: TFPT's misalignment angle theta_i ~ 170 deg (the seam value pi(1-phi_seam)) IS the hilltop where the anharmonic factor diverges, so Omega_a h^2 CAN be tuned to Omega_DM -- but near the hilltop the relic is exponentially sensitive to theta_i and QCD/string corrections, so it is a viable SCENARIO, not a sharp prediction. (4) CONTRACT [O]: F_relic(f_a=M_scal/128, theta_i~170 deg, N_DW=1) =? Omega_DM is a kill test for the determinant-line axion BRANCH, not the theory; the E8 scan leaves no free singlet WIMP (128=(16,4)+(16,4) matter spinor), so the axion is the natural DM line, abundance is transfer/cosmology, never a compiler output. Python-only (analytic estimate; the full finite-T chi(T) ODE is standard cosmology, flagged). POST-INFLATIONARY REFRAMING [C] (2026-07-10, FR.DM.02): the 170 deg hilltop is a PRE-INFLATIONARY fixed-angle reading; given H_inf/f_a~66>1 (R^2 branch) it carries CDM isocurvature >> Planck beta_iso<0.038, so it is SUPERSEDED by the post-inflationary scenario (theta_i a horizon average, NOT observable; relic from f_a + N_DW=|C|=1, v470/v472). Over-production at 170 deg is moot post-inflationary.

Recorded status: Physical [C] (hilltop scenario SUPERSEDED by post-inflationary reframing FR.DM.02; angle not observable)

Original ledger status

SYNTH.INVENTORY.01

SYNTH.INVENTORY.01

THE RESIDUAL INVENTORY (one constant, one anchor, one clock to find; the COMPLETE machine-pinned gap list): (A) ONE-CONSTANT INVENTORY [I] - 2/3 = |Z2|/N_fam appears exactly in seven independent places across both sectors (flavor: Koide branch point, transfer-gap base (2/3)^6, attractor inside the physical basin; gravity: Nariai entropy bound, SdS branch separation, canonical amplitude+frequency, canonical curvature base (2/3)^N_fam); ANCHOR TRIPTYCH [I]: configuration chi_a = (t-1)^2(t-2), Nariai cubic (t-1)^2(t+2) = traceless anchor, clock quadratic (lam-1)(lam+2); Nariai = (t-1) x clock; a = e2+e3. (B) RELOCATION THEOREM [I]+[P]: the cosmological one-loop clock correction eps = (c/24pi) Lambda/Mbar^2 = 7.6e-122 (c = 8 = the seam central charge, frozen rho_L) is deficient by 121.5 orders against the needed O(1) gap, and the deficit IS the Lambda hierarchy 2 alpha^-1/ln10 = 119.0 (+2.5 prefactors, the v60 split) => the seam clock must live at the SEAM scale, where the only gapped generator is the established boundary transfer operator; the bridge reaches its final form: ONE [P] identification 'transfer operator = seam Nariai clock'. (C) RESIDUAL TABLE (typing contract): exactly FIVE structural objects remain - R1 seam quantum clock [P] (HOR.CLOCK.01), R2 seam net holomorphic + c=8 [P]/[A] (GATE.METRIC.05/06/07), R3 seam determinant => EH form [A] (SEAM.AREACOEFF.03 residual), R4 H2 dictionary [A]/[P] (GATE.RU.01/CONTRACT.U.01), R5 parabolic realisation of Q carrying P1 [P] (GATE.QGEO.01/FLAV.SHEET.03) - plus the two irreducibles (one scale v_geo by dimensional analysis v78; the primitive pi) and the frozen data surfaces (gamma_CP, n_s/A_s, theta13, m_tau, r). COMPLETENESS is itself the claim: a sixth structural gap would FAIL v105. Nothing closed here; everything that remains is named, typed and counted

Recorded status: Identity [I] (inventory + relocation arithmetic) + typing contract (gap completeness)

Original ledger status

HOR.CLOCK.02

HOR.CLOCK.02

QUANTUM-CLOCK TARGET (R1 made quantitative; nothing fitted): the Ginsparg-Perry multi-mode clock has per-l equations lambda^2+lambda+(l(l+1)-2)=0 - l=0 anchor pair {1,-2}, l=1 zero modes {0,-1}, l>=2 complex with Re=-1/2=-delta (audit). NEW CROSS-LINK [I]: the classical decay set (l=0,1) = {0,-1,-2} = -Spec(V) = -N_fam x cusp weights - the classical seam clock decays exactly on the grading that carries the transfer operator's eigenspaces (FLAV.QGEO.01/FLAV.DIAMOND.02): structural support for the relocation identification (SYNTH.INVENTORY.01 R1). THE QUANTUM TARGET [I]: transfer rates {0, Delta, 6ln3} are not weight-linear; rate(2)/rate(1) = log_{3/2}(3) = 1+log_{3/2}(2) = 2.7095; exact identity (1/3)^6 = ((2/3)^6)^{log_{3/2}3}; required bend log_{9/4}(3) = 1.35476 per weight step. COUPLING LANDSCAPE [I]: kappa = (c/24pi)(Lambda/Mbar^2), c=8: cosmological 7.6e-122 vs seam 1/(3pi) = 0.106 - the only viable regime, borderline non-perturbative; one-loop linear response cannot fix the bend (O(1) resummation or exact seam construction required). STATUS [P]: R1 = 'produce the bend log_{3/2}3 on the cusp ladder at coupling O(1/3pi)'; identification NOT closed

Recorded status: Identity [I] (tower, cross-link, target arithmetic, coupling) + Physical [P] (identification)

Original ledger status

GRAV.H0.01

GRAV.H0.01

COSMOLOGICAL-CONSTANT BRANCH H0 = 66.5..67.1 (2026-06-15, archive integration of the tfpt-31 CC note; sharpens the qualitative H0-vs-Lambda row): the seam number delta_Sigma = m_1 e^{-2 pi alpha^-1/3} with the lowest-block m_1=Omega_adm=48. (1) [N] delta_Sigma^lead = 48 e^{-2 pi*137.036/3} ~ 1.085e-123. (2) [E] convention split M_Pl^4/Mbar^4 = (8 pi)^2 = 631.65 (unreduced vs reduced Planck density -- must be displayed). (3) [N] rho_Lambda = M_Pl^4 delta_Sigma ~ 2.4e-47 GeV^4 (observed vacuum order). (4) [N] 123-orders cross-link |log10 delta_Sigma| ~ 122.96, consistent with the v60 split 122.948. (5) [C] under the flatness closure H0^lead=66.51, H0^disc=67.10 km/s/Mpc -- 1.6..0.5 sigma BELOW Planck (67.36+-0.54), ~6 sigma below SH0ES (73.0+-1.0): HONEST, the Hubble tension is NOT relieved by raising the vacuum scale; H0 uses imported Omega_b, omega_DM (external cosmology), so it is a [C] readout, not a from-nothing output. Python-only (the (8pi)^2 ratio is on the Wolfram path via v60)

Recorded status: Numerical [N] (delta_Sigma, 123-orders) + physical bridge [C] (H0 flatness readout)

Original ledger status

DM.AXION.SPINE.01

DM.AXION.SPINE.01

AXION DM SPINE-ANGLE BRANCH theta_i = pi N_fam/g_car = 3 pi/5 = 108 deg (2026-06-15): an ALTERNATIVE, more ROBUST misalignment angle than the determinant-line hilltop theta_i ~ 170 deg (FR.DM.03/v185, which over-produces Omega_a h^2 ~ 0.66 ~ 5.5x). (1) [I] RATIONAL MOTIVE: theta_i = pi N_fam/g_car = 3 pi/5 = 108 deg EXACTLY (the central spine quotient 3/5 = N_fam/g_car, a rational multiple of pi, NOT tuned to the relic). (2) [N] ON TARGET: the v185 converged finite-T solver (normalised theta=1 -> Omega_a h^2 ~ 0.03) reaches Omega_DM h^2 = 0.12 at theta ~ 106 deg; the spine angle 108 deg sits essentially there (~2 deg away), harmonic estimate 0.03 theta^2 = 0.107 confirms the order, a mild anharmonic factor lifts to ~0.12. (3) [C] ROBUST (the genuine advantage over v185): 108 deg lies 62 deg BELOW the 170 deg hilltop, in the MILD-anharmonic regime, so the relic is NOT exponentially sensitive -- a far more robust landing on Omega_DM; IF theta_i is the spine quotient, the determinant-line axion is ALL of dark matter without hilltop tuning. (4) [O] HONEST -- AN ALTERNATIVE ANSATZ: theta_i = 3 pi/5 (spine motive) and theta_i = pi(1-phi_seam) ~ 170 deg (seam-value motive, v185) are MUTUALLY EXCLUSIVE readings of the same angle; neither is forced -- the full finite-T solver decides. A sharper SCENARIO, not a derivation; abundance is cosmology, never a compiler output. (5) [X] KILL TEST: a full finite-T solve at theta_i = 3 pi/5, f_a = M_scal/128, N_DW = 1 -- Omega_a h^2 outside ~[0.08,0.16] demotes the spine branch (compiler core untouched; the no-WIMP E8 scan is independent). Python-only. POST-INFLATIONARY REFRAMING [C] (2026-07-10, FR.DM.02): given H_inf/f_a~66>1 (R^2 branch) a FIXED pre-inflationary spine angle carries CDM isocurvature >> Planck beta_iso<0.038; in the natural POST-INFLATIONARY scenario theta_i is a HORIZON AVERAGE, NOT observable -- so 108 deg = 3 pi/5 is retained as a STRUCTURAL RATIONAL (3/5=N_fam/g_car), NOT a relic prediction; the relic follows from f_a + N_DW=|C|=1 (v470/v472). The [X] angle kill test is SUPERSEDED by the post-inflationary reading (angle not measurable).

Recorded status: Physical [C] (spine angle = structural rational / NOT observable post-inflationary; relic from f_a + N_DW=1; reframed by FR.DM.02)

Original ledger status

DM.AXION.PENTAGON.01

DM.AXION.PENTAGON.01

THE 'UNMAPPED' ICOSAHEDRAL/GOLDEN E8 STRUCTURE SURFACES IN THE ONE EXTERNAL COSMOLOGICAL INPUT theta_i (2026-06-26, v429): a geometric re-reading answering the parsimony question 'why does so much idle E8 structure exist?' for the one case where the idle structure has a job. [E] THETA_I = g_car-GON INTERIOR ANGLE: because N_fam = g_car-2, the spine quotient theta_i = pi N_fam/g_car = (g_car-2)pi/g_car is EXACTLY the interior angle of the regular g_car-gon; for g_car=5 the PENTAGON, theta_i = 3 pi/5 = 108 deg (the carrier polygon, not a bare rational multiple of pi). [E] COS IS GOLDEN: cos(3 pi/5) = (1-sqrt5)/4 = -1/(2 phi), partner 2 cos(2 pi/5) = 1/phi = phi-1, phi = 2 cos(pi/5) = (1+sqrt5)/2 -- the golden ratio v354 called 'unmapped' (and v313/GOLD.ATOMS.01 named the g_car=5 signature) IS theta_i's angular data. [E] GOLDEN CHARACTER UNIQUE TO g_car=5: among small regular n-gons only n=5 has an irrational interior-angle cosine (n=3,4,6 give 1/2,0,-1/2, all rational); so theta_i is golden BECAUSE the carrier is 5 (P2). [C] BRIDGE (NO STATUS CHANGE): connects E8.REVERSE.AUDIT.01/GOLD.ATOMS.01 (phi = the unmapped g_car=5 signature) to DM.AXION.SPINE.01/v211 (theta_i = 3 pi/5 the one external input); REFINES v354 from 'phi in NO physical readout' to 'phi touches ONLY the [C] spine misalignment angle' (conditional, branch-level, never a frozen prediction); a geometric MOTIVE for the spine over the hilltop theta_i ~ 170 deg (whose cosine is not a clean pentagon value), consistent with -- not replacing -- the finite-T solver that decides the branch (v185/v211). Does NOT derive theta_i, does NOT upgrade DM.AXION.SPINE.01 (stays [C]), closes no gate. Wolfram-mirrored, Python (sympy)

Recorded status: Identity [E] (theta_i = regular g_car-gon interior angle; cos = -1/(2 phi); golden character unique to g_car=5) + [C] bridge re-reading (no status change)

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

FLAV.NUSCALE.01

FLAV.NUSCALE.01

ABSOLUTE NEUTRINO-MASS SCALE TYPED HONESTLY (2026-06-18): does NOT fabricate a Sigma m_nu number (would contradict the v184 firewall); closes the PMNS bookkeeping instead. [E] the absolute scale reduces to ONE seesaw ratio m_3 = (y_nu v_EW)^2/M_R -- one irreducible UV input like v_geo (No-Unit, v153); the ratios (m2/m3, ordering, PMNS angles v270) are pinned. [N] the observed m_3 = sqrt(dm2_atm) = 0.050 eV with the TFPT PS->GUT scale window M_R in [M_PS=4.2e13, M_GUT=2.4e15] GeV (v249) needs a third-generation Dirac Yukawa y_nu in [0.26, 2.0] -- O(1), Yukawa-natural, no tuning. [O] the y_nu=1 seesaw scale M_R=v_EW^2/m_3=6.1e14 GeV has log_c3(M_R/Mbar)=2.57 (non-integer), not a TFPT compiler output; (y_nu,M_R) trade off so the absolute Sigma m_nu stays one open UV input. [C] the normal-ordering floor Sigma m_nu = m_2+m_3 = 0.0586 eV is consistent with Planck+BAO (<0.12 eV) and DESI 2024 (~0.072 eV). [X] a cosmological Sigma < 0.0586 eV excludes the NO m1~0 spectrum. UPDATE 2026-07-14 (v481/FLAV.NUSCALE.02): under the CARRIER normalisation y_nu = y_t (minimal 16.16.10 Yukawa sector, [P]) the (y_nu, M_R) trade-off collapses to M_R alone; the required M_R = 9.3e13 GeV sits INSIDE the PS window at log_c3(Mbar/M_R) = 3.15; the integer rung c3^3 Mbar is DECLINED at 1-loop (m_3 40% low). The absolute scale stays [O]; candidate class, frozen record untouched.

Recorded status: Bookkeeping [E] + window [N]/[C] + [O] absolute scale + [X] kill

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

FR.DYNAMICS.01

FR.DYNAMICS.01

THE DISCRETE->DYNAMIC LENS ON F_transfer (2026-06-19): asks whether the main-branch mechanism -- a gapped, positivity-preserving relaxation to a UNIQUE attractor (the local-averaging update m<-(A+2I)/4 m -> the E8 marks, gap 6 log(3/2)) -- is also the shape of the four F_transfer instances, or an unrelated bolt-on. Answer: ALL FOUR share the SAME shape (a gapped contraction/flow to a unique attractor: Perron-Frobenius / Boltzmann H-theorem / RG fixed point), but only ONE has the SEAM rate. [E] F_pole (Koide) IS the seam dynamics: the source->pole/branch relaxation is the Moebius map with fixed-point multiplier F'=(2/3)^6 = lambda_2 = the seam-clock subleading eigenvalue (v82/v54); |F'|<1 => a unique attractor at the SEAM rate (gap 6 log(3/2)), two starts converge at rate lambda_2^n. [C] F_Boltzmann (eta_B): the baryon asymmetry is the slow mode of a positivity-preserving Boltzmann operator; washout kappa_f in (0,1) converges to the unique balance (homog. part decays, gap=W>0); compiler fixes A_Lambda=10 (in M_1 and m~_1); the RATE is thermal, NOT the seam gap. [C] F_relic (axion): the misalignment field's comoving number density relaxes to a CONSTANT once H<~m_a (adiabatic invariant, a fixed point); seed theta_i=3pi/5=(N_fam/g_car)pi; the RATE is cosmological. [I] F_QCD (m_p/m_e): the 1-loop RG flow with the carrier coefficient b3=-7 (b0=11-2 nf/3=7, nf=2 N_fam; asymptotic freedom) has the Gaussian UV fixed point as attractor (alpha_s->0 toward the UV), Lambda_QCD the dynamically generated IR scale; b3 from the carrier, the flow standard RG. [O] VERDICT: one shape (gapped relaxation/flow to a unique attractor) underlies all four = the main-branch discrete->dynamic principle; F_pole has the seam rate exactly ((2/3)^6), the other three share only the shape (external rates: thermal/cosmological/RG). So F_transfer is the downstream readout end of the one principle, NOT a bolt-on; the theory's simplicity is preserved precisely because the external rates are honestly fenced (v187), not because they reduce to the seam.

Recorded status: Dynamical-systems unification [E/C] (one shape / one seam-rate)