Original claim records.

Original ledger status

FLAV.TH13.PRESSURE.01

FLAV.TH13.PRESSURE.01

THE theta13 PRESSURE POINT -- THE HONEST WEAK SPOT, QUANTIFIED AND PRE-REGISTERED (2026-06-22). [N] TENSION: sin^2 theta13 = phi0 e^{-5/6} = 0.023108 vs NuFIT 6.0 NO (0.02195 +- 0.00058) is +2.0 sigma -- the most-tensioned CORE prediction (v62/v307). [E] SEPARATE CHANNEL: theta13 is the carrier hypercharge trace (exponent gamma=tr_E Y^2=5/6 EXACT, v268), NOT the seesaw mu-tau breaking that sets theta12 (eps=3 phi0/4 induces only ~1.6e-3 << 0.023) -- distinct channels, a theta13 pull does not move theta12. [N] NO CHEAP RELIEF: phi0(theta13)=e^{5/6} sin^2 theta13_exp=0.0505 is ~5% below the axiom 0.05317; PMNS theta13 RG running is <1% (NO) so cannot close a 5% gap, and the exponent 5/6 is exact -- no freeze-respecting sub-leading correction relieves it; prediction stays frozen (REG.FREEZE.01). [X] PRE-REGISTERED KILL: a stable sin^2 theta13 away from 0.023108 at >3 sigma (JUNO/global) flags the carrier-trace/seed-grammar reading. [E] SEED-HYPERPLANE CONSISTENCY: exactly the v306 leave-one-out outlier (theta13 the single ~2 sigma channel, others ~1 sigma) -- one honest pressure point, not a pattern.

Recorded status: Numerical/data [N]/[X] (theta13 pressure point)

Original ledger status

FORM.QGEO.BW.01

FORM.QGEO.BW.01

LEAN: QGEO.SYM.01 FROM SEAM.EQUIV.01 VIA BISOGNANO-WICHMANN (2026-06-22). Lean 4 formalisation (TfptCarrier/BWKeystone.lean) of the v323 linkage: the nodes RotationInvariantVacuum -> GeometricModularFlow -> Mu4ModularSymmetry -> StateInvariance (=QGEO.SYM.01) assembled with the cited Bisognano-Wichmann/Hislop-Longo steps as named axioms, composed over the v308 chain (seamEquivChain discharges SeamIsE8). The theorem bedrockReducesToRotationInvariance : RotationInvariantVacuum -> StateInvariance shows the WHOLE bedrock QGEO.SYM.01 reduces to the SINGLE shared open premise RotationInvariantVacuum (the two open bedrock items collapse to one). #print axioms confirms the residual = the v308 cited steps + recovery_gap + the named BW steps + RotationInvariantVacuum (no hidden assumption). Plus a decide-proven discriminator bw_strictly_stronger: (1|4) and not(4|1) -- the BW geometric flow (period 1) is strictly stronger than the v309 clock invariance (period 4). Built end-to-end (lake build) on Lean v4.29.1 + Mathlib. The VALUE is the machine-checked collapse of the two bedrock items to one shared premise, NOT a from-scratch proof -- it does NOT close QGEO.SYM.01.

Recorded status: Formal

Original ledger status

QGEO.OSGAP.01

QGEO.OSGAP.01

CLOSING THE OS STEP: THE BULK GAP IS THE TRANSFER GAP (2026-06-22, second quantization) + the single sufficient premise. The v308 chain left ONE analytic input -- the OS identification 'OS-reconstructed bulk gap = transfer gap'. [E] OS GAP = TRANSFER GAP: the OS/Euclidean many-body Hamiltonian is dGamma(-log T) (T the v221/v302 recovery transfer); its spectrum is the set of sums of single-mode energies, so the many-body (bulk) gap = the smallest positive single-mode energy = 6 ln(3/2), INDEPENDENT of the number of modes -- discharges the v308 OS input at the many-body level. [E] H => omega o rho = omega: under the premise H the covariance is rotation-covariant C=f(L), so K=log((1-C)/C)=g(L) commutes with rho=exp(i(pi/2)L) ([rho,K]=0 = QGEO.SYM.01 + geometric flow, v201/v309/v323). [E] H => SRE => holomorphic => (E8)_1: |det Cartan(E8)|=1 vs D8=4 (v237/v308). [E] SINGLE SUFFICIENT PREMISE: both bedrock IDs (QGEO.SYM.01 + SEAM.EQUIV.01) follow from the ONE premise H = 'raw collar = rotation-invariant flat tau=i pillowcase state', Lean-pinned (FORM.SEAMEQUIV.01 + FORM.QGEO.BW.01). [O] RESIDUAL: the NECESSITY of H on the raw (continuum) collar (NEG: a non-rotation-invariant collar breaks mark-locality). Sharpens v240/v308/v323/v325; does NOT close the bedrock.

Recorded status: Reduction [E]/[O] (OS gap = transfer gap + single premise)

Original ledger status

QGAMB.MEASURE.01

QGAMB.MEASURE.01

CONSTRUCTING THE AMBIENT MEASURE ON THE GAP-DECOUPLED ADMISSIBLE SECTOR (2026-06-22) as a bona fide Osterwalder-Schrader object, with the honest fence (the constructive step v275's roadmap calls for). [E] REFLECTION POSITIVITY: the seam transfer T (v221/v311; spectrum {1,(2/3)^6,(1/3)^6}) is symmetric PSD, so the finite-volume transfer-matrix measures are RP (OS-0). [E] EXPONENTIAL CLUSTERING: the connected 2-pt C(n)/C(n-1) -> lambda_2=(2/3)^6 (corr. length xi=1/Delta, Delta=6 ln(3/2)). [E] TIGHTNESS => PROJECTIVE LIMIT: chi=sum_n C(n)=729/665 is FINITE, so Var(S_Lambda)/Lambda -> chi converges => the finite-volume measures are uniformly tight (Prokhorov) and the projective limit mu=lim mu_Lambda EXISTS on the admissible sector. [E] OS RECONSTRUCTION: RP + clustering + positive transfer give H_OS=-log T>=0 with unique vacuum and gap 6 ln(3/2) (v240) -- mu is a genuine OS measure on the admissible sector. [E] NEG: an ungapped transfer (lambda_2->1) sends xi,chi->inf and Var/Lambda->inf, tightness FAILS -- the construction is the gap. [O] THE FULL AMBIENT MEASURE: the non-admissible (metric/dressed) sector is NOT built; the full 4D QG.AMB.01 needs the metric-direction measure + its coupling. By the gap-decoupling margin Delta-31/(4 pi^2)~1.648>0 (v76/v275) the physical readouts do NOT need it, but QG.AMB.01 stays open.

Recorded status: Construction [E]/[O] (admissible-sector OS measure)

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

Original ledger status

FORM.CARTAN.DET.01

FORM.CARTAN.DET.01

LEAN: THE CARRIER CARTAN DETERMINANTS AS REAL Matrix.det COMPUTATIONS (2026-06-22). Lean 4 (TfptCarrier/CartanDeterminants.lean) grounds the carrier piece of the holomorphy/anyon discriminator in ACTUAL determinants of the integer Cartan matrices, proved (kernel decide, no extra axiom) rather than asserted: |det Cartan(A3)|=4=|mu4| (3x3, via Matrix.det_fin_three) and |det Cartan(D5)|=4 (5x5, via decide at maxRecDepth 4000), giving the carrier |det Gram(D5(+)A3)|=4*4=16=dim S+ (the v281 anyon count 16 -> the tower 16->4->1). For the rank-8 case the 8x8 Leibniz determinant is not kernel-decidable (Mathlib's own Mathlib.Data.Matrix.Cartan leaves E8_det=1 as a proof_wanted, proving only the smaller G2/F4 dets by decide), so instead the UNIMODULARITY -- the holomorphy discriminator |det Cartan(E8)|=1 (E8 has ONE anyon/primary, vs D8's four) -- is proved PRINCIPALLY and kernel-only: cartanE8 * cartanE8inv = 1 by decide on the 8x8 PRODUCT (~512 mults, feasible) gives IsUnit(cartanE8.det) via det(E8)*det(E8inv)=det(1)=1 (cartanE8_det_isUnit). The sign det=+1 then follows from positive-definiteness (standard). Built end-to-end (lake build) on Lean v4.29.1 + Mathlib. The VALUE is grounding BOTH the carrier anyon count AND the rank-8 holomorphy discriminator (E8 unimodular = one anyon) in real determinants/matrix algebra, no native_decide.

Recorded status: Formal

Original ledger status

QGEO.NECESS.01

QGEO.NECESS.01

THE NECESSITY OF H REDUCED (2026-06-22): rotation-invariance of the seam DtN is EQUIVALENT to the four marks sitting at the square (tau=i), so the one open lemma is exactly the order-4 CM selection (the necessity companion to v329's sufficiency). [E] SQUARE => [rho,Lambda]=0: with marks at {0,pi/2,pi,3pi/2} the curvature is Z4-symmetric (Fourier support 0 mod 4), M_f couples only modes differing by 4Z, [rho,Lambda]=0 (the v201/v210 sufficiency, recomputed as a DtN |k|+M_f operator). [E] NECESSITY: moving a mark off the square breaks Z4 and gives [rho,Lambda]!=0 -- so rotation-invariance of the DtN is EQUIVALENT to the square configuration, not merely implied. [E] ORDER-4 CM: the cross-ratio of the square points (1,i,-1,-i) is 2 => j=1728, the lemniscatic CM modulus tau=i with an order-4 automorphism -- the UNIQUE 4-config carrying the mu4 deck (v214/v267); so H <=> square <=> order-4 CM <=> mu4. [E] NEG: a Z2 (period-2) mark set commutes with rho^2 but not rho. [O] SHARPENED RESIDUAL: 'necessity of H' is now exactly 'the raw dynamics places the four Gauss-Bonnet marks (v216) at the order-4 CM (square) point' -- the marks are forced to be 4, the square is the unique order-4 CM config, but the dynamical SELECTION of the square is the irreducible residual (not closed).

Recorded status: Reduction [E]/[O] (necessity of H = the order-4 CM selection)

Original ledger status

QGAMB.METRIC.01

QGAMB.METRIC.01

THE METRIC SECTOR OF QG.AMB.01 CHARACTERIZED (2026-06-22): the obstruction is exactly the conformal-mode (Gibbons-Hawking-Perry) problem, the physical sector is gap-insulated, and the only route is the conditional IDG taming (makes v330's metric-sector fence precise). [E] CONFORMAL-MODE WRONG SIGN: c_conf(D)=-(D-1)(D-2)/4 is NEGATIVE for D>=3 (c_conf(4)=-3/2) while the transverse-traceless coefficient is positive -- the conformal-factor problem (Gibbons-Hawking-Perry 1978). [E] MEASURE OBSTRUCTION: with a negative kinetic coefficient exp(-S)~exp(+|c_conf|phi^2) DIVERGES over the conformal mode, so the bare metric-sector measure is not directly definable. [E] PHYSICAL SECTOR INSULATED: the obstruction is in the conformal/gauge direction, NOT the admissible sector (transverse, gapped, positive, v330), with gap-decoupling margin Delta-31/(4pi^2)~1.648>0 (v76). [C] IDG CONDITIONAL ROUTE: the entire form factor a(z)=e^{z/M^2} (v259/v304) dresses the conformal propagator 1/(p^2 a) with no extra pole (exp has no zeros) -- conditional taming (Tomboulis/BMS). [E] NEG: a polynomial (R+R^2) truncation a(z)=1+z/M^2 crosses zero at z=-M^2 (the Stelle ghost, v304/v278). [O] METRIC SECTOR OPEN: the full QG.AMB.01 metric-sector measure needs the conformal mode resolved nonperturbatively (GHP contour rotation, or the IDG resummation) -- gap-decoupled from every physical readout (v76/v275/v330) but NOT constructed. A precise characterization, NOT a closure.

Recorded status: Characterization [E]/[C]/[O] (metric-sector = the conformal-mode obstruction)

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

Original ledger status

FORM.MU4COMM.01

FORM.MU4COMM.01

LEAN: THE mu4 MARK-LOCALITY COMMUTATION AS REAL LINEAR ALGEBRA (2026-06-22). Lean 4 (TfptCarrier/Mu4Commutation.lean) turns the v201/v309/v323 finite-model fact (the mu4 clock rho=diag(i^n) commutes with a DtN sub-principal coupling IFF that coupling is mark-local, i.e. couples only Fourier modes differing by a multiple of 4) into an EXACT, kernel-checked statement over the Gaussian integers Z[i]: [E] i^4=1 (an offset-4 mode shift is invisible to the mu4 clock) and i^2=-1 (an offset-2 shift flips the sign, so rho sees it), by decide; [E] mu4_commutes_offset4: rho * M4 = M4 * rho for a concrete offset-4 coupling on 6 modes (the Z4-invariant/mark-local case), by decide; [E] mu4_not_commutes_offset2: rho * M2 != M2 * rho for an offset-2 coupling (the non-mark-local negative control), by decide. Built end-to-end (lake build) on Lean v4.29.1 + Mathlib. The VALUE is grounding the v201 block-diagonality criterion (mark-locality <=> omega o rho = omega) in exact, kernel-decidable linear algebra over Z[i], no native_decide.

Recorded status: Formal

Original ledger status

QGEO.CMSELECT.01

QGEO.CMSELECT.01

THE CM-SELECTION MECHANISM (2026-06-22): tau=i (the square) is the UNIQUE order-4 modulus and the attractor of mark-equilibration, so the last keystone residual is 'the deck acts geometrically', not 'why the square' (the v331 follow-up). [E] ORDER-4 MODULAR ELEMENT: S=[[0,-1],[1,0]] in SL(2,Z) has S^2=-I, S^4=I (order 4) and fixes tau=i (S.i=-1/i=i); i is the unique order-4 elliptic point of PSL(2,Z) (the only other elliptic point, rho, is order 3). [E] DECK ORDER -> CM POINT (the selector): order-4 deck -> cross-ratio 2 -> j=1728 -> tau=i (square); order-3 deck -> equianharmonic lambda (lambda^2-lambda+1=0) -> j=0 -> tau=rho (hexagon); the carrier deck |mu4|=4 (anchor-derived) selects tau=i uniquely, not rho. [E] MARK-EQUILIBRATION ATTRACTOR: four points on the circle minimizing the log-energy E=-sum log|z_i-z_j| (Fekete points) converge to EQUAL spacing (gaps pi/2 = the square) from random starts, and the square's energy beats random perturbations -- the unique (mod rotation) attractor of symmetric mark-equilibration. [E] NEG: an order-3 (hexagonal) deck selects tau=rho (j=0), NOT the square (j=1728) -- deck-order-specific. [O] SHARPENED RESIDUAL: given the mu4 deck, tau=i is FORCED (arithmetic) and is the equilibration attractor (dynamical); only that the seam recovery dynamics IS this mu4 equilibration acting GEOMETRICALLY (a conformal automorphism, = QGEO.SYM.01) vs an abstract Z4 on labels stays open -- the residual sharpens from 'why the square' to 'the deck acts geometrically'. NOT a closure.

Recorded status: Reduction [E]/[O] (CM selection = unique order-4 modulus + equilibration attractor)

Original ledger status

QGAMB.CONFORMAL.01

QGAMB.CONFORMAL.01

THE CONFORMAL-MODE RESOLUTION (2026-06-22): the Gibbons-Hawking-Perry contour rotation (IR sign) + the infinite-derivative (IDG) dressing (UV pole) give a CONDITIONALLY convergent metric-sector measure; the residual is the nonperturbative validity of the contour (the v332 follow-up). [E] THE OBSTRUCTION: c_conf(4)=-(D-1)(D-2)/4=-3/2<0, so the unrotated conformal Gaussian integral(exp(+|c|phi^2)) DIVERGES. [E] GHP CONTOUR ROTATION: phi->i phi flips (i phi)^2=-phi^2, so +|c|phi^2 -> -|c|phi^2 and integral(exp(-|c|phi^2))=sqrt(pi/|c|) is FINITE -- the Gibbons-Hawking-Perry 1978 prescription makes the conformal measure convergent. [E] IDG UV DRESSING: the entire form factor a(p^2)=exp(p^2/M^2) is nowhere zero (no ghost pole, v304), the dressed per-mode action (1/2)|c| k^2 a(k^2) phi^2 is positive after GHP and UV-suppressed. [E] NEG: a polynomial truncation a=1+p^2/M^2 crosses zero at p^2=-M^2 (the Stelle ghost, v304/v278). [C] CONDITIONAL CONSTRUCTION: GHP (IR sign) + IDG (UV pole) give a formally convergent metric-sector Gaussian mode-by-mode -- a conditional construction (conditional on the rotation contour AND entire analyticity, v304). [O] THE RESIDUAL: whether the GHP-rotated IDG-dressed measure is the CORRECT nonperturbative QG.AMB measure (the contour rotation's nonperturbative validity, Euclidean QG's long-standing issue); gap-decoupled (Delta-31/(4 pi^2)~1.648>0, v76), so it blocks no test. NOT a closure.

Recorded status: Construction [E]/[C]/[O] (conformal-mode GHP+IDG conditional resolution)

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

Original ledger status

SEAM.EQUIV.UNIFY.01

SEAM.EQUIV.UNIFY.01

THE KEYSTONE UNIFICATION (2026-06-22): there is ONE open theorem (SEAM.EQUIV.01), QGEO.SYM.01 is its COROLLARY (a conformal-net axiom), and QG.AMB.01 is a decoupled general QG problem, NOT a TFPT gate -- collapsing the 'two open structural items' narrative to 'one solvable theorem + one decoupled foreign problem'. [E] QGEO.SYM.01 = COROLLARY: a chiral conformal net has a Moebius-covariant vacuum (the unique invariant positive-energy vector, a NET AXIOM); rotations U(1) < Moebius => the vacuum is rotation-invariant; the mu4 clock = rotation by pi/2 ((e^{i pi/2})^4=1) fixes it => omega o rho = omega. So SEAM.EQUIV.01 => QGEO.SYM.01 with NO extra premise (the v323 'rotation-invariant vacuum' is a net axiom); machine-pinned in Lean as qgeoSymIsCorollary. [E] THE ONE KEYSTONE THEOREM: SEAM.EQUIV.01 = a construction theorem (c=g_car+N_fam=8, det Cartan E8=1, gap 6 ln(3/2)>0 derived) with EXACTLY 1 open continuum lemma (rigorous continuum OS reconstruction + invertibility of the raw collar); 5 of 6 links cited/derived. [E] QG.AMB.01 DECOUPLED: margin Delta-31/(4pi^2)~1.648>0 (v76/v311/v330/v332) => no TFPT prediction depends on it; the general Euclidean-QG conformal-factor problem (GHP 1978), inherited not TFPT-specific. [E] COLLAPSED STATUS: open structural items 2 -> 1 (SEAM.EQUIV.01); QGEO.SYM.01 corollary; QG.AMB.01 decoupled; live residual = v_geo + G_net(=SEAM.EQUIV.01) + F_transfer. [O] the one residual = SEAM.EQUIV.01's continuum OS reconstruction (Lean-pinned FORM.SEAMEQUIV.01 + FORM.QGEO.BW.01). A synthesis/inventory module (like v275/v318); does NOT close SEAM.EQUIV.01.

Recorded status: Synthesis/reduction [E]/[O] (one keystone theorem; QGEO.SYM corollary; QG.AMB decoupled)

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

Original ledger status

SEAM.EQUIV.CONTINUUM.01

SEAM.EQUIV.CONTINUUM.01

THE ONE OPEN LEMMA OF SEAM.EQUIV.01, stated precisely and mapped to the recent rigorous literature (2026-06-22): the continuum-limit and OS-reconstruction legs are now CITABLE, the genuinely-open residual narrows to 'the raw collar is a gapped quasi-free state whose massless scaling limit is the c=8 (E8)_1 net'. [C] CONTINUUM LEG: Osborne-Stottmeister (CFT from Lattice Fermions, doi:10.1007/s00220-022-04521-8, CMP 398 (2023) 219) give, building on the MMST operator-algebraic (wavelet/Wilson-Kadanoff) renormalization framework (Morinelli-Morsella-Stottmeister-Tanimoto, CMP 387 (2021) 299; PRL 127 (2021) 230601), the chiral-CFT scaling limit of free lattice fermions (Koo-Saleur -> Virasoro, correct c); WZW range rank <= c <= D (D Majorana copies). (E8)_1: c=8, rank 8, D=16 Majoranas (SO(16)_1 -> (E8)_1), 8<=8<=16 IN range; the collar is gapped quasi-free (CAR). [C] OS LEG: Adamo-Moriwaki-Tanimoto (arXiv:2407.18222, 2024) prove the conformal OS axioms (linear growth) for unitary VOAs incl. WZW/lattice VOAs; (E8)_1 is the even self-dual rank-8 lattice VOA. [E] TARGET PINNED: c=g_car+N_fam=8, det Cartan E8=1, the D=16 Majorana SO(16)_1 IS the carrier-16, the mu4 extension IS the seam glue. [O] OPEN RESIDUAL: c=8 alone does NOT pin the net (SO(16)_1 also c=8, det Cartan D8=4), so the open lemma = the holomorphy discriminator det K=1 (v277/v281/v335). A literature-mapping/reduction; does NOT close SEAM.EQUIV.01.

Recorded status: Reduction [C]/[O] (continuum lemma narrowed + literature-anchored)

Original ledger status

DECOUPLING.THEOREM.01

DECOUPLING.THEOREM.01

THE DECOUPLING THEOREM (consolidated, citable, 2026-06-22): every TFPT dimensionless readout factors through the gapped admissible sector and is INDEPENDENT of the ambient QG measure -- the theorem that makes the QG.AMB.01 reclassification (v335) honest. [E] GAP MARGIN: Delta - 2*dim(E8)*c3^2 = 6 ln(3/2) - 496/(64 pi^2) = 6 ln(3/2) - 31/(4 pi^2) ~ 1.648 > 0 (the ambient back-reaction scale 2*248*c3^2 = 31/(4 pi^2) exactly). [E] FACTORIZATION: every readout (mass ratios, mixings, alpha^-1, R+R^2) is a function of the admissible gapped transfer spectrum {1,(2/3)^6,(1/3)^6} + the discrete kernel alone; the ambient couples only above the gap. [E] THE THEOREM: margin>0 => exponential clustering (lambda_2=(2/3)^6) with finite susceptibility chi=1/(1-(2/3)^6)=729/665, so the ambient contribution is gap-suppressed => no readout depends on the ambient measure => QG.AMB.01 decoupled. [E] NEG CONTROL: gap closed (lambda_2->1) => chi diverges => fails (non-vacuous). [E] COROLLARY: zero frozen kill tests depend on the ambient measure. Consolidates v76/v311/v330/v332; does NOT construct the ambient measure (that is QG.AMB.01).

Recorded status: Theorem [E] (factorization through the gap => ambient-measure independence)

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

Original ledger status

THETA13.BUDGET.01

THETA13.BUDGET.01

THE THETA13 SUB-LEADING BUDGET vs the current global fit (2026-06-22): the +2 sigma pressure point (v328) quantified against BOTH NuFIT 6.0 normal-ordering variants and JUNO; neither defuses nor excludes -- fences correctly. [N] SK-DEPENDENT TENSION: sin^2 theta13 = phi0 e^{-5/6} = 0.023108 is +2.0 sigma vs the no-SK central (0.02195 +- 0.00058) and +1.7 sigma vs the with-SK NO best fit (0.02215 +- 0.00057) -- a ~0.3 sigma spread from one systematic, NOT a clean 2 sigma. [E] WITHIN 3 SIGMA: 0.023108 < the with-SK 3 sigma upper bound 0.02388, INSIDE the allowed region (not falsified). [N] SUB-LEADING BUDGET: moving 0.023108 to the with-SK central needs d(sin^2 theta13) = -0.00096 (-4.1%); RG running < 1% and the exponent 5/6 is exact, so ~3% would need a sub-leading channel larger than natural -- no freeze-respecting relief (v328). [X] JUNO DECIDES: sub-1% precision on sin^2 2theta13 (sigma ~ 1.5e-4) turns 1.7-2.0 sigma into ~6 sigma either way -- near-term pre-registered kill/confirm. [E] one honest pressure point (v306 seed-hyperplane outlier, v328), correctly fenced.

Recorded status: Data-confrontation [N]/[E]/[X] (mild +1.7-2.0 sigma; within 3 sigma; JUNO decides)

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

ALPHA.QUILLEN.01

ALPHA.QUILLEN.01

THE ALPHA FIXED POINT AS THE STATIONARITY OF A U(1) DETERMINANT LINE (2026-06-22): reformulates the EM closure from 'a very cleverly built fixed point' into 'the stationarity of a named functional', identifying every ingredient as an index / heat-kernel coefficient / discriminant form -- the 'derive the FORM' step (external review). F_{U(1)} = a^3 - 2 c3^3 a^2 - (4/5) c3^6 M ln(1/phi_seam) = 0 written in Quillen form: [a^3 - 2 c3^3 a^2] (determinant-line variation) = [8 b1 c3^6] (anomaly counterterm) * [ln(1/phi_seam)] (seam response), i.e. delta log det Delta_U(1) + counterterm + seam response = 0. [E] M=41 is a U(1) INDEX (EM Ward, v48): (4/5)M = 8 b1 = 164/5 with b1=41/10 the SM one-loop U(1)_Y beta (GUT-norm, v159/v246), so M=10 b1; the counterterm coefficient is 8 b1 c3^6 = (rank E8) b1 c3^6. [E] c3=1/(8 pi) is the GAUSS-BONNET boundary coefficient (8 = rank E8, v216); c3^3 (Quillen-metric) and c3^6 (counterterm) are heat-kernel powers. [E] the exponent -5/4 = -q(D5) is a DISCRIMINANT form (q(D5)+q(A3)=2, v1/v154); phi_base=1/(6 pi)=(4/3)c3 carries q(A3): c3/phi_base=3/4. [E] delta_top=Omega_adm c3^4 (Omega_adm=48). [E] the Quillen split holds at the alpha^-1=137.0359992 root. [E] NO NEW GATE: alpha^-1 stays closed [E] (unique root + ablation, v3); v341 adds NO open item -- it SHARPENS the pre-existing [P] physical Ward origin EM.WARD.01 ('why THIS function') toward [E] by naming every coefficient. [O] the one still-open part IS EM.WARD.01's residual (now sharper): the from-first-principles AQFT proof that F_U(1) is the EXACT Quillen functional of the seam U(1) (the variational principle DERIVED, not assembled). Not a new gate; not closed.

Recorded status: Reformulation [E]/[O] (alpha = stationarity of a named U(1) determinant line; sharpens the existing [P] EM.WARD.01; no new gate)

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

ALPHA.QUILLEN.EXACT.01

ALPHA.QUILLEN.EXACT.01

Names the Quillen determinant-line VARIATION as a tracked [O] target (2026-06-23, review Point 10): delta_tau(log det_zeta Delta_U(1) + 8 b1 c3^6 log phi_seam)=0 on the determinant line over the mu4 seam moduli -- i.e. F_U(1) IS the exact zeta-regularised Quillen functional of the seam U(1), not merely an assembled fixed point. Elevates EM.WARD.01's residual (v341/v342) to its own citable target so the one remaining EM obligation is trackable separately from the seam-net identification, WITHOUT creating a second independent open problem (it is a FACE of SEAM.EQUIV.01). [E] the Quillen split holds at the root a^3-2 c3^3 a^2 = 8 b1 c3^6 ln(1/phi_seam) at alpha^-1=137.0359992 (F_U(1)=0 IS the stationarity, v341). [E] every coefficient is a named atom: 8 b1=(4/5)*41 a U(1) index, c3=1/(8 pi) the Gauss-Bonnet boundary coeff (c3^3,c3^6 heat-kernel powers), q(D5)+q(A3)=2 discriminant forms (v341/v48/v216). [E] the value alpha^-1=137.0359992168 stays closed (unique root+ablation, v3) -- only 'why this functional' is open. [O] THE TARGET: the from-first-principles AQFT/zeta proof of the variation. [C] FACE OF SEAM.EQUIV.01 (v336): the seam U(1) determinant line lives on the same holomorphic seam net, so once the net is (E8)_1 its U(1) sub-determinant is fixed -- not a second gate. No new number (reuses v341, Wolfram-mirrored). UPDATE 2026-07-14 (v484/SEAM.CONTACT.UNIT.01): the target's c3-ladder rule MERGES with HYP.PHI0.PUNCTURE.01 into one analytic step -- the contact unit c3-per-insertion is the KMS seam unit (v239), derived for the finite cycle sector; the remaining [O] is the diagonal zeta-renormalisation + multiplicity matching (41 = 10 b1). UPDATE 2026-07-14 (v485): the computable side is COMPLETE (diagonal zero at the KMS scale, closed-form mark determinant, 41 = Y^2-weighted count of the same 48 states); the target's remaining [O] is now EXACTLY its v382 typing -- the SEAM.EQUIV.01 face -- with no separate analytic unknown left. UPDATED 2026-08-27 (v974): both named faces now carry COMPUTED witnesses. The diagonal-zeta face is EXECUTED as the BFK gluing on the seam circle (gluing constant EXACTLY 2^-N, derived symbolically N = 1..4 at general lengths; jump matrix at KMS R_0 = 16 c3 circ(2,-1,0,-1) = (G_m|_marks)^-1; det'R_0 = 2^16 c3^3, glued product (2 pi)^2; the v485 scale channel reproduced exactly via the KMS unit) -- vs the v484 mark matrix there is NO global proportionality (kernels in SWAPPED mu4 channels), but the correspondence is channel-wise exact (same eigenbasis, |spec| {0,2,2,4}, doublet ratio 4/ln2 with c3 cancelling): the diagonal-zeta face is thereby SHARPENED to the channel-swap question. The finite Quillen identity is verified TWO-SIDED on the twist torus (Berry integral == Poincare-Lelong divisor integral == +1, difference an exact form, transition winding == Chern), typed conditional on the quasi-free rigidity premise (measured, not proven -- SEAM.STATE.RPMIXING.01). STAYS [O]: 'why this functional' is not closed -- the remaining content is typed as {rigidity premise} + {channel-swap question} + {continuum Bismut-Freed identification of the exact-form difference field}; alpha^-1 = 137.0359992168 re-anchored (unique root on the scanned window, split residual 6.4e-58 at 50 digits). EXECUTED NOTE (2026-08-28, completeness wave): the rigidity premise of the finite Quillen identity is now executed at the finite CAR level (v995: 33 mixing directions killed by KMS alone; covariance redundant; 196608 -> 0); type-III/continuum stays [O]. The finite-collar detline curvature converges exponentially to 2pi with rate ~0.6936 ~ ln 2 (v996) -- a numerical Bismut-Freed shadow, not the continuum theorem. STAYS [O]. Python-only / Wolfram mirror deferred. RELATIVE-DETERMINANT NOTE (2026-08-29, review wave 4): the correct object is the RELATIVE determinant Q(A) = log[det' Delta_A / det' Delta_{A0}] + 8 b1 c3^6 log phi(A); the BFK constant 2^{-4} is A/tau/alpha-INDEPENDENT at fixed cut number, so delta log 2^{-4} = 0 -- no physical compensation needed (consistent with COMPENSATION_INTERNAL + the reviewer's correction). Absolute normalization is fixed by the reference A0. Contract stays [O]. LATE EVENING (2026-08-30, v1014): finite restriction isomorphism verified (c_phase constancy 3.7e-16, conjugation covariance exact, C = W_bulk = W_seam = +1 / mirror -1); orientation fixes the conjugate branch (2 -> 1); the residual constant phase is fixed by the A0 reference normalization -- recorded. Continuum Bismut-Freed stays [O]. Contract stays [O].

Recorded status: Named target [E]/[O] (the Quillen determinant-line variation-exactness; a face of SEAM.EQUIV.01, elevates EM.WARD.01's residual to a citable target; no new gate; 2026-08-28: the v974 CHANNEL-SWAP face resolved at the finite level by mu4-character grading, v985; completeness wave: finite KMS rigidity-premise [E] v995, ln-2-rate detline shadow v996 -- continuum Bismut-Freed stays [O])

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.