Publication history: 2026-06-15

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• The Sheet Diamond is a discrete geometry with two axes (v218_diamond_axis_geometry, tfpt_2_standard_model, [E]). Sharpens v94/v95 with three exact [E]lemmas (no new numbers). (1) Axis curvature: along the centered cross the determinant is linear on the winding axis \det(C{+}xU)=14{+}6x (slope 6{=}|R^+(A_3)|) and quadratic on the sheet axis \det(C{+}yV)=14{+}14y{+}4y^2 (2nd difference 8{=}\mathrm{rank}\,E_8); the anchor block has \det B(C{+}xU)=2\det(C{+}xU) and sheet curvature 6{=}|R^+(A_3)| — two curvatures (8,6)=(\mathrm{rank}\,E_8,|R^+(A_3)|). (2) Plücker transfer ladder: \mathrm{Pl}(K)\to\mathrm{Pl}(C)\to\mathrm{Pl}(F) lifts in steps (1,8,10)=(N_\Phi,\mathrm{rank}\,E_8,A_\Lambda) then (1,8,16)=(N_\Phi,\mathrm{rank}\,E_8,\dim S^+) — the decuple then the full generation (identity [E], source\topole reading [C]). (3) Spectral ramification: for Q,K,C,F the cubic discriminant factors as q(r)^2\,\mathrm{Disc}(q) with squares (1,3,4,6) and kernels (13,48,65,105), F carrying 105=3{\cdot}5{\cdot}7. The anchor-defect spectrum and pair-sum/staircase blocks are honest audit fingerprints (28{=}2\dim G_2, 52{=}\dim F_4 stay audit-only, not spine, as in v94/v95); F as the transfer-completion corner is a heuristic, not a hard filter. Ledger DIAMOND.AXIS.01, DIAMOND.PLUCKER.01, DIAMOND.SPECTRAL.01; Wolfram-mirrored (249/249).

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• The four marks emerge from Gauss–Bonnet — count derived, not assumed (v216_marks_gauss_bonnet, tfpt_research_contracts, [E]; ledger QGEO.MARKS.03). The K1 lever of the v215 kill-test (“exactly four marks”) is executed: if the marks are \Z_2 branch points (deficit \pi) on the flat seam sphere (\chi=2, the same \chi as the 8 in c_3), Gauss–Bonnet forces n\pi=2\pi\chi=4\pi, so n=2\chi=4=|\mu_4|=\Nfam+1. The closed Euclidean sphere 2-orbifolds are exactly (2,3,6), (2,4,4), (3,3,3), (2,2,2,2), and three independent criteria — all cone orders =2 (the |\Z_2| sheet branch), \mathrm{rank}\,H^1=\#\text{marks}-1=3=\Nfam (the three generations pick the 4-mark square over the 3-mark hexagonal), and a free order-4 deck — converge on the pillowcase (2,2,2,2). The numerical sibling v217_marks_emergence_scan ([C], ledger QGEO.EMERGE.01) confirms it on the actual DtN/state (number n and positions free, the 4-square config is the unique joint minimiser of clock-invariance + 3-family cohomology + gap (2/3)^6). The mark count and equality move from input to derived; only the square modulus (cross-ratio 2, the order-4 clock) stays the one carrier input, and the from-zero raw-seam emergence QGEO.REALIZE.01 stays [O]. v216 exact (Wolfram extension \to248/248); v217 numerical (Python-only). Suite \to 217 modules.

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• QGEO.SYM.01 as a kill-test, not a proof-promise (v215_seam_deck_killtest, tfpt_research_contracts, [E]/[O]; ledger QGEO.KILL.01). A foundational symmetry cannot be derived from nothing (Bisognano–Wichmann would presuppose the covariance it should produce), so the bedrock \omega\circ\rho=\omega is recast as four independently-falsifiable predictions about the raw seam DtN. The non-circular reduction (v198/v199/v201) gives \omega\circ\rho=\omega\Leftrightarrow[\rho,C]=0 with |k| commuting exactly, so the residual is the bounded sub-principal M_f (equivalently the raw Gaussian bulk form A is \mu_4-deck-invariant). Levers: K1 exactly four marks (b_1=\#\text{marks}-1=3=\Nfam\Rightarrow\#\text{marks}=4=|\mu_4|); K2 the square config (cross-ratio 2\Rightarrow j=1728, \mathrm{Aut}=\Z/4; order 4 selects \Z/4 not the j=0 \Z/6; generic \Rightarrow\Z/2); K3 mod-4 sub-principal support ([\rho,M_f]=0\Leftrightarrow f \Z_4-invariant); K4 transfer gap (2/3)^6=64/729. Freeze-bound via freeze_file.csv (seam_deck_symmetry), carrier-side [E](regression guards), with the decisive kill deferred to QGEO.REALIZE.01 [O](the raw collar DtN must produce four square marks without inputting them — an emergence test). A kill-test, not a closure. Python-only (falsification layer; the exact sub-parts j=1728 and (2/3)^6 are Wolfram-mirrored via v214/v54/v56). Suite \to 215 modules.

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• Pillowcase reduction of QGEO.SYM.01 (v214_seam_pillowcase, tfpt_research_contracts, [E]/[O]; ledger QGEO.PILLOW.01). The two separately-tracked open QGEO residuals — QGEO.ISO.01 (v180: the carrier clock is an order-4 isometry of the seam metric) and QGEO.SUBPRIN.01 (v201: the DtN sub-principal symbol is mark-local, the seam flat away from the \mu_4 marks) — are shown to be one statement: the seam carries the uniformising flat orbifold (pillowcase) metric. (1) The four marks make the Euclidean orbifold S^2(2,2,2,2) (\chi_{\mathrm{orb}}=2-4(1-\tfrac12)=0), so by Troyanov uniformisation the metric is flat (unique up to scale) with curvature only at the cone points (Gauss–Bonnet 4\pi=2\pi\chi) — this is the v201 “flat away from the marks”. (2) New link: cross-ratio(\mu_4)=2 (v168) \Rightarrow j=1728 (j(\lambda)=256(\lambda^2-\lambda+1)^3/(\lambda^2(\lambda-1)^2); all six harmonic cross-ratios give 1728) \Rightarrow the square modulus \tau=i, whose CM by \Z[i] derives the order-4 clock z\mapsto iz (explicit (x,y)\mapsto(-x,iy) on y^2=x^3-x); generic cross-ratio gives j\notin\{0,1728\} and only \Z/2. (3) Unification: “seam = uniformising flat pillowcase metric” implies both v201 and v180, so two residuals collapse to one canonical-metric premise. [O]It does not close QGEO.SYM.01: the choice “RP seam metric = the constant-curvature representative” stays open, milder and more canonical than the bare isometry premise. Wolfram-mirrored (the exact orbifold/j-invariant/CM arithmetic); Klein-J values mpmath-numerical. Suite \to 214 modules.

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• F_{\mathrm{transfer}} formalised as a typed functor with four axioms (v213_ftransfer_functor, tfpt_research_contracts, [C]). The four frontier transfers are consolidated into ONE functor F_{\mathrm{transfer}}=F_{\mathrm{observable}}\circ F_{\mathrm{threshold}} \circ F_{\mathrm{RG}}, each instance a discrete compiler kernel [E]composed with an external continuous solver [C]: (1) \mu_4-deck equivariance (the Koide multiplier \lambda_2{=}(2/3)^6{=}64/729 is the deck transfer eigenvalue); (2) Plücker preservation (53{=}a^T(R{+}Q)\mathbf1, \mathrm{Pl}(F){=}(1,22,30), \|\mathrm{Pl}(K)\|_1{=}11); (3) positivity/stochasticity (\operatorname{spec}T positive, \kappa_f\in(0,1)); (4) external modules explicit (b_3{=}{-}7 a carrier output). The four instances are F_{\mathrm{pole}} (v183), F_{\mathrm{Boltzmann}} (v212), F_{\mathrm{relic}} (v211), F_{\mathrm{QCD}} (v164). CONTRACT.F.01 is the third research contract alongside (U_{\mathrm{wall}}) and (G_{\mathrm{metric}}), the structural complement of the v187 typing guard — an architectural consolidation, not a closure of any frontier number. Ledger CONTRACT.F.01.

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• Axion DM spine-angle branch \theta_i=\pi\Nfam/\gcar=3\pi/5 (v211_axion_spine_angle, tfpt_4_frontier, [C]). A more robust misalignment angle than the determinant-line hilltop \theta_i\approx170^\circ (v185, which over-produces \Omega_a h^2\approx0.66): the central spine quotient gives \theta_i=3\pi/5=108^\circ exactly (no fit), the finite-T solver reaches \Omega_{\mathrm{DM}} at {\approx}106^\circ, and 108^\circ sits in the mild-anharmonic regime (62^\circ below the hill-top) — not exponentially sensitive. An alternative ansatz to \theta_i=\pi(1-\varphi_\Sigma) (mutually exclusive, the full solver decides, DM.AXION.SPINE.01); [X]\Omega_a h^2 outside {\sim}[0.08,0.16] demotes it. A sharper scenario, not a derivation.
• Leptogenesis scalaron-decuple branch (v212_leptogenesis_decuple, tfpt_4_frontier, [C]). Both Boltzmann inputs share the decuple A_\Lambda=10=|E(K_5)|: M_1=M_{\mathrm{scal}}(\phiz)^2/A_\Lambda\approx8.65\times10^9 GeV and \tilde m_1=m_3/A_\Lambda\approx5 meV. M_1 uses only \{M_{\mathrm{scal}},\phiz,A_\Lambda\} — no hidden seesaw scale, cleaner than v184's M_R\varphi_0^4 — and lands in the thermal window where \eta_B\approx1.2\times10^{-9} brackets the observed 6.1\times10^{-10}. The coupling mechanism is posited not derived, so \eta_B stays [C]; [X]a precise Boltzmann/RGE solve outside the band falls the route, not the theory (FR.ETAB.04; Route A independent).

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• The cohomology character grading is now Lean-formalised (CohomologyGrading.lean, ledger FORM.QGEO.03, [O]). A new module machine-proves the Cohom node of the QGEO proof tree (v177; audit: pass, no sorry/admit, axioms propext, Classical.choice, Quot.sound only): the three H^1(\PP\setminus\mu_4) eigenforms \omega_k=z^{k-1}/(z^4-1) (k{=}1,2,3) have pullback character \rho^*\omega_k=i^k\omega_k under the clock \rho:z\mapsto iz (each an exact rational-function identity, the denominator clock-invariant since i^4{=}1), so the grading is (i,-1,-i) with weights (1,2,3) = the A_3 exponents =\operatorname{Spec}(Q_+), rank 3=\Nfam. The Module parity is also proved: the reflection \sigma:z\mapsto1/z satisfies \sigma^*\omega_1=\omega_3, \sigma^*\omega_2=\omega_2, \sigma^*\omega_3=\omega_1 (swap \omega_1\!\leftrightarrow\!\omega_3, \omega_2 fixed). Signature-locked in AuditContract.lean. The geometric Cohom/Module-parity nodes are now [E]; the Marks/Kernel obligations and the Module uniqueness stay [O].

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• The Möbius uniformisation normal form is now Lean-formalised (Mobius Uniformisation.lean, ledger FORM.QGEO.02, [O]). A new module machine-proves the constructive Uniform node of the QGEO proof tree (v177; audit: pass, no sorry/admit, axioms propext, Classical.choice, Quot.sound only): the clock \rho:z\mapsto iz has \rho^4{=}\mathrm{id} and \rho^2{\neq}\mathrm{id} (order exactly 4); the reflection \sigma:z\mapsto1/z is an involution with \sigma\rho\sigma=\rho^{-1} (so \langle\rho,\sigma \rangle is the dihedral D_4 of order 8); a non-fixed orbit \{a,ia,-a,-ia\} scales to \mu_4=\{1,i,-1,-i\}; \sigma permutes \mu_4 (fixes 1,-1, swaps i,-i); and the multiplier classification “z\mapsto\zeta z has order exactly 4\Leftrightarrow\zeta=\pm i”. Signature-locked in AuditContract.lean. This formalises the geometric half of the seam realisation given the four marks and the clock; the raw-seam marking obligation QGEO.MARKS.01 stays [O], not closed.

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• The mark-local \Rightarrow\omega\circ\rho=\omega implication is now Lean-formalised (SeamDeckClosure.lean, ledger FORM.QGEO.01, [O]). A new module in the carrier-rigidity Lean project machine-proves the algebraic core of v201/v210 (audit: pass, no sorry/admit, no domain axioms — #print axioms = propext, Classical.choice, Quot.sound only): (i) the 4th-root character orthogonality \sum_{j<4}\zeta^j=(\text{if }\zeta{=}1\text{ then }4\text{ else }0) for \zeta^4{=}1 (so a \mu_4-mark sum is supported only on modes \equiv0\bmod4); (ii) the clock generator -i has order 4; (iii) markLocal_blockDiagonal: a mark-local Toeplitz symbol connects only equal clock-characters, [\rho,M_f]=0; (iv) the premise is a typed structure SeamDeckPremise (the physical seam DtN is mark-local) — consumed, not proved, exactly as CalderonProjector encodes the Paper-1 analytic input; (v) SeamDeckPremise.clock_invariant: given the premise, the clock commutes with the DtN, whence \omega\circ\rho=\omega. So the implication is now [E](formally proved); the premise (the physical seam being mark-local) stays [O]— the one fundamental seam-identification postulate, not closed.

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• Mark-local DtN \Rightarrow\omega\circ\rho=\omega, certified on realistic Steklov profiles and at the state level (v210_mark_local_dtn, tfpt_research_contracts, [O]). A numerical sharpening of QGEO.SUBPRIN.01/v201: a real von-Mises curvature bump summed over the four \mu_4 marks, f(\theta)=\sum_{j=0}^3 g(\theta-j\pi/2), builds the Steklov DtN \Lambda=|D_\theta|+M_f whose off-(\mathrm{mod}\,4) Fourier support vanishes to <10^{-16}, \|[\rho,\Lambda]\|<10^{-15}, and — the genuinely new step — the quasi-free covariance C=\tfrac12(1+\operatorname{sgn}H_1) is clock-invariant (\rho C\rho^\dagger=C to <10^{-13}), i.e. the actual \omega\circ\rho=\omega. Negative controls (single off-centre bump, \Z_3 source, four generic marks) break both by O(1); convergence stable for N\in\{16,32,64\}. This certifies the implication; the premise that the physical seam is mark-local stays [O](it does not close QGEO.SYM.01; net existence and full-cone RP remain the [E]of v175). Ledger QGEO.MARKLOCAL.01. Python-only (the exact mark-sum identity is Wolfram-mirrored via v201).

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• Muon g-2 as a seam vertex (v204_muon_seam_g2, tfpt_4_frontier, [C]). The carrier's second-order topological defect \delta_2=\tfrac54\delta_{\mathrm{top}}^2 projected through the seam-loop phase gives a_\mu^{\mathrm{seam}}=\delta_2/(2\pi)=45/(524288\,\pi^9)\approx2.879\times10^{-9} (0.81\sigma vs the dispersive \Delta a_\mu; {\sim}1.5\sigma vs lattice/CMD-3). The value is exact [E]; the vertex identification is the [C]bridge. Ledger FR.MUONG2.01; Wolfram-mirrored.
• An independent gravitational 3/4 (v205_xi_threequarter, tfpt_4_frontier, [E]/[C]). \xi=\cthree/\varphi_{\mathrm{tree}}=3/4 exactly (Einstein limit of \kappa^2=\xi\phiz/\cthree^2) — the same 3/4=q(A_3)=\ln(m/\mu) as the seam-determinant replica (v152), an over-determination. Ledger GRAV.XI.01; Wolfram-mirrored.
• Quantitative H_0 from the \Lambda branch (v206_h0_lambda_branch, tfpt_4_frontier, [C]). \delta_\Sigma=48\,e^{-2\pi\ainv/3}\approx1.085\times10^{-123}, the (8\pi)^2 Planck-convention split, and H_0=66.5–67.1 km/s/Mpc (below Planck, far below SH0ES — the Hubble tension is not relieved). Ledger GRAV.H0.01.
• Asymptotic Safety as a second QG route (v207_asymptotic_safety, tfpt_4_frontier, [O]). A complementary continuum-FRG argument (a non-Gaussian UV fixed point from the same axioms; y^2=16\cthree^2=1/(4\pi^2)) — a plausibility cross-check, not load-bearing, does not close G_{\mathrm{metric}}. Ledger GRAV.ASYMP.01.
• Black-hole thermodynamics from the seam (v208_bh_ thermodynamics, tfpt_horizon_ readouts, [E]/[C]). Modular T_H=\kappa/(2\pi) (the 2\pi=1/(4\cthree) seam unit, ties to v198/v199) and the scalaron-corrected Wald entropy S_W=(A/4G)(1+R_h/3M_s^2) (exact from v28). Ledger HOR.BHTHERMO.01; Wolfram-mirrored.
• The black hole as a seam fixed point (v209_bh_ regular_core, tfpt_horizon_ readouts, [C]). No singularity (\varphi\to\varphi_\star at the gapped attractor (2/3)^6); the maximal BH = the anchor (Nariai roots (1,1,-2)); information via Page recovery; a Planck-scale holographic floor. The superseded RN/torsion metric is not resurrected. Ledger HOR.BHCORE.01.

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• The Möbius seam is the boundary Lorentz structure (tfpt_3, [O]). Added a paragraph to the “Möbius origin of \pi” section: \mathrm{M\ddot{o}b}(\hat{\mathbb C})\cong\mathrm{PSL}(2,\mathbb C) \cong\mathrm{SO}^+(3,1) (Penrose & Rindler, Spinors and Space-time, Vol. 1, 1.2–1.4), the celestial sphere of null directions via stereographic projection. This gives the self-consistency loop a spacetime meaning — the carrier clock z\mapsto iz is an elliptic \mathrm{PSL}(2,\mathbb C) rotation (v180) and the RP\toOS causal cone is the same Lorentz structure — so “Möbius origin of \pi” and “one Lorentzian cone” are two faces of one boundary \mathrm{PSL}(2,\mathbb C). A foundation citation, not a new claim (\pi stays primitive).

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• Haloscope coupling tied to c_3 (tfpt_4_frontier, [C]). Made explicit: in the determinant-line normalization the axion–photon anomaly coefficient is g_{a\gamma\gamma}=-4c_3=-1/(2\pi) (y^2=16c_3^2=1/(4\pi^2)\approx0.0253), so the haloscope F\tilde F coupling is set by the same c_3 that fixes \alpha and \beta_{\mathrm{rad}}=\varphi_0/4\pi — a [C]structural relation (the coefficient, not a parameter-free physical g_{a\gamma\gamma}). The earlier small-angle \theta_i=\varphi_0 reading (old determinant-line note, a much higher axion mass) is superseded by the closed near-hilltop \theta_i=\pi(1-\varphi_{\mathrm{seam}})=170.4^\circ, recorded as a retired reading and guarded by v188 (a new sentinel forbids that stale axion mass from re-entering the active docs).

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• HOR.EHT.01 (v203, [E]/[C]/[X]). The surviving core of the old UFE/black-hole notes (not the RN-type metric — superseded by the Nariai/seam=horizon readouts v101–v104/v190; only the polarization signature survives): a local achromatic polarization-rotation intercept around a horizon-scale black hole, \beta_{\mathrm{BH}}(r)=16c_3^4\,Q_e^{\mathrm{eff}}Q_m^{\mathrm{eff}}/r^2. The coupling 16c_3^4=1/(256\pi^4)=\delta_{\mathrm{top}}/3 is exact ([E], Wolfram-mirrored) — the same top-form coefficient \delta_{\mathrm{top}}=48c_3^4 that fixes the \alpha-kernel precision-zone correction, one row from the cosmic-birefringence seed \beta_{\mathrm{rad}}=\varphi_0/4\pi. TFPT fixes the 1/r^2 shape, achromaticity and sign-flip ([C]); the amplitude Q_eQ_m is an MHD/GR weight, never a pixel prediction. Dated kill test [X]: the residual intercept must pass three nulls (frequency, spatial 1/r^2, sign-flip) after honest GRMHD subtraction. Integrated into tfpt_horizon_readouts (new EHT section), the ledger, registry, Wolfram (243/243), and the website (predictions.ts). Suite 202 modules.

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• FR.RAREKAON.01 (v202, [C]). The closed TFPT CKM point (s_{12}{=}\lambda_C, s_{23}{=}\varphi_0/(1{+}\lambda_C){=}|V_{cb}|, s_{13}{=}\lambda_C^3/3, \delta{=}\pi/3{+}3\lambda_C^2{=}1.19823 rad; v18/v88, no flavor fit) feeds the cleanest FCNC probe. With standard external short-distance input (Brod–Gorbahn–Stamou X_t,P_c,\kappa_\pm) it gives \mathrm{BR}(K^+\!\to\pi^+\nu\bar\nu)=9.45\times10^{-11} and \mathrm{BR}(K_L\to\pi^0\nu\bar\nu)=3.33\times10^{-11} — a [C]downstream flavor readout, not a compiler power (the SD functions are external). Recomputed from the current CKM point (an earlier archive scaffold quoted \mathrm{BR}(K_L)=3.47\times10^{-11} from an \Im(\lambda_t)/\lambda^5 slip, corrected here). Grossman–Nir ratio 0.352\ll4.3; NA62 (13.0^{+3.3}_{-3.0})\times10^{-11} is \sim1.2\sigma above. Dated kill test [X]: a stable NA62 \mathrm{BR}(K^+) outside [7,12]\times10^{-11}, or a KOTO-II \mathrm{BR}(K_L) off the GN point, breaks the flavor bridge (core untouched). Integrated into tfpt_2_standard_model ( rare kaon), the ledger, v187 guard (new FR.RAREKAON. family), registry, and the website (predictions.ts). Python-only. Suite 201 modules.

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• QGEO.SUBPRIN.01 (v201, [E]/[O]). The v199 bedrock residual — “the bounded sub-principal symbol of the raw seam DtN has no off-character (mod 4) matrix elements” — is reduced one genuine step further: block-diagonality is not an independent postulate. Writing the DtN as \Lambda=|k|+M_f with M_f the bounded sub-principal piece = multiplication by a curvature f(\theta) (standard Steklov structure), M_f is \mu_4-character-block-diagonal iff f is \Z_4-invariant ([E]; principal |k| already commutes, v198); and a \mu_4-mark sum f=\sum_{j=0}^3 g(\theta-2\pi j/4) has f_m=4g_m[m\equiv0\bmod4] for any profile g, hence is automatically \Z_4-invariant ([E]). So the \mu_4-mark orbit (forced by v195) forces the sub-principal symbol block-diagonal; 3 marks (\Z_3) and 4 generic marks break it (negative controls). The residual collapses to “the DtN sub-principal symbol is mark-local (seam flat away from the \mu_4 marks = conformal deck, v177)”, structurally definitional — the narrowest form yet of QGEO.SYM.01, [O]. Registered in run_all.py, the ledger, tfpt_research_contracts, origin_theory; Wolfram-mirrored (the mark-sum Fourier identity is exact; extension now 242/242). Suite 200 modules.

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• Axion relic solver (experiments/ftransfer/axion_relic/relic_solver.py, [C]). The first real F_{\mathrm{transfer}} pipeline computation (work package C / review 6.2): a standard misalignment relic with a numerically-computed anharmonic factor F(\theta_i)\approx4 at the hilltop. Honest finding: at the predicted \theta_i\approx170^\circ the estimate over-produces dark matter, \Omega_a h^2\sim0.6–2.3 (robustly >0.12), because the large \theta_i^2\approx8.8 times F overshoots. So the determinant-line axion as the dominant DM is in mild tension (it would prefer \theta_i\sim120–130^\circ or extra dilution) — this refines v185's optimistic “can be all-DM” toward an over-production tension. The near-hilltop regime is O(1)-uncertain, so a full finite-T solve decides; over-production kills only the axion-as-dominant-DM branch, not the compiler. Reflected in tfpt_4_frontier (dark-matter section) and the v185 docstring; experiments-only, not a suite/ledger claim. No refitted exponents; \theta_i=\pi(1-\varphi_{\mathrm{seam}}) only.
• Full finite-T solve confirms it (axion_relic/full_finiteT_solve.py). A converged nonlinear misalignment solve (\theta''+(3+\mathrm{d}\ln H/\mathrm{d}N)\theta'+(m_a(T)/H)^2\sin\theta=0, lattice \chi(T)\propto T^{-8.16}, realistic g_*(T); normalised so \theta_i{=}1\to\Omega_a h^2\approx0.03, the standard value) gives \Omega_a h^2\approx0.66 at the predicted \theta_i\approx170^\circ — \sim5.5\times above \Omega_{\mathrm{DM}}=0.12, reached only at \theta_i\approx106^\circ. The over-production is thus confirmed (not the optimistic “all-DM”); tfpt_4_frontier, v185 docstring and the website updated accordingly. Stays [C]; kills only the axion-as-dominant-DM branch.