A registered result in its source context
Original ledger classification: Physical [C] (hilltop scenario SUPERSEDED by post-inflationary reframing FR.DM.02; angle not observable)
Recorded statement: 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}…
Statement, assumptions and sources
Paper context: Frontier and open physical interfaces
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FR.DM.03
Original ledger classification: Physical [C] (hilltop scenario SUPERSEDED by post-inflationary reframing FR.DM.02; angle not observable)
Original claim text
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0.038, so it is SUPERSEDED by the post-inflationary scenario (theta_i a horizon average, NOT observable; relic from f_a + N_DW=|C|=1, v470/v472).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.
Original classification detail
Physical [C]: f_a=M_scal/128 axion can be all DM only near the theta_i~170 hilltop (exponentially sensitive) -> scenario, branch kill test not theory
Dependencies as recorded
FR.DM.01; FR.DM.02; v25_frontier_conjectures.py
Open the original ledger source, row 180Location recorded in the ledger
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- Frontier and open physical interfaces
Sections that explicitly cite this claim
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- 2026-06-14 (F_transfer round: eta_B honest test v184, axion relic v185, discipline guard v187)Research changelog; TFPT — Introduction and reading guide
Navigation through a shared verification script
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- Research Contract — FTRANSFER.GENERATING.01 (four transfer bridges from one generating functional)tfpt research contracts
- 2026-06-15 (F_transfer workshop: the axion relic solver — an honest over-production tension)Research changelog; TFPT — Introduction and reading guide
- 2026-06-26 ( v429 — the `unmapped' golden [formula in source] structure is the geometry of the one external input [formula in source] )Research changelog; TFPT — Introduction and reading guide
- Neutrinostfpt 2 standard model
- Certifiability and recommended ordertfpt research contracts
- =150 2026-08-28 (CXXXVIII) (the master-object wave, part 2 — the second external bird's-eye review (``one 4D lattice [formula in source] one seam simple current [formula in source] one unitary dilation [formula in source] one determinant line [formula in source] one [formula in source] '') adjudicated: its four machine-checkable candidate results verified and integrated as FOUR new modules (suite [formula in source] , ledger [formula in source] : one new row FLAV.NUSCALE.05; three contract rows updated, NO status-marker moves). (1) v983_ simple_ current_ generator.py: the SEAM.SIMPLECURRENT.GENERATOR.01 generator is identified — the glue vector [formula in source] with [formula in source] , [formula in source] , order 4 in the discriminant group [formula in source] of [formula in source] ; isotropic glue [formula in source] even unimodular rank-8 overlattice ( [formula in source] ); coset root census [formula in source] — the odd fusion powers of the ONE class carry the full [formula in source] spinor sector; kill tests (vector-class / mismatched glue) fire; holomorphy shadow [formula in source] vs [formula in source] at the lattice level; the analytic half (G1–G4) stays . (2) v984_ markov_ qca_ dilation.py: the DISCRETE leg of DYN.UNITARY.DILATION.01 realized constructively — the collision step [formula in source] is exactly unitary, the Stinespring identity [formula in source] holds symbolically, [formula in source] and six fresh ancillas give [formula in source] exactly (radius-1 collision band); must-fail fires ( [formula in source] ); typed remark AGAINST the review text: a reused mod-3 adder ancilla still reproduces the populations exactly; the continuous Hamiltonian/OS legs stay . (3) v985_ quillen_ channel_ swap.py: the v974 CHANNEL-SWAP face of ALPHA.QUILLEN.EXACT.01 resolved at the finite level by [formula in source] -character grading — the deck swap [formula in source] maps the jump spectrum [formula in source] onto the mark pattern [formula in source] exactly (odd swap fails), the graded [formula in source] difference is [formula in source] -free [formula in source] , the channelwise unit ratio is uniform [formula in source] ; continuum Bismut–Freed, KMS rigidity and the [formula in source] compensation stay . (4) v986_ nu_ scalaron_ rung.py: the SCALARON-TRACE RUNG [formula in source] GeV — a structured point INSIDE the v481 window, [formula in source] from the 1-loop requirement (the review claimed [formula in source] 1\%; the honest value is 1.8), [formula in source] sharper than the declined integer rung; exact ladder position [formula in source] , [formula in source] from the closed [formula in source] Clebsch door — adjacency TYPED, not consumed (v488 killed the Clebsch mechanism; the generation-blind scalaron trace is a different class, itself ); kill test [formula in source] eV; new row FLAV.NUSCALE.05 [C]/[N], no seesaw closure. The remaining review content is typed, not consumed: the axion line ( [formula in source] , [formula in source] ) and the Riemann–Roch carrier ARE the existing v185/v211/v189; the 4D action, chiral measure, OS package, bulk dictionary, determinant-line unification, [formula in source] , transduction matrix and joint likelihood stay open contracts exactly as registered on 2026-08-27. Paper surfaces: tfpt_research_contracts (three executed-update paragraphs), tfpt_2_standard_model (scalaron-trace rung paragraph).)Research changelog; TFPT — Introduction and reading guide
- NeutrinosStandard Model and flavor structure
- Research Contract — FTRANSFER.GENERATING.01 (four transfer bridges from one generating functional)tfpt research contracts
All 15 linked sections
- Research Contract — FTRANSFER.GENERATING.01 (four transfer bridges from one generating functional)
- Dark matter — the candidate is fixed, the scale is pending
- Front matter / support
- 2026-06-24 (Two new tracked targets + axion-branch consistency: v408, v409)
- Certifiability and recommended order
- 2026-06-15 (frontier: two sharper [C] scenario branches — axion angle + leptogenesis)
- Certifiability and recommended order
Registered verification modules
- v185_axion_relic_solver.pyRegistered verification module · registry
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axion relic, honest misalignment estimate: the determinant-line axion f_a=M_scal/128≈2.39e11 GeV (m_a≈23.8 µeV) CAN provide all dark matter, but ONLY near the θ_i≈170° hilltop where the relic is exponentially sensitive — so the axion DM branch stays a [C] SCENARIO. The harmonic misalignment UNDER-produces at this f_a (prefactor ~0.026/θ², θ~O(1) gives ~21% of Ω_DM, need θ_eff²~4.7), so the 170° hilltop anharmonic enhancement is REQUIRED to reach Ω_DM; near the hilltop the relic is exponentially sensitive (and QCD/string-sensitive), hence a scenario, not a sharp prediction. Contract F_relic(f_a,θ_i,N_DW)=?Ω_DM is a kill test for the BRANCH not the theory (no free singlet WIMP: 128=(16,4)+(16,4) matter spinor).
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