Original ledger status
FR.DM.02
determinant-line axion f_a=M_scal/(2 dim S+ |mu4|)=M_scal/128~2.39e11 GeV, m_a~23.8 ueV. POST-INFLATIONARY REFRAMING [C] (2026-07-10; isocurvature analysis experiments/theory-contracts/axion01-06): the R^2 branch fixes H_inf=pi Mbar sqrt(A_s r/2)~1.6e13 GeV, so H_inf/f_a~66>1 and H_inf/(2pi f_a)~10 -- a FIXED pre-inflationary misalignment angle (108 deg spine DM.AXION.SPINE.01 or 170 deg hilltop FR.DM.03) is INCONSISTENT (CDM isocurvature >> Planck beta_iso<0.038). The natural DIAL-FREE resolution is POST-INFLATIONARY PQ breaking: theta_i is a horizon average (NOT a prediction), the relic follows from f_a alone -- f_a~2.39e11 sits in the post-inflationary window (Omega_a h^2~O(0.1-0.5)). DOMAIN-WALL-SAFE: N_DW = seam det-line index = inflow level |C|=1 (v470/v472) => N_DW=1 [C]. The axion branch is REFRAMED not killed: drop the fixed angle as observable, keep f_a + N_DW=1. NOT closed (relic O(1) string/wall uncertainty; N_DW identification [C])
Recorded status: Physical [C] (post-inflationary reframing)
Dependencies, status detail and source
Canonical status: Physical [C]: post-inflationary determinant-line axion, relic from f_a (in window), N_DW=|C|=1 domain-wall-safe; the fixed pre-inflationary spine/hilltop angle is inconsistent (isocurvature) and NOT observable -- reframed, not a closed hit
Dependencies: FR.DM.01; M_scal=c3^{7/2}Mbar; v470; v472
Scripts: v25_frontier_conjectures.py
Location: tfpt_4
Original CSV, line 36Original ledger status
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)
Dependencies, status detail and source
Canonical status: 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: FR.DM.01; FR.DM.02; v25_frontier_conjectures.py
Scripts: v185_axion_relic_solver.py
Location: tfpt_4_frontier
Original CSV, line 180Original ledger status
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)
Dependencies, status detail and source
Canonical status: Physical [C]: theta_i = pi N_fam/g_car = 3 pi/5 = 108 deg (spine quotient) lands on Omega_DM ~106 deg ROBUSTLY (mild-anharmonic, far below the 170 deg hilltop) -- a more robust DM branch than v185; an alternative ansatz, the full solver decides; kill test outside ~[0.08,0.16] demotes the branch
Dependencies: FR.DM.01; FR.DM.02; FR.DM.03; v185_axion_relic_solver.py
Scripts: v211_axion_spine_angle.py
Location: tfpt_4_frontier
Original CSV, line 299