A registered result in its source context
Original ledger classification: axion relic finite-T solve DECIDES the branch -- spine 3pi/5 lands on Omega_DM (in band), hilltop 170deg over-produces [C]/[X]
Recorded statement: Track 3 (2026-06-23, F_transfer): the axion relic abundance from the FINITE-T misalignment ODE -- promotes experiments/ftransfer/axion_relic and DECIDES the two competing TFPT angle branches, replacing the v326 adiabatic toy. Does NOT…
Statement, assumptions and sources
Paper context: Frontier and open physical interfaces
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FR.RELIC.SOLVE.01
Original ledger classification: axion relic finite-T solve DECIDES the branch -- spine 3pi/5 lands on Omega_DM (in band), hilltop 170deg over-produces [C]/[X]
Original claim text
Track 3 (2026-06-23, F_transfer): the axion relic abundance from the FINITE-T misalignment ODE -- promotes experiments/ftransfer/axion_relic and DECIDES the two competing TFPT angle branches, replacing the v326 adiabatic toy. Does NOT re-fix the candidate scales (f_a=M_scal/128, m_a; v185/v211); integrates the nonlinear ODE theta'' + (3+dlnH/dN)theta' + (m_a(T)/H)^2 sin theta = 0 with the lattice topological susceptibility m_a(T)=m_a min(1,(T_QCD/T)^{n/2}) (n=8.16) and realistic g_*(T). [I] candidate scales f_a=M_scal/(2 dim S^+ |mu4|)=M_scal/128~2.39e11 GeV, m_a~23.8 ueV, N_DW=1 (determinant-line atoms). [C] the frozen SPINE angle theta_i=3pi/5=108deg=pi N_fam/g_car gives Omega_a h^2~0.12 in [0.08,0.16] (brackets Omega_DM=0.12) with NO tuning -- the robust dominant-DM branch. [X] the HILLTOP theta_i~170deg over-produces (Omega_a h^2~0.65, ~5.4x) -- disfavoured/fine-tuned. [X] kill: a finite-T solve robustly outside [0.08,0.16] for the spine across lattice chi(T)/g_* variations drops the dominant axion-DM branch.
Original classification detail
[I] the candidate scales; [C] the spine in-band relic (finite-T misalignment + lattice chi(T)); [X] the hilltop over-production + the spine kill test. A typed solver that decides the branch; the relic stays [C] (lattice chi(T) + cosmology inputs).
Dependencies as recorded
v185; v211; v25
Open the original ledger source, row 85Location recorded in the ledger
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- Frontier and open physical interfaces
Sections that explicitly cite this claim
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- 2026-06-23 (Track 3 — the [formula in source] functor promoted from contracts to TYPED runnable solvers with kill tests: Koide source [formula in source] pole ( v371), [formula in source] Boltzmann ( v372), axion finite- [formula in source] relic ( v373), [formula in source] uncertainty budget ( v374))Research changelog; TFPT — Introduction and reading guide
Navigation through a shared verification script
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- The hard reduction: the live residual as typed interfacesTFPT — Introduction and reading guide
- SummaryFrontier and open physical interfaces
- Front matter / supportTFPT — Introduction and reading guide; Verification reference catalog
- 2026-06-24 (A falsifiable clock probe of the frontier: v397 how external is the ``external physics''?)Research changelog; TFPT — Introduction and reading guide
Registered verification modules
- v373_ftransfer_relic.pyRegistered verification module · frontier
Read the description recorded in the module registry
Track 3 (F_transfer): the axion relic from the FINITE-T misalignment ODE -- promotes the experiments/ftransfer solve and DECIDES the two TFPT angle branches, replacing the v326 adiabatic toy. f_a=M_scal/128~2.4e11 GeV, m_a~23.8 ueV, lattice chi(T) n=8.16. [I] candidate scales fixed by the determinant-line atoms (128=2 dim S^+ |mu4|). [C] the frozen SPINE angle 3pi/5=108deg=pi N_fam/g_car gives Omega_a h^2~0.12 in [0.08,0.16] (lands on Omega_DM untuned) -- the robust dominant-DM branch. [X] the HILLTOP 170deg over-produces (~5.4x) -- disfavoured/fine-tuned. [X] kill: a finite-T solve robustly outside [0.08,0.16] for the spine across chi(T)/g_* drops the dominant axion-DM branch. Stays [C]/[X].
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