PP20 ζ(p) transcription fix

PP20 magnification factor ζ(p) — transcription bug fix¶

Date: 2026-04-28 Module (at the time): progenax.gravoturb.pp20_magnification → now gravoturb.theory.dense_gas_sfr Companion fix: swindlax.physics.density_gradient (already locked, 29 regression tests)

What changed¶

No production code outside pp20_magnification.py was modified. No JSON / NetCDF / committed validation outputs were regenerated.

The bug¶

Inline form prior to this fix:

zeta = (3.0 - p) / (2.6 - 2.0 * p) ** 1.5

Three transcription errors against PP20 Eq. 6 (Parmentier & Pasquali 2020, ApJ 903, 56, page 2):

1. The constant 2.6 was moved inside the 3/2 power.

2. The (3 − p) factor lost its 3/2 exponent.

3. The multiplicative factor 2.6·(2 − p) was garbled into linear (2.6 − 2p).

Numerical impact: the buggy denominator 2.6 − 2p vanishes at p = 1.3, which the docstring rationalised as a “domain limit.” PP20 Eq. 6 has no singularity at p = 1.3; the only true singularity is at p = 2 (singular isothermal collapse). The buggy form gave ζ(0.5) ≈ 1.235, ζ(1) ≈ 4.30 (clamped via max(., 1.0)), and arbitrary post-clamp values for p ≥ 1.3 — none of which match PP20.

The fix¶

Canonical form, derived from the integral definition ζ = ∫ρ^(3/2)dV / (M·√⟨ρ⟩) for a power-law profile ρ(r) = ρ_R(r/R)^(−p) on a sphere of outer radius R:

P_MAX = 1.95

@jax.jit
def magnification_factor(p):
    p_safe = jnp.clip(p, 0.0, P_MAX)
    return 2.0 * (3.0 - p_safe) ** 1.5 / (3.0 ** 1.5 * (2.0 - p_safe))

Equivalent to PP20 Eq. 6 to 0.08% — PP20’s “2.6” is the rounded value of 3^(3/2)/2 = 2.598. Spot values now reproduce PP20 / analytic anchors:

P_MAX = 1.95 keeps gradients well-behaved under HMC/NUTS by shielding the p → 2 divergence, matching the same convention used in swindlax.physics.density_gradient and PP20 Fig. 1.

Test-count delta¶

The test_knobs_pipeline.py ModuleNotFoundError: progenax.profiles.mass_segregation predates this work (commit 13df53f removed the module without removing the test); not in scope.

Verification¶

• All 71 tests across test_parmentier.py + test_pp20_zeta_canonical.py pass.

• Full progenax suite: 812 passed, 0 failed (excluding the pre-existing collection error).

• magnification_factor_with_core and zeta_from_field were not modified — they are independent of the analytic typo (numerical integration / 3D-field measurement). A new test in test_pp20_zeta_canonical.py confirms magnification_factor_with_core(p, r_c/R) approaches the corrected analytic magnification_factor(p) as r_c/R → 0 (parametrised over p ∈ {0.5, 1.0, 1.5}).

• A test_no_buggy_inline_zeta_form_in_progenax source-text scanner is in place; it walks src/progenax/ and fails if any of (2.6 - 2.0 * p), (2.6 - 2*p), 2.6 - 2.0*p, 2.6 - 2 * p reappears in live source.

Validation artefacts (resolved in the 2026-06 rewrite)¶

At the time of this fix, the legacy validation/turbulence/bm19_fdf_suite/ suite still held stale, typo-rationalising claims (e.g. a “singularity at p = 1.3” caption in its VALIDATION_SUMMARY.md, and b5/b6/e5 comparison plots drawn against the buggy analytic ζ curve). These were flagged for regeneration rather than fixed in the 2026-04-28 commit.

They were not regenerated — they were removed. The entire bm19_fdf_suite (and the progenax.gravoturb / cluster.fdf* modules it imported) was deleted in the 2026-06 clean-room rewrite. The corrected ζ(p) and the honest gravoturbulent validation now live in the experimental gravoturb package, whose acceptance suite prints its ζ anchors (AC3) and the BM19 cornerstone (AC6) — see src/experimental/gravoturb/VALIDATION_SUMMARY.md. There is no longer a monolithic bm19_pipeline/BM19Result orchestrator; the forward chain is composed from gravoturb.theory.* + gravoturb.realization.*.

References¶

• Parmentier, G. & Pasquali, A. 2020, ApJ, 903, 56 (arXiv:2009.10652), Eq. 6.

• Kainulainen, J., Federrath, C., & Henning, T. 2014, Science, 344, 183 — observational anchor for ζ(p ≈ 1.67) ≈ 1.79.

• Companion fix and full integral derivation: swindlax/src/swindlax/physics/density_gradient.py.

• Hardening report: papers/rosen-burkhart-swindle-2026/reviews/audit-2026-04-28-pp20-validation.md.