MeanField/reports/archive/recent_sources.md

Sources and integration notes for recent.tex

The fragment covers native harmonics (Sept. 19), negative-density localization, density-only Q2/Q3/Q4 and log assessment, final coupled-convergence controls, compatible rotating n3 family, pressure/gravity consistency, physical slices, and the resulting next priorities. It is approximately 7,700 words, with 14 small wrapped longtables and two figures. It deliberately does not duplicate the preceding Sep. 18 reduced-surface study except to explain the transition from an affine restricted diagnostic to a native prescription.

Integration

• Required standard packages: amsmath, longtable, graphicx, hyperref (as already planned). No custom command definitions are required. Grouped tables set tab spacing to 3 pt and explicitly wrap columns; total prescribed column widths are <=147 mm before internal tab spacing.
• Figure references assume compilation and Pandoc conversion with reports/ as the resource directory: figures/n3_ldu_meridional.png and figures/n1p5_rotating_refinement.pdf.
• The third planned figure figures/frozen_linear_rates.pdf can be added by the root in the frozen-comparison section or an appendix; its multiple-panel layout may merit a full page.
• Sections describe Sept. 19 state and producer commits, not the still-pending final main integration. Root must separately write the exact selected branch disposition and final main commit.
• All internal labels begin recent-, avoiding likely collision with the early report fragment.
• No fresh FEM runs or audits were performed for this report fragment; it is a synthesis of the immutable studied outputs and their existing audits.
• The old negative-density report's recommendation for derived density is explicitly identified as historical and superseded by the user's decision to keep density independent. The later preference to defer positivity is also explicit. Do not silently carry that old recommendation forward.
• Important no-overclaim rules are repeated where they matter: finite-budget endpoints are not floors; equal-update trajectories are not same-model speedups; quadrature agreement is not mesh convergence; sampled positivity is not global positivity; the n3 force/h virial alone passing does not meet the overall milestone; raw J or angular velocity is not a critical fraction.

Primary repository reports read

Original source checkout root: /Users/tboudreaux/.codex/.chatgpt-projects/g-p-6a6b3f2194ec8191bebcd59075897f1d/worktrees/preconditioner-improvement

1. experiments/SPHERICAL_HARMONIC_SURFACE_2026-09-19.md
   • Native all-m L4 prescription, typed contracts, fixed reference basis, Q4/Q3 geometry/displacement, scalar trace-mass normalization, single-rank scope, five six-update live controls, excluded-force and local diagnostics.
   • Producer: 7b0eb8d92d0f550f1fe3fb19cd8eecc52dc80c56.
2. experiments/NEGATIVE_DENSITY_INVESTIGATION_2026-09-19.md
   • Four frozen states, independent closure projection identity, all 96 outer cells, root-sliced measures, positive nodal values, seed-vs-root mechanism, exact one-dimensional quadratic projections, interpretive scope.
   • Producers: 9c22934d52b369f96364e781d6a4843939ec9523 and d1a594808f960bbaeeb6df8a8ce6a95458765b19.
3. experiments/DENSITY_ORDER_STUDY_2026-09-19.md
   • Frozen common-q26 and error-q30 controls; all 12 live density-order cases; selected quadrature rules, block sizes, cost scopes, central forcing and initializer distinctions; 48 contract tests per order.
   • Producers: frozen 241621c; coupled Q2 c0e8551; Q3 cd71f37; Q4 e054c74; final comparison generator c0a496e.
4. experiments/COUPLED_CONVERGENCE_STUDY_2026-09-19.md
   • Five initial nonlinear controls, matched gravity-path pair, all 11 frozen inverse pairs, weak coupled direction analysis, compatible n3 pair, display refinement, validation and next priorities.
   • Final integration/report commit: d7acb0d399aac5ac4c36d834a954c1c959042b81.
5. experiments/N3_COMPATIBLE_FAMILY_2026-09-19.md
   • Explicit K factor, independent Lane–Emden compatibility check, exact shared specifications and caveats for the live pair.
6. experiments/FIELD_COUPLING_REVIEW_2026-09-19.md
   • Actual material triangular structure contains the exact h-to-rho action; independent vs LDU feedback, possible exact DG mass and H1 mass improvements, optional future EOS-aware field Schur and closure affine-target trial path.
7. experiments/MODEL_SLICES.md
   • Physical-plane cut and source immutability; element-owned DG traces, independent outlines, field raster before colormap, display errors/limits, use/replay parameters and geometry/plotting checks.
8. experiments/REDUCED_SURFACE_STUDY_2026-09-18.md
   • Read for bridge/context only; preceding early-history fragment should contain its detailed restricted-vs-full system results.

Separate source checkout: /Users/tboudreaux/.codex/.chatgpt-projects/g-p-6a6b3f2194ec8191bebcd59075897f1d/worktrees/log-density-assessment

9. experiments/LOG_DENSITY_ASSESSMENT_2026-09-19.md
   • Mathematical distinction between exponentiating coefficients and pointwise exponential, vacuum singularity, independent vanishing factor, 1D moment fits, weighted-mass response/conditioning, general-EOS and support contracts.
   • Separate assessment branch at 90580b2; no coupled stellar log solve.

Raw evidence and concise analysis read

Archive target supplied by root: working/research/diagnostics/<campaign>/ in the main repository. Original workspace diagnostics/ will remain a symlink to that archived path.

Campaign names:

• spherical_harmonic_surface_2026-09-19/
• negative_density_2026-09-19/
• density_order_2026-09-19/
• log_density_2026-09-19/
• coupled_convergence_2026-09-19/
• n3_mass_compatibility_2026-09-19/

Additional analyses read directly:

• coupled_convergence_2026-09-19/N3_COMPATIBLE_RESULTS.md
• coupled_convergence_2026-09-19/PRESSURE_MOMENT_NOTE.md

High-value existing evidence links for root's archive appendix:

• coupled_convergence_2026-09-19/STUDY_INDEX.json
• coupled_convergence_2026-09-19/CONTROL_RESULTS.md and .json
• coupled_convergence_2026-09-19/linear_analysis/FINAL_INTERPRETATION.md
• coupled_convergence_2026-09-19/n3_direction_difference/README.md
• coupled_convergence_2026-09-19/SLICE_REFINEMENT_SUMMARY.json
• coupled_convergence_2026-09-19/validation/validation.json
• coupled_convergence_2026-09-19/figures_n3_v2/slice_tests.log
• density_order_2026-09-19/final_analysis/coupled_outcomes.csv
• density_order_2026-09-19/final_analysis/trial_stages.csv
• negative_density_2026-09-19/regions_campaign_audit_v1.json
• spherical_harmonic_surface_2026-09-19/campaign_audit.json

Figure sources

All below are relative to original workspace diagnostics, or to the archive's working/research/diagnostics/ after reorganization.

• Report figures/n3_ldu_meridional.png: coupled_convergence_2026-09-19/figures_n3_v2/n3_J0p035_K0p99_ldu_xz.png
• Report figures/n1p5_rotating_refinement.pdf: coupled_convergence_2026-09-19/figures_slices_v2/n1p5_rotating_xz_s4_s8.pdf
• Optional report figures/frozen_linear_rates.pdf: coupled_convergence_2026-09-19/figures/linear_rates/frozen_linear_rates.pdf
• Additional useful density-order figure: density_order_2026-09-19/final_analysis/density_order_comparison.png
• Additional sign-location figure: negative_density_2026-09-19/figures/surface_density_traces.png

External primary-source context retained from the studied reports

The numeric results and equations in the fragment are primarily local evidence and explicit derivations. If adding a bibliography, these are the primary sources referenced by the underlying reports (no new online verification in this report-writing subtask):

• Cheng, Cheng and Lin, Expanding solutions near unstable Lane–Emden stars, equations (1.14)–(1.15) and Theorem 3.1: https://arxiv.org/html/2305.10218#S3.SS1 This supplies the sharp energy bound and Lane–Emden mass relation. The beta bound is our inference with the steady virial identity, not a quoted theorem.
• MESA star/private/star_utils.f90: https://github.com/MESAHub/mesa/blob/main/star/private/star_utils.f90
• MESA T(tau) atmosphere documentation: https://docs.mesastar.org/en/latest/atm/t-tau.html
• Vijaywargiya and Fu, Two Finite Element Approaches for the Porous Medium Equation That Are Positivity Preserving and Energy Stable (2024): https://link.springer.com/article/10.1007/s10915-024-02642-x
• Fu and Xu, High-order space-time finite element methods for the Poisson–Nernst–Planck equations: Positivity and unconditional energy stability: https://arxiv.org/abs/2105.01163
• Zhang and Shu review (historical alternative only, not currently adopted): https://www.math.purdue.edu/~zhan1966/research/paper/review.pdf

The condensed fragment mentions MESA only as context and does not import PDE positivity theorems as guarantees for this steady stellar system.