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ramanujan-challenge/optional/OPTIONAL_IMPROVEMENTS.md
allaun 1d5273264d feat: add optional enhancements for Ramanujan Problem 2.8 
- Positive-cone transport certificates (p28_positive_cone.py, POSITIVE_CONE_CERTIFICATE.md, POSITIVE_CONE_MANUSCRIPT_SECTION.tex)
- Optimized differential gauge (p28_optimized_gauge.py, OPTIMIZED_GAUGE_CERTIFICATE.md)
- Adversarial provenance supplements (p28_mutation_sensitivity.py, solution_pre_positive_cone.tex)
- FAMM SCARS advisory records (FAMM_SCARS.md, p28_famm_scars.json, p28_famm_scars_validator.py)
- Overview documentation (OPTIONAL_IMPROVEMENTS.md, ADVERSARIAL_AUDIT.md)

These are independent, replayable supplements developed after the original exact closure.
They can be verified independently with 'bash run_checks.sh' in the certificates directory.
2026-07-31 05:04:48 -05:00

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Problem 2.8 formula-optimization supplements

These files isolate the formula optimizations developed after the original exact closure. They can be reviewed or replayed independently of the manuscript build.

Positive-cone transport

  • certificates/p28_positive_cone.py
  • certificates/POSITIVE_CONE_CERTIFICATE.md
  • certificates/POSITIVE_CONE_MANUSCRIPT_SECTION.tex

The checker reconstructs the authoritative transfer, applies the exact Pascal conjugation, and verifies 100 grouped obligations: all 16 transfer identities, all 285 strictly positive numerator coefficients, positive denominators and limit entries, and both transformed seed rows. In the revised manuscript this elementary contraction is the active all-four-column proof.

Optimized differential gauge

  • certificates/p28_optimized_gauge.py
  • certificates/OPTIMIZED_GAUGE_CERTIFICATE.md

The checker clears the rational gauge before expansion and verifies 176 scalar polynomial obligations. It is an optional independent replay; the original 16-entry gauge remains in certificates/p28_standalone_equations.py.

Adversarial and provenance supplements

  • certificates/p28_mutation_sensitivity.py corrupts one coefficient in each optimized certificate and requires both altered copies to fail.
  • certificates/solution_pre_positive_cone.tex preserves the complete pre-replacement manuscript.
  • FAMM_SCARS.md, certificates/p28_famm_scars.json, and certificates/p28_famm_scars_validator.py record scoped advisory failure memory. They grant no hard-pruning authority.

Replay the complete mandatory path with:

bash run_checks.sh