allaun/ramanujan-challenge: Ramanujan Challenge Problem 2.8 Solution & Proof

Ramanujan Challenge Problem 2.8 Solution & Proof

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allaun 39806d4423 docs(p28): state the actual motivation -- the problem was used as an instrument Adds the framing that explains the disproportionate machinery: Problem 2.8 was approached as a test case for an existing pipeline (encoding, exact-arithmetic verification, excluded-route registry), not as an isolated puzzle. A well-posed external problem with an objectively checkable answer is a good defect-finding instrument because it cannot be argued with. That is why a Coq-and-Lean treatment of leading zeros sits under a pi formula: absurd overhead for one limit, reasonable for a codec other work depends on. Same for the mutation testing, authority tags, and impossibility registry. Notes the congruence with the challenge's own section 1, which presents these problems as benchmark instruments with structured verification. Adds 'What the exercise found', since if the problem is an instrument then the defects it exposed are part of the result: - defects in the argument, repaired pre-release (false ODE-normalisation uniqueness, invalid norm-inequality direction, unproved holomorphy in the maximum-modulus step, Birkhoff-Poincare as a black box, an untied scalar operator that could have been a surrogate, Q/P vs P/Q orientation) - defects in the verification machinery -- the failures that let bad results pass (checks succeeding with the CAS absent, quo_rem trusting a zero remainder, irreducibility/GCD standing in for arguments) - defects still open, found during independent replay (run_checks.sh exit-code inversion, the false assertion at line 107, the Sage 10.9 coercion error masking it, and the Lean-only radix DFA facing regeneration erasure) The last group is left open rather than tidied away: a validated tool would not still be producing these, and the point of running the instrument is that it is. Co-Authored-By: Claude Opus 5 <noreply@anthropic.com> Claude-Session: https://claude.ai/code/session_01WY6SfRYvm8zFKMX9GcjS8u	2026-07-31 04:33:26 -05:00
docs/proofs	feat(p28): harden exact proof equations	2026-07-31 15:33:21 +07:00
experiments/ramanujan_28/submission	docs(p28): state the actual motivation -- the problem was used as an instrument	2026-07-31 04:33:26 -05:00

allaun 39806d4423 docs(p28): state the actual motivation -- the problem was used as an instrument

Adds the framing that explains the disproportionate machinery: Problem 2.8 was
approached as a test case for an existing pipeline (encoding, exact-arithmetic
verification, excluded-route registry), not as an isolated puzzle. A well-posed
external problem with an objectively checkable answer is a good defect-finding
instrument because it cannot be argued with.

That is why a Coq-and-Lean treatment of leading zeros sits under a pi formula:
absurd overhead for one limit, reasonable for a codec other work depends on.
Same for the mutation testing, authority tags, and impossibility registry.

Notes the congruence with the challenge's own section 1, which presents these
problems as benchmark instruments with structured verification.

Adds 'What the exercise found', since if the problem is an instrument then the
defects it exposed are part of the result:
  - defects in the argument, repaired pre-release (false ODE-normalisation
    uniqueness, invalid norm-inequality direction, unproved holomorphy in the
    maximum-modulus step, Birkhoff-Poincare as a black box, an untied scalar
    operator that could have been a surrogate, Q/P vs P/Q orientation)
  - defects in the verification machinery -- the failures that let bad results
    pass (checks succeeding with the CAS absent, quo_rem trusting a zero
    remainder, irreducibility/GCD standing in for arguments)
  - defects still open, found during independent replay (run_checks.sh exit-code
    inversion, the false assertion at line 107, the Sage 10.9 coercion error
    masking it, and the Lean-only radix DFA facing regeneration erasure)

The last group is left open rather than tidied away: a validated tool would not
still be producing these, and the point of running the instrument is that it is.

Co-Authored-By: Claude Opus 5 <noreply@anthropic.com>
Claude-Session: https://claude.ai/code/session_01WY6SfRYvm8zFKMX9GcjS8u

2026-07-31 04:33:26 -05:00

docs/proofs

feat(p28): harden exact proof equations

2026-07-31 15:33:21 +07:00

experiments/ramanujan_28/submission

docs(p28): state the actual motivation -- the problem was used as an instrument

2026-07-31 04:33:26 -05:00