Milestone 5: orbit-membership-aware scaffold

[mdheller]

Summary

Start Milestone 5 with an orbit-membership-aware scaffold for the four-prime cohort:

{257, 313, 353, 457}

This PR adds:

• data/milestone5/m5_four_prime_baseline.json
• schemas/milestone5_orbit_candidate.schema.json
• scripts/milestone5_orbit_scaffold.py
• .github/workflows/milestone-5-orbit-scaffold.yml
• proof-adapter.json update for BSD-M5-004-orbit-membership-scaffold

Scope

Scaffold only. No rank exactness, second independent point, four-descent execution, BSD-I, BSD-II, or Sha-finiteness claim is made.

The scaffold verifies inherited P1 points on each curve, classifies the four target primes by failure mode, and emits digest-addressed scaffold events.

Target split

257 and 457

No second generator was found in inherited bounded searches. Future controller-routed work requires extended search, four-descent, or another explicitly scoped method.

313 and 353

Historical false positives were caused by treating descent-image difference as sufficient. Future controller-routed work must test torsion-orbit membership before any independence claim.

Required non-claim

This milestone does not address rank exactness for primes where independent-generator search returns negative within stated bounds.

Expected validation

• Milestone 5 scaffold workflow passes.
• SocioSphere proof-apparatus validation passes.
• BSD adapter remains fail-closed: draft / E7, no gate marked pass, no claim promotion.

Refs #10.

[mdheller]

Milestone 5 scaffold status update.

The PR is intentionally fail-closed and remains open. GitHub has not attached any workflow runs or commit statuses to the current head b663bb3edf87bd79795e518b5c04db7607493a5f through the connector-visible status APIs, despite a tracked source change on the branch.

Implemented in this PR:

• four-prime baseline for {257, 313, 353, 457};
• orbit-membership-aware candidate schema;
• scaffold runner scripts/milestone5_orbit_scaffold.py;
• Milestone 5 adapter claim BSD-M5-004-orbit-membership-scaffold at draft / E7;
• explicit non-claim that negative search within declared bounds does not prove rank exactness;
• workflow milestone-5-orbit-scaffold.yml.

Local arithmetic sanity check on inherited P1 values passed for all four targets against E_n: y^2 = x^3 - n^2 x:

257: P1 on curve = true; target_class = no_second_generator_found
313: P1 on curve = true; target_class = historical_false_positive_requires_orbit_filter
353: P1 on curve = true; target_class = historical_false_positive_requires_orbit_filter
457: P1 on curve = true; target_class = no_second_generator_found

This PR should not merge until GitHub Actions / SocioSphere validation is observed or the workflow-trigger anomaly is resolved.