Generate solver architecture and public contract docs from sources of truth

[siddhss5]

Problem

Public documentation and architecture comments have drifted from v6 behavior:

• docs/architecture.md says 11 solvers while the registry contains 13.
• It documents arm.ik() and an unchanged (solutions, is_ls) result rather than the current solve()/diagnostic API.
• It describes base85 pickle artifacts, module-import priming, one-iteration refinement, and opt-in rescue that no longer match production behavior.
• Source docstrings still refer to a forthcoming Cython port and first-solve symbolic preprocessing.
• Strong “every IK branch” wording does not distinguish soundness, recovered branches, known numerical gaps, and conditional 7R sampling.

Proposed direction

• Generate solver counts, family tables, arm counts, backend availability, and benchmark fields from the registry/manifest.
• Keep one normative solve-contract document shared by API docs and generated artifact docstrings.
• State separate guarantees for 6R isolated-branch recovery, 7R conditional branch enumeration, redundancy sampling, winding representatives, refinement, and rescue.
• Maintain a visible list of known completeness limitations linked to their issues.
• Move historical phase notes out of production docstrings into ADRs or issue history.

Acceptance criteria

• Architecture/API documentation matches the M8 canonical solve pipeline.
• Registry-derived facts are generated and checked for drift.
• Public claims distinguish soundness from completeness and sampling coverage.
• Generated artifact docs and Manipulator.solve docs describe identical option semantics.
• Stale Cython/base85/first-call/opt-in-rescue descriptions are removed or corrected.
• Documentation CI fails when generated contract sections drift.

This issue should land after the M8 behavioral contract stabilizes.