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r-irber-irbe/proof-skills/skills/lean-formalization-breakdown/SKILL.md

lean-formalization-breakdown

Skill3 starsChanged 24 days agoApache-2.0View on GitHub

USE FOR: architectural deconstruction of Lean 4 codebases, censuses, DAG analysis, and verification audits. DO NOT USE FOR: authoring new Lean proofs (@lean-proof), simple typo fixes (@lean-doc-improvement). TRIGGERS: formalization-breakdown, proof-breakdown, census, landmark-dag, lean-breakdown.

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SKILL.md

1. Run automated census and DAG topology analysis

Authoritative protocol for architectural deconstruction and multi-wave analysis of monumental Lean 4 formalizations (derived from the Fermat's Last Theorem 28-wave and Navier-Stokes & Euler 8-wave campaigns).

Routing

  • USE FOR:
    • Deconstructing monumental Lean 4 codebases (100 to 60,000+ modules) into structured, human-navigable mathematical layers.
    • Running automated static and kernel censuses (modules, lines, theorems, lemmas, definitions, structures, axioms, sorries).
    • Verifying import DAG topology, detecting cycles, computing topological layer depth and longest dependency paths.
    • Identifying landmark theorems, boundary adapters, and comparator challenge interfaces.
    • Decomposing mathematical proof engines into sequential multi-stage pipelines.
    • Mapping formal mathematical substrates into downstream packages and domain libraries.

Workflow

+-----------------------------------------------------------------------------+
| Wave 1: Static Census & Macro Architecture                                  |
|   - scripts/lean/formalization_breakdown.py                                 |
|   - Module inventory, lines of code, declaration counts, DAG depth          |
+-----------------------------------------------------------------------------+
                                       |
                                       v
+-----------------------------------------------------------------------------+
| Wave 2: Dual-Kernel Verification & Axiom Audit                              |
|   - Zero-sorry validation, comparator challenge verification                |

## Recovery & STOP

- If `formalization_breakdown.py` detects an import cycle or unresolvable path, halt downstream wave scaffolding and report the structural blocker first.
- If `sorry` declarations appear in implementation modules, isolate them in Wave 2 before claiming substrate readiness.

## Handoffs

- **Predecessors**: `agent:gateway`, `skill:lean-blueprint`
- **Successors**: `skill:lean-pedagogical-exposition` (human-readable math and pedagogical synthesis), `skill:lean-zettelkasten` (knowledge graph storage),
  `skill:lean-enforcement` (CI gate enforcement).
- **Source Guide**: [`references/formalization_breakdown_guide.md`](../../references/formalization_breakdown_guide.md)

## Detailed reference

Full reference and lookup tables:
[`references/lean-formalization-breakdown-handbook.md`](../../references/lean-formalization-breakdown-handbook.md).

## See also

- [`../../references/lean-formalization-breakdown-handbook.md`](../../references/lean-formalization-breakdown-handbook.md) -- Handbook
- [`../lean-gateway/SKILL.md`](../lean-gateway/SKILL.md) -- Top-level skill router

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