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Formalize anchored barriers and checked finite cycle extraction - #5
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Local no-descent tests cannot be propagated forward while resetting their comparison level: 3 → 10 → 5 passes at 3 and fails at 10. This change formalizes fixed-barrier windows, proves exact splitting and the greatest invariant kernel characterization, and connects kernel emptiness to the existing Collatz conjecture statement.
An executable interval-prefix checker is proved equivalent to all sampled states lying in [b,u]. A successful check through u−b+1 steps extracts a positive-period closed orbit using the existing pigeonhole theorem. The result needs no assumption about future boundedness.
Validation: the new Lean module builds; all 21 theorem axiom footprints use only propext, Quot.sound, and Classical.choice; 62,208 independent split-window cases and 3,456 interval cases pass; Lean rejects two deliberately false certificates. Moving-barrier, insufficient-prefix, and nontrivial 5n+1-cycle controls pass. The repository proof-escape scanner and whitespace checks pass. CI now runs the dedicated audit. The full library build is also being checked.
These are structural research tools, not a Collatz proof or a claim of frontier mathematical novelty. Research notes identify the remaining unbounded obligation and distinguish existing line/commit volume from mathematical discoveries.