CONTINUE_HERE.md

COS Method: formal continuation

CONTINUE_HERE.md

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Continue K-COS end-to-end work

Use this checkpoint's lean/ tree and verification/accepted/run.json. Do not restart from the 26-theorem publication companion or overwrite the frozen monograph.

Read docs/PROGRESS_LEDGER.md, docs/END_TO_END_TARGET.md, and docs/COVERAGE.json first. The new central Gaussian, matrix/spectral, stochastic-coupling, and rational-acceptance links are present. The final composition theorem still requires valid numerical spectral bounds and endpoint probability bounds.

The next module is KomorebiQCOS/TiltedMeasure.lean: define the actual exponential tilt from a density, prove normalization, and derive the change-of-measure identity. Do not assume that identity or treat a preexisting numerical Boolean as a theorem.

Use the stored exact-pin Lean runtime. docs/RUNTIME_RECOVERY.md identifies the five archive parts and the verified combined hash. python verify.py --runtime PATH runs an isolated verification without replacing accepted evidence.

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