Recovery of the original future residue

For each natural r, residueMAP is the existing fixed-order actual cell-mass maximizer for residueTarget and futureWord(r) under the original J. All words, ties and zero-mass observations remain in its total domain.

Theorem 1.4 (Summable errors recover Z1).

Lean statement: D5/S3/Observer/ProbabilisticClosure/TrajectoryLaws/TwelveStateFutureRecovery.actual_future_residue_recovery

Proof. Machine-checked in Lean as D5/S3/Observer/ProbabilisticClosure/TrajectoryLaws/TwelveStateFutureRecovery.actual_future_residue_recovery (✓ std3). ∎

Source. Repository-derived.

Commentary.

On exactly the original J, every initial-residue MAP error at length r is at most ofReal((11/2)*rho^(r/2)), and these estimates are almost surely eventually equal to Z1. The source conclusion requires measurability of Z1; this proof uses a summable coefficient obtained before merging the twelve original hidden lifts. Actual state/future cylinder masses feed the actual MAP estimate. Their word probabilities factor through the six original phase/residue labels. Distinct initial residues remain distinct under every common word, so full affinity for such a pair equals its killed-pair survival affinity. The actual two-step affinity and specified_survival give the same rho=sqrt(15)/4. The proof does not infer an initial F/T phase decoder.

trureturing — Discovering truth

Recovery of the original future residue

Abstract

References

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trureturing — Discovering truth

Recovery of the original future residue

Abstract

References