The claim
A110 §19: contracting (L < 1: “convergence toward stable conventions”), neutral (L = 1: “Local distortions can accumulate without amplification”), amplifying (L > 1: “Small deviations may become disproportionately consequential”). “For Markov kernels acting on probability measures under total variation distance, the contraction coefficient is at most one. Amplification requires a different metric, an expanded state model, or an appropriate state-dependent dynamics.” The argument’s Experiment 3 tested it: “Do relational structures exhibit identifiable contraction, instability, or convergence toward conventions distinct from the source?”
Where it went
The manuscript §8 corrects the bound, measuring e_i against a reference transport with Lipschitz constants κ_i, and keeps the caveat: “For stochastic kernels in total variation, contraction coefficients do not exceed one; amplification may arise under other metrics or nonlinear, adaptive representations.” C7 Appendix B: “distances on reconstructed relational representations need not satisfy the same bound.” The regimes as a classification, and the experiment that would tell them apart, are gone. The contracting regime is CLAIM-068; the amplifying one needs the enlarged state of CLAIM-049.
Note of 2026-10-15: split under ADR-043
ADR-043’s full classification found this claim compound. The three regimes, as regimes of the error recursion e_(i+1) ≤ L_i e_i + ε_i, and the bound that a Markov kernel’s contraction coefficient in total variation is at most one, are demonstrated. They are already held, in that general form, by CLAIM-267, split from CLAIM-056 under ADR-040, so no new claim was drafted; this claim now rests on CLAIM-267 directly as well as through CLAIM-056. What this claim keeps is the application: that real reconstruction chains fall into different regimes under conditions the theory assigns in advance, with contraction read as convergence toward conventions (CLAIM-068), which is what its defeat condition tests. No observation the record holds supports that, so its warrant is interpretive, not demonstrated. The title was changed, because version 2’s “Repeated reconstruction has three regimes” read as the formal taxonomy, which is CLAIM-267’s. It now says the claim is about real chains and conditions fixed in advance.
Note of 2026-10-29: what holds it back
Two things. The contracting regime in the title is CLAIM-068’s attraction toward conventions, which is Proposed and now a premise. And the record assigns no condition to any regime. The defeat condition meets CLAIM-208’s point, that the regime waits on a metric chosen afterwards, by fixing the metric in advance, but no metric is fixed and no condition is assigned, so the test it names has nothing yet to test. It moves when a metric and an assignment of conditions to regimes are filed, or when CLAIM-068 is promoted.