nucleation

CLAIM-056: Local transport errors in a reconstruction chain are bounded by the per-step discrepancies weighted by the sensitivity of the later reconstructions, so the same local error can be damped, accumulated or amplified, and local similarity can coexist with large global drift; the bound measures departure from a reference transport, not whether the act survives

3 min read

Properties10
StatusActive
Version4
Rolethesis
Warrantinterpretive
Tagsmathematics, probabilistic-modeling
Linepragmatic-transport
Workswhat-survives-translation
Rests onCLAIM-106 — Pragmatic fidelity is a graded, potentially asymmetric property of transport, not an equivalence relation; equivalence is its zero-distortion limit, CLAIM-267 — Per-step discrepancies between a chain of maps and a reference chain compound through the sensitivity of the later steps, so the same local error can be damped, accumulated or amplified, and closeness at every step can coexist with large end-to-end divergence
SupportsCLAIM-081 — Retaining information about the ancestor and drifting in the population's distribution are different profiles: a chain can forget where it started while staying far from the original, so convergence is not preservation and transmission is not degradation, CLAIM-114 — Drift along a reconstruction chain can be marked by a pragmatic phase change, the first generation at which a different communicative configuration dominates, which per-step error in surface content does not show, CLAIM-059 — Repeated reconstruction chains fall into different regimes under conditions assigned in advance, contracting toward conventions, accumulating neutrally or amplifying, and amplification needs a metric other than total variation, an enlarged state or state-dependent dynamics
Objected byCLAIM-031 — A reconstruction chain reorganizes observational constraints rather than only accumulating metric error: a text can change greatly while keeping a few consequential constraints, and one changed constraint can change the act, CLAIM-208 — The compositional predictions are upper bounds whose constants cannot be estimated from serial-reproduction data in a metric fixed beforehand, so the compositional half of the success criterion cannot fail

Graph View

The claim

A50: “similarity is not transitive”, and “assuming a metric”, per-step closeness ε gives only d(u_0, u_n) ≤ nε. With local discrepancy ε_i and Lipschitz constant L_i for the later dynamics, e_(i+1) ≤ L_i e_i + ε_i, so e_n ≤ (∏ L_j) e_0 + Σ ε_i ∏_(j>i) L_j. “This tells us that the impact of local translation errors depends on the dynamics of subsequent interpretation.” Three regimes: contractive (L < 1, distortions dampen), neutral (L = 1, errors accumulate), expansive (L > 1, errors amplify).

Manuscript §8 has the same recursion with κ_i, and adds: “For stochastic kernels in total variation, contraction coefficients do not exceed one; amplification may arise under other metrics or nonlinear, adaptive representations. Crucially, the bound quantifies departure relative to a reference transport, not loss of every communicative virtue.” That last sentence descends from A52 §5.2: “Interpret the bound as a statement about error propagation, not a claim that all communicative changes are errors.”

What it does not say

That drift is random: A50 went on to attraction (CLAIM-068). Nor that it holds for directed, non-metric distortion (QUESTION-017).

  • That a small error means the act survived, or a large one that it did not. A chain reorganizes constraints, and one changed constraint can change the act while the scalar error stays small (CLAIM-031).
  • That the bound predicts drift. It is an upper bound. Its constants belong to the retellers’ kernels, which a chain with one retelling per node cannot estimate (CLAIM-208).

Note of 2026-10-13: the general content is filed separately

Under ADR-040, the error recursion and its three regimes is filed on its own as CLAIM-267, in the formal-apparatus line, resting on no claim. This claim now rests on it for the general content, and keeps CLAIM-106’s graded fidelity, which makes the discrepancy a transport error. Claims in other lines that need only the general content cite CLAIM-267, so setting pragmatic-transport aside does not take it from them.

Note of 2026-10-19: the warrant

The derivation is CLAIM-267’s. This claim applies it to serial reconstruction chains, reading the per-step discrepancy as a transport error against a reference transport, which rests on CLAIM-106’s graded fidelity. Whether end-to-end drift in real chains follows the per-step discrepancies and the later steps’ sensitivity is what the defeat condition tests, and no such measurement is held. So the warrant is interpretive. CLAIM-031 and CLAIM-208 object to it and are unanswered.

Note of 2026-10-29: the concessions written in

The note of 2026-10-19 left CLAIM-031 and CLAIM-208 unanswered. Both are conceded here, by the title and the defeat condition, not answered. What the claim adds to CLAIM-267 is that a serial reconstruction chain is a composition of transports measured against a reference transport (CLAIM-106). The new condition tests exactly that. Promoted by the tenth status review on the owner’s ruling.

Backlinks