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CLAIM-401: The conditions an effective description is commonly asked to meet are not of one kind: predictive sufficiency and approximation fidelity are adequacy relative to a declared target, metric and horizon; tractability restricts the operations under which adequacy is assessed; dynamical independence and memory closure are relations of the representation to the system, memory relative to a chosen projection; so a matrix over them as independent binary axes conflates kinds

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Properties11
StatusActive
Version3
Rolethesis
Warrantinterpretive
Tagscomplex-systems, information-theory, philosophy-of-science
Linedistributed-agency, formal-apparatus
AnswersQUESTION-324 — Are the conditions an effective description is asked to meet (predictive sufficiency, dynamical independence, memory closure, approximation fidelity, tractability) of one logical kind, or are some of them parameters of the regime under which the others are assessed rather than conditions in their own right?
Bears onQUESTION-252 — For the conditions an effective description is asked to meet (predictive sufficiency for a declared target, dynamical independence of the omitted variables, memory closure under a declared projection, approximation fidelity in a declared metric and horizon, and tractability within a declared budget), which can fail while all the others hold, and which such configurations are impossible in which model classes?
Rests onCLAIM-152 — Any individuation built on sufficiency is relative to the target it is sufficient for: fix the outcomes differently and a different partition wins, so no boundary drawn this way is universal, CLAIM-348 — No coarse-graining is normatively adequate in general because it preserves stability, prediction or aggregate performance: a description adequate for an institution's performance can merge states its members' claims must distinguish, so adequacy is fixed by the evaluative target, and the target cannot be justified solely by the description that preserves it, CLAIM-397 — For a scalar stationary process with autocovariance C, the Mori–Zwanzig memory kernels for the projection onto the current value are fixed by C alone, through C(m+1) = Σ_{k≤m} c_k C(m−k); the memory vanishes iff C is geometric, and when C has finite Hankel rank d the memory has Hankel rank exactly d − 1, CLAIM-304 — A rendering can keep a distinction recoverable in principle and make it infeasible to recover: if pseudorandom generators exist, a uniformly random bit can be encoded so that an unbounded receiver recovers it except with probability at most 2⁻⁽ⁿ⁺¹⁾, while no efficient receiver does non-negligibly better than chance
GroundsTHEORY-752 — In optimal prediction of a Hamiltonian system with separable energy and canonical initial law, projected by conditional expectation, the t-model's leading-order memory term tPLQLx makes the effective Hamiltonian of the resolved variables non-increasing, so the eliminated variables' memory enters as a damping that grows linearly in time
UsesTERM-065 — effective-description regime: the system, query family, intervention family, resource bounds, tolerance and horizon under which a candidate description's adequacy is assessed, ℛ = (X, 𝒬, ℐ, ℬ, ε, τ), kept apart from the description T it evaluates, so that rival descriptions are compared under one regime and whether each is adequate, Adequate(T; ℛ), is settled once the regime is stated

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The claim

The owner’s leave-one-out design (QUESTION-252) treated five “virtues” of an effective description as binary axes. At U4 the owner noticed that working through it “has potentially already altered our characterization of those “virtues"". A4: “Notice that (P) and (A) look increasingly like evaluation criteria, while (D) and (M) describe different aspects of system–representation structure. (C) describes resource accessibility. These may not be five virtues of the same logical kind.” A5 took it further: approximation fidelity “is not necessarily an independent property alongside predictive sufficiency. It may specify the degree to which a prediction or dynamical relation is preserved. Computational tractability need not be another virtue of the same logical type. It can instead restrict the operations over which preservation is evaluated.” So A5 replaced them with one relation, Adequate(T; 𝒬, ℐ, ℬ, ε, τ), which is the regime TERM-065.

The kinds, with the record’s support:

  • Adequacy for a target. Predictive sufficiency is sufficiency for a declared future, and what is sufficient for one target need not be for another (CLAIM-152). Approximation fidelity is a degree in a declared metric over a declared horizon. CLAIM-348: “adequacy is fixed by the evaluative target”.
  • A restriction on operations. Tractability is relative to a budget and a class of procedures. CLAIM-304’s distinction is recoverable in principle and infeasible to recover: the same representation passes or fails with the budget.
  • Relations of the representation to the system. Dynamical independence compares the coarse variable’s own past with the micro past for predicting its future (THEORY-820, THEORY-733). Memory closure is a property of the coarse variable’s own law (CLAIM-397) under a chosen projection. A5 wrote that “Memory closure and dynamical autonomy remain genuine structural conditions”. That is not quite so for memory: different projections give different splits into Markov term and memory (THEORY-752). QUESTION-222 keeps the caution that the split into drift, memory and noise depends on the projection, so “an arbitrary norm of the memory kernel is not, by itself, a representation-invariant measure of emergence”; CLAIM-397 is “Not about other projections”.

So of the five, only dynamical independence needs nothing declared beyond the micro state and the coarse-graining. A matrix over the five as binary axes mixes a degree, a restriction and three relations, and a cell can be filled or emptied by moving a parameter rather than by a fact about the system. That is A3’s own warning, “we could make an ablation succeed simply by moving the goalposts”, applied to the axes.

What it does not say

  • Not that the five reduce to three. A4: “This is not necessarily a reduction from five properties to three. Rather, it suggests that our initial coordinates were mixing different kinds of questions.”
  • Not that the structural pair is free of choices. Dependence needs the micro state named, and memory the projection.
  • Not that the leave-one-out question is empty. Once the regime is fixed, each cell is a fact about a model class, and QUESTION-252 asks for them.

Note of 2026-10-26: one kernel, several verdicts

CASE-164 computes on one exactly known 192-state kernel conditions this claim says are of different kinds, and they come apart as it says.

  • Relations of the representation to the system. The agents with phase are informationally closed on the declared intact law and fail global strong lumpability (defect 0.42).
  • Adequacy for a target. Their deficiency for the next pair of rule integrities is 0.5051 bits under one declared intervention mixture. For the ordinary intervention alone it is 0 on the intact support and 0.918 bits on the damaged one, so the verdict moves with the source law and the target.
  • A budget. At 300 training windows a fitted predictor shows a negative gain where the exact defect is 0.0930 bits, and at 1,200 all 12 repetitions show a positive one (dmarx/PerspectiveLab@9f82bfd experiments/closure_estimation/). The same test of sufficiency passes or fails with the sample.

In CASE-163, identifying a mechanism’s class and recovering its parameters are separate verdicts, and each depends on what probes the budget allows. These are witnesses of the distinctions in one stipulated model, not an argument for the classification. The claim is unchanged.

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