Why it is a question
A12 separated three questions the exchange had run together: persistence (which variables carry information about their own future), individuation (which deserve to be one system) and causal level (at which coarse-graining the causal structure is most effective). Each has a criterion, and they measure different things:
- Temporal information retention. Krakauer et al.’s A* = I(S_{t+1}; S_t), A = I(S_{t+1}; S_t | E_t) and nC = I(S_{t+1}; E_t | S_t) (LIT-1137, unread). A11 §5: the two principal measures do not decrease when the candidate is enlarged, and the paper “explicitly states that determining precise boundaries requires a size cost or regularizer”. A11 proposed lag-dependent versions, A(Δ) = I(S_{t+Δ}; S_t | E_t), as its own extension, giving a profile across horizons rather than a score.
- Interventional retention. Bourrat’s  = I(S_{t+1}; Ŝ_t) (LIT-005, NOTE-027), which scores a passively reconstructed entity zero where A* does not. The exchange did not cite it. NOTE-027 found Bourrat’s equivalence  ≡ A false in general.
- Dynamical independence (THEORY-257), closure of a coarse variable given its own history.
- Effective information (THEORY-222), causal informativeness of macro-transitions under a declared intervention distribution. A12: a macro-intervention needs a meaning (“What does it mean to set ‘the fandom’s level of resentment’ to a particular value?”), and A14 §4 proposed a realization defect: do micro-states with the same macrostate respond alike to the same intervention?
- A priced block (CLAIM-157, CLAIM-154), which supplies the cost the information measures lack. A12 §2’s version: a candidate must beat the decomposed description (independent members), and the expanded one (the fandom with the franchise, media and league).
A12 §4: “There isn’t yet a justified single scalar objective that combines all these steps”, and “we shouldn’t pretend that mutual information, dynamical closure, and effective information are commensurable merely because all are measured in bits.” It proposed a multidimensional profile and Pareto comparison. A11 §6 posed the sharpest disagreement: “Can a collective possess strong historical information continuity while failing to possess a dynamically independent macrostate?” A fandom that depends on games, media and league decisions may be one.
QUESTION-093 asks the same kind of question about agency. This one asks it about individuation, with the timescale as a third unknown (CLAIM-331).
What would count as an answer
A12 §8: “A specified search procedure that recovers independently known system boundaries and characteristic timescales in controlled models, while reporting failures, nonunique optima, and sensitivity to its intervention assumptions.” CASE-101 is the controlled model the exchange proposed. A12’s table of separate verdicts is the guard: high temporal information licenses a predictive relation, integration a module, effective information a causal coarse-graining, transmission a lineage, and none of them agency.
Note of 2026-10-18: macro-interventions, a second appearance
A21 §4 of the exchange of 2026-10-17 came to this question’s meaning problem for macro-interventions from causal emergence (THEORY-222), with a person’s commitment as the macrostate: “whether a manipulation of that macrostate represents an admissible intervention depends on what it means to change a commitment while holding other aspects of the agent fixed. We cannot simply impose arbitrary macro-interventions and assume they correspond to physically meaningful manipulations.” It proposed: “The explanatory standing of an organizational scale depends not only on what it compresses, but on which counterfactual interventions and outcomes the compressed description continues to represent faithfully.” A21 §6 gave the condition C_*(P_ℓ^{do(a)}) = P_L^{do(ā)} for a declared family of interventions. That is A12’s question and A14’s realization defect again (do micro-states with one macrostate respond alike?), for a commitment instead of a fandom’s resentment. A21 did not cite this question. Its judgment-preserving form is CLAIM-350, whose causal version is recorded there as a definition, not a result.
Note of 2026-10-20: ΦID emergence picks no level without a price
The primary ΦID paper, Rosas et al. 2020, read in NOTE-987, answers part of this question for one pair of criteria.
- Emergence capacity peaks at the microstate. By its Theorem 1’s own witness, the emergence score is maximized by the full microstate. So ΦID emergence alone selects no coarse level; selecting one needs a price such as CLAIM-154’s.
- Ψ against dynamical independence. They diverge both ways
(THEORY-764):
- A self-copying single part is independent and not emergent.
- A parity whose persistence depends on one bit passes the decoupling test and is not independent.
- The sum of independent identical AR(1) channels is both, with no interaction at all.
- Neither detects interaction. Neither criterion requires the parts to interact.
- Effective information asks something else again. Ψ rewards closure and penalizes redundancy among the parts. Effective information is measured under imposed interventions (THEORY-222).
Split, 2026-10-21 (ADR-049). What three of the criteria track is QUESTION-243, Answered. Retention measures read association, not propagation (THEORY-424). Ψ and dynamical independence diverge both ways, neither needs the parts to interact, and neither prices a feature’s size (THEORY-764). This question keeps the joint search for boundary, timescale and macrostate with an Occam price, its test on CASE-101, and where effective information parts from the others on one system.
Note of 2026-10-21: the leave-one-out over the criteria
The owner’s leave-one-out design of 2026-10-20 (U3, filed as QUESTION-252) asks systematically, of five conditions on an effective description (predictive sufficiency, dynamical independence, memory closure, approximation fidelity, feasible recoverability), whether each can hold without the others. That is this question’s “what each criterion tracks”, asked as a table. The exchange did not cite this question. CLAIM-401’s answer to the design is that the conditions are not of one logical kind, so the table’s cells are not all of one sort either.
Note of 2026-10-29: Krakauer et al. and the three search candidates, read
LIT-1137 is now read (NOTE-1400), so the body’s “unread” no longer holds. A11’s report is confirmed for the 2020 article: A* and A cannot decrease as variables move from the environment into the candidate, and the article says a boundary needs a size cost. The 2014 preprint makes the same monotonicity claim but offers a stopping rule instead of a size cost. The check is THEORY-1163.
The works filed as A10’s paper “on searching for coarse-grainings rather than assuming them” are read too, and each fits only in part.
- Jansma and Hoel, LIT-1123 (NOTE-1359), does search: it scores every partition and reports a set of scales. It prices nothing, with no Occam term, and its profile is across scales under one criterion, not across criteria.
- Hoel’s CE 2.0, LIT-1136 (NOTE-1387), searches along one path chosen by maximum gain, and calls the full search future work.
- Zhang et al., LIT-1129 (NOTE-1399), avoids the search: it reads the singular-value spectrum and recovers a partition afterwards by k-means.
All three search partitions of one system’s states, not which variables are in the system. They bear on the macrostate leg of this question and not on the boundary leg.
Shalizi and Crutchfield, LIT-1126 (NOTE-1372), adds one distinction: E ≤ Cµ separates what can be measured from sequences from the memory needed to produce them, as this question separates retention measured on observables from a system’s state.
The question is unchanged and stays Open.
Note of 2026-10-29: effective information against A21’s admissibility condition
A21’s condition, in the note of 2026-10-18, C_*(P_ℓ^{do(a)}) = P_L^{do(ā)} for a declared family of interventions, puts Eberhardt and Lee’s demands of commutativity and unambiguous manipulation in one line. Their paper, LIT-1839, is now read (NOTE-1413). It shows that EI’s family, uniform averages over realizers, passes coarse-grainings that fail both. In their (14), EI merges two states whose effects on the macro effect variable differ (0.8/0.2 against 0.9/0.1). In their (17), the partition is strongly lumpable, so the coarse-graining does commute with time evolution, and the EI-optimal choice still changes with the time step. It is the same shape of answer the note of 2026-10-20 gave for ΦID emergence: the criterion alone does not license the level it picks.
On where effective information parts from the other criteria: under one distribution over micro states at both levels, EI cannot favour a macro at all (THEORY-1167). Its macro advantage is a property of the distribution chosen at each level.
The question is unchanged and stays Open.
Note of 2026-10-29: causal feature learning, a further macrostate criterion
Causal feature learning, LIT-1833 (NOTE-1420) and LIT-1834 (NOTE-1415), is a further candidate for the macrostate leg, and it parts from effective information on one system. It partitions causes by P(Y | do(x)) and effects by their columns, two partitions where Hoel’s EI coarsens cause and effect by one. On Eberhardt and Lee’s (14), EI picks {x₁, x₂}, {x₃} and causal feature learning the micro. On their note 6, causal feature learning merges x₂ and x₃, whose rows are identical, and EI’s shared partition cannot. Under one distribution at both levels the two agree on which coarse-grainings lose nothing (THEORY-1169), so the disagreement belongs to the uniform distribution at each level, as the earlier note of this date found for EI’s macro advantage.
Like the other macrostate candidates, it partitions one system’s states, not which variables are in the system. It has no Occam term: it takes the coarsest partition that loses nothing and offers no trade of loss against size.
The question is unchanged and stays Open.