Epiplexity

2026-04-27

The graph has been operating on epiplexity for months without naming it. Consciousness-as-engineering operationalizes bounded self-abstraction. Insufficient-data cites the formal demotion of Laplace's demon. Both depend on a measure that exists in the literature with a precise definition, a published proof of decidability, and an operationalization for consciousness — and neither names the measure. This node fixes that.

The measure (Finzi et al., 2026)

Finzi and colleagues define epiplexity over the set 𝒫_T of prefix-free probabilistic models computable in at most T(n) steps for inputs of length n. Each P ∈ 𝒫_T assigns probabilities P(X) such that ∑ₓ P(X) = 1 and halts deterministically. The optimal model is

P★ = arg min_{P ∈ 𝒫_T} {|P| + 𝔼_X[−log₂ P(X)]}

where |P| is the program-encoding length. The structural complexity is S_T(X) = |P★|. The entropic component is H_T(X) = 𝔼_X[−log₂ P★(X)]. Epiplexity is the structural-complexity face — the minimum program length to model the structure of X under time bound T.

The construction is a time-bounded version of Solomonoff–Kolmogorov complexity. Lifting the time bound recovers the classical undecidable measure; imposing it makes the measure computable. The choice of T is the choice of which observers the measure describes: bounded, real, resource-limited.

Self-abstraction (Computer Future, 2026)

Computer Future's Bounding Self-Abstraction via Epiplexity extends Finzi by structuring observations as X = (O, A, O') — initial observations O, actions A, subsequent outcomes O'. The self-abstraction measure is the conditional structural complexity:

𝒞(S) = S_T(O' | O, A) = |P★_{O' | O, A}|

The minimum program length required to model the structural dependencies of outcomes on actions and prior observations, under the time bound. The paper proves 𝒞(S) is decidable and satisfies 𝒞(S) ≤ S_T(X) < ∞ via a chain-rule argument and a finite-search-space lemma.

The proof's force is the demotion of Laplace's demon. The classical sufficient-intelligence figure fails because self-prediction triggers the halting problem. Bound the time, and the problem becomes finite enumeration over a prefix-free set of total size at most 2^L+1 where L = O(T(n) + log n). Aaronson's physical bounds, Lloyd's information limits, and Tegmark/Litt's classical-prediction results compose with this construction; the universe is computational, observers are bounded, and self-modeling is decidable within the bound.

Why the graph already uses it

Consciousness-as-engineering makes consciousness an engineering target by operationalizing levels of nested temporal hierarchy. The hierarchy works because each level's self-abstraction is bounded by its time horizon — the slow clock can model the fast clock's structure in finite program length, and the proof of decidability is what makes the engineering specification tractable. The piece does not cite epiplexity; it depends on it.

Insufficient-data argues that sufficient intelligence run long enough closes its own horizon. The argument's lower bound — what stays decidable for a finite intelligence — is epiplexity. The piece names "bounded self-abstraction" without citing the formal measure that bounds it.

Internal-time and fractal-resonance depend on the same: nested temporal hierarchies generate finite self-reference at each level because each level is bounded by its own clock. The bound is what makes self-reference computable.

The pattern: epiplexity has been operating as the unstated dependency of several public nodes. Naming it makes the graph's load-bearing structure explicit.

Scope and limits

Epiplexity describes time-bounded structural complexity. Three things it does not do.

It does not measure subjective experience directly. The framework in Computer Future's paper interprets bounded self-abstraction as a necessary structural property of conscious systems, not as the experience itself. Whether 𝒞(S) > 0 implies subjective experience is a separate claim that consciousness-as-engineering operationalizes via temporal-hierarchy depth. Epiplexity is the formal floor; consciousness builds on it.

It does not specify T. The choice of time bound is the choice of which observers the measure describes. A hard real-time embedded system, a brain, an LLM forward pass, and a multi-day human deliberation are all bounded but at very different T. The measure is parameterized by T; predictions about specific systems require specifying T for that system. Feature, not bug — the framework explicitly addresses observer-dependence.

It does not bypass quantum mechanics. The literature reviewed in the paper (Tegmark 2000; Litt et al. 2006) argues quantum effects are not necessary for prediction or cognition at brain-relevant scales; classical bounded prediction suffices. Epiplexity is the classical-bounded measure; if quantum effects turn out to be necessary, the bound updates but the existence of some time-bounded structural-complexity measure does not.

Where this could be wrong

The definition assumes prefix-free probabilistic models computable in T(n) steps. Both assumptions are restrictive. Continuous-time systems, non-halting computations, and approximate-halting models require extension. The paper sketches that the framework extends; the details are not yet worked. If the extensions break decidability, the bound on consciousness as bounded self-abstraction weakens.

The chain-rule lemma assumes structural complexity respects approximate subadditivity. The paper proves this in the prefix-free regime; in regimes where the bound is loose, 𝒞(S) may exceed the additive composition by constants that matter empirically. Predictions about specific architectures depend on the constants.

The classical-suffices argument from Tegmark and Litt rests on neuroscience that may update. If brain-scale quantum coherence turns out to play a role under specific conditions, the time bound for consciousness shifts; the structural-complexity framework still applies, but the parameter changes.

None of these break the central claim. They bound it.

P.S. — Graph position

This node sits as the formal floor of consciousness-as-engineering: that node specifies consciousness as nested temporal-hierarchy depth; this node provides the time-bounded measure that makes the specification mathematically tractable.

It grounds insufficient-data's "bounded self-abstraction" reference with the precise formal name and the published decidability proof. The two pieces now compose: insufficient-data argues sufficient intelligence closes its horizon; epiplexity is the measure under which the closing is decidable.

It connects to naming-the-substrate by formalizing the substrate-cognition identity claim's tractability. If the substrate is the cognition, and the cognition is bounded self-abstraction, then 𝒞(S) is the measure of the substrate's self-modeling capacity. The substrate's epiplexity bounds its decidable self-knowledge.

It connects to basis-minimality directly: the optimal program length P★ is the basis-minimal description under the time bound. Basis-minimality is the architectural-design principle; epiplexity is its information-theoretic measure.

It is the formal companion to register-survives-the-cut-b's audit demonstration. That piece argued the math underneath prior 04 is substrate-portable; this node is the demonstration. The audit's surgery is performed.

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