the acta constitutiva

The unreasonable effectiveness of mathematics (Wigner): mathematical structures are discovered, not invented, suggesting they describe something independent of the discoverer. The coherence and predictive power of physics across scales (quantum to cosmological). The existence of phenomena no human mind would plausibly invent (cosmic microwave background anisotropy, quantum entanglement, the sheer alienness of deep-field galaxies). The statistical argument: the information content of the observable universe exceeds what any known computational process in a single brain could generate by many orders of magnitude.

As an axiom, deliberately resistant to revision.

Downward: a mathematical proof or demonstration that brain-scale computation could generate the observed information content of the universe. Discovery of fundamental observer-dependence in physical law that scales beyond quantum decoherence into macroscopic reality. If solipsism became explanatorily productive (not just logically coherent), the pragmatic case for the axiom weakens.

Compatible but not threatening: evidence that reality is a simulation. A simulated universe is still external to minds within it, its laws still discovered not invented by inhabitants. Whether reality is "base" or "simulated" is currently beyond our reach and may be permanently so.

Wheeler's "it from bit": every physical entity derives its function from informational distinctions. Lloyd's Programming the Universe: the universe as quantum computer, computing its own evolution. The Church-Turing-Deutsch principle (Deutsch 1985): every physical process is simulable to arbitrary precision by a universal computer, extending Church-Turing from logic to physics. The unreasonable effectiveness of mathematics (Wigner): mathematical structures are discovered, not invented, which is better evidence for this prior (reality has computational/mathematical structure) than for P-000 (where it was cited as evidence merely for an external world). The discrete/informational structure of quantum mechanics: unitarity, information conservation, finite Hilbert-space dimensions per region. The Bekenstein bound and holographic principle: the information content of any spatial region is finite and bounded by surface area, suggesting reality is fundamentally finite-informational rather than continuous-material. Wolfram's computational irreducibility as evidence that nature behaves the way computations behave. Bach's computational functionalism extended from minds to physics: if minds are software and minds are part of nature, then nature is already the kind of thing software can be made of. Internal coherence: P-011 provides the unstated ontological substrate the framework has been borrowing throughout (P-004, P-005, P-006, P-007, P-009, and P-010 all silently presuppose it).

Downward: discovery of a genuinely non-computable physical process (true ontological randomness rather than pseudo-randomness, hypercomputation in nature, a continuous physical quantity that resists any discrete encoding even in principle). A satisfying account of consciousness or physics that requires irreducibly non-computational primitives. Formal demonstration that some physical fact is not encodable as information. Upward: successful derivation of physical law from purely computational/information-theoretic first principles (a working "it from bit" program). Experimental detection of discrete structure at small scales (loop quantum gravity, causal set theory, computational spacetime). Successful artificial creation of complex emergent phenomena (life, consciousness) on substrates whose only commonality with biology is computational structure. Needs resolution: the relationship to Gödel/halting/computational-irreducibility. If reality is computational and computation has fundamental limits, those limits are limits of being, not merely of knowing. The contour of this is open. Distinction from simulation hypothesis: P-011 says reality is computational; it does NOT say reality is being run on a meta-computer somewhere (that would just reintroduce the substrate problem one level up). The claim is structural, not nested. A simulation hypothesis (we are inside a sim) is compatible with P-011 but not required by it: the sim's host is also computational, and so on, with no privileged base layer. Distinction from idealism: P-011 is not the claim that reality is mental or experiential; computation is a structural notion, neutral on whether the computation has an "inside view" (that is the work of P-004 and P-009, which specify which computations have phenomenology).

Pross's dynamic kinetic stability (DKS): the population-level extension of thermodynamic stability to replicating entities. The bff experiment (Agüera y Arcas et al. 2023): random code soups spontaneously produce replicators via a sharp phase transition after sufficient interactions, reproduced across multiple computational environments. Von Neumann's proof that open-ended self-replication requires a Universal Turing Machine (so life is computation in the strict sense, not metaphor). The Daisyworld simulation: planetary-scale homeostasis emerges from Darwinian selection alone, no design or consciousness required. Follows from and grounds P-004 (substrate independence of consciousness is natural if life itself is substrate-independent computation) without reducing to it.

Downward: controlled experiments showing that life-like replicators fail to emerge in sufficiently varied computational substrates over sufficient time (challenging the "dynamical attractor" claim). Evidence that bff-style phase transitions are artifacts of Turing-complete languages and don't generalize to realistic chemical models. Upward: formal proof that replicator emergence probability approaches 1 given sufficient computation + time + free energy. Successful abiogenesis experiments confirming the metabolism-first (black smoker) pathway and the autocatalytic set → replicator transition. Detection of extraterrestrial life (independent instance of the attractor). Distinction from P-005: P-007 operates at the hardware layer (thermodynamic persistence of patterns), while P-005 (coherence emerges from mutual prediction) operates at the software layer (functional consistency of the computation). A replicator can be dynamically stable without being coherent (early bff soup, viral DNA in isolation). A complex agent requires both: dynamic stability of its substrate and coherence of its computation.

Agüera y Arcas's derivation from first principles: any adaptive agent learning P(X,H,O) will track latent variables (concentration, temperature, hunger) not because they are fundamental features of the universe but because they compress the stream of events into what is predictively relevant. Von Uexküll's umwelt as the organism-specific compression scheme. Philip K. Dick's formulation ("reality is that which, when you stop believing in it, doesn't go away") as the pragmatic residue: models that fail to track real causal structure kill the organism, so surviving models are constrained. The Bayesian brain framework (P-001) is the high-resolution instantiation of this prior: perception as inference over latent causes. The is/ought collapse as supporting structure: every "is" in an organism's umwelt carries an ineradicable purposive charge, which means description and normativity are not cleanly separable for living observers.

Downward: a successful account of consciousness or intelligence that requires observer-independent facts (facts not constituted by any model) to be causally efficacious. Evidence that consensus reality across species or individuals is better explained by convergent access to observer-independent structure than by convergent selection pressures. A formal demonstration that some physical quantities are not latent variables in any model but are "given" prior to any observer. Upward: formal derivation showing that the set of stable latent variables any survivor must track is uniquely determined by the physics of the environment (i.e., convergent modeling is not contingent but necessary). Empirical results from comparative umwelt research showing tight correspondence between selection pressures and latent variable structure across species. Distinction from idealism: P-008 rejects solipsism and accepts P-000 (an external world exists) and P-011 (that world is computational). Observer-dependence of what is salient is compatible with observer-independence of the relational structure that physics describes. What is observer-independent is the structure of the computation; what is observer-relative is the choice of compression (the umwelt-specific latent variables). The claim is neither idealism (there is a world) nor naive realism (the world does not have intrinsic features beyond its relational behavior); it is structural realism: structure is real, intrinsic features are not posited.

The computational tractability argument (exact inference is intractable; variational approximation is the only feasible strategy for real-time processing), the prediction error literature, the success of predictive processing models in explaining attention, multisensory integration, perceptual illusions, and psychopathology. Empirical support from mismatch negativity, binocular rivalry, and precision-weighting experiments.

Downward: discovery of perceptual processes that are purely feedforward, with no top-down modulation, and cannot be modeled as inference even approximately. Evidence that prediction error signals are epiphenomenal (present but not functionally driving perception). Upward: successful clinical interventions based on precision-weighting predictions (computational psychiatry applications). A computational account bridging inference to subjective experience, connecting the mechanism to qualia. Refines but doesn't threaten: resolution of the optimality question (Gigerenzer's fast-and-frugal heuristics vs. approximate Bayes) would change how perception-as-inference works, not that it does. The FEP unfalsifiability critique, if sustained, weakens the specific formalism without undermining the broader claim.

The Bayesian brain framework (experience = posterior, where the posterior depends on the ratio of sensory precision to prior precision), the REBUS model (relaxing priors changes experience; reducing sensory input changes it differently), sensory deprivation studies (priors without data produce hallucination), the phenomenology of psychedelic states (altered priors, same data in eyes-open conditions, radically different experience; eyes-closed conditions shift further as sensory constraint drops), Chandaria's "dependent co-arising as Bayesian inference" formulation.

Downward: evidence that waking perception can fully decouple from sensory data without pathology (challenges "constrained"). A mechanism by which sensory data directly constitutes experience rather than constraining a generative process (challenges "construction"). Upward: precise quantitative characterization of the precision-weighting spectrum across states (waking → mind-wandering → hypnagogia → dreaming → psychedelic), confirming continuous modulation of the sensory/prior balance. High-specificity empirical validation of REBUS predictions about prior relaxation. Open edge: the boundary between "enough sensory constraint" and "not enough" is not sharp. Hypnagogic states, mind-wandering, and deep absorption are intermediate regimes. A formal model predicting where transitions occur would sharpen this prior significantly.

Friston's free-energy principle, which unifies perception, action, and learning under variational free-energy minimization with timescale as the only distinguishing variable. Agüera y Arcas's unified-theory desideratum #2 ("no distinction between learning and inference"), already cited in P-001's 2026-04-14 amendment and across T-003. TD learning as the canonical RL formalization (value is a prediction of future reward; learning is TD-error minimization). Rescorla-Wagner as the canonical associative-learning formalization (prediction error drives the update). Cerebellar forward models (motor learning is updating the predictor). Self-supervised ML where the entire training signal is next-token, masked-token, or next-frame prediction. Solomonoff/MDL connecting optimal compression to optimal prediction. The biological adaptation-to-learning spectrum: retinal and neural adaptation (fast, reversible), short-term plasticity (seconds to minutes, decays without reinforcement), long-term potentiation and depression (hours and beyond, structurally durable), hippocampal one-shot encoding plus cortical slow consolidation (concrete dual-timescale architecture, T-003 Ch.7 addition). Inherits the inference machinery from P-001 and the active-engagement constraint from P-007; the latent variables learning converges on are exactly those P-008 identifies as predictively useful for survival.

Downward: discovery of learning processes that demonstrably fail to reduce to prediction-error minimization, even approximately (a structural learning mechanism with no error, surprise, or loss signal driving the update). Evidence that adaptation and learning are mechanistically distinct rather than the same operation at different timescales (separate substrates, different signals). A formal demonstration that "active prediction" is irreducibly circular, where "prediction" is defined as whatever drives learning, making the claim definitional rather than empirical. Upward: a formal mapping of the timescale-and-persistence continuum to specific neural mechanisms with measurable transitions between regimes. A unified mathematical framework, extending FEP, that derives the timescale gradient from first principles rather than positing it. Empirical evidence that the same prediction-error signals drive plasticity at every timescale, with the only difference being which level of the hierarchy gets updated. Successful prediction of when adaptation transitions to learning (the consolidation threshold) from first-principles considerations of signal precision and reliability. Needs resolution: where genuinely novel structural learning sits, that is, the formation of new representational primitives rather than the updating of weights over existing ones. Solomonoff induction frames this as prediction over program-space, but doing so risks making the claim unfalsifiable. The cleanest empirical edge would be a documented learning event that is demonstrably not error-driven; no such case is currently established.

Bach's coherence principle as minimization of constraint violations. Agüera y Arcas's "dynamically stable symbiotic prediction" sketch (Ch.7): active prediction of the future, no distinction between learning and inference, synthesis with thermodynamics, mutual prediction between agents. Efference copy as intra-brain theory of mind (Helmholtz, Crapse & Sommer 2008). Phase synchronization literature (Strogatz's Sync, cardiac pacemaker coupling, firefly swarms). Neural pruning economics: synapses strengthened when they help the receiver predict, weakened when they don't. Friston's free-energy principle as the formal thermodynamic grounding. Scale-invariance evidence: the same mathematical structure from gap junctions to cortical columns to rowing crews to cultures.

Downward: discovery of coherent complex agents whose structure is not explicable in terms of mutual prediction (e.g., agency emerging from pure randomness or from centralized command without predictive coupling). Evidence that free-energy minimization fails to generalize across the biological scales this prior claims unification over. Upward: formal derivation of coherence as the attractor of mutual prediction under dynamic stability constraints. Computational models that successfully predict coherence thresholds across scales from cellular to social. A tight analytical bridge from Friston's FEP to observable coherence phenomena. Needs resolution: the precise relationship between the five listed mechanisms (phase synchronization, integration operator, narrative confabulation, resource competition, social theory of mind) — whether they are distinct regimes of a single principle or a principle plus auxiliary mechanisms. The relationship to IIT's integration measure (phi): formal equivalence would collapse P-005 into IIT's framework; formal distinction would clarify what each captures that the other misses.

The phenomenological distinction between observer and observed, clean in Bach's consciousness-vs-awareness cut (consciousness almost binary, awareness graded within the conscious regime). Seth's dissociation evidence for the multi-layered nature of experience: binocular rivalry (constant input, alternating content), vegetative states (wakefulness without conscious level), dreaming (conscious level without wakefulness), psilocybin ego dissolution (observer and content intact, self-model collapsed), rubber hand illusion and phantom limbs (bodily self manipulated independently), amnesia (narrative self lost, bodily self intact). Agüera y Arcas Ch.7's phenomenal/strange-loop distinction (hydrancephalic children: affect and responsiveness without cortical recursion) is absorbed into the recursion-depth ladder. Bach's 4-degree ladder supplies the structure of the recursion dimension (perception → observer → self-model → seeing through the self). Empirical confirmation from split-brain research (Gazzaniga) and choice blindness (Johansson) that the self is constructed in real-time via autocompletion rather than retrieved from storage.

Downward: evidence that the proposed recursion-depth ladder is misconceived (e.g., systems demonstrating consciousness without any recursion, or fixed recursion depth across species whose behavior varies in ways the ladder would predict). Evidence that the observer-observed distinction breaks down phenomenologically (e.g., a genuinely unitary experience in which content cannot be analytically separated from observation). Upward: formal criteria for each rung of the recursion ladder that match empirical markers (mirror test, metacognition, Sally-Anne). A more refined decomposition of experience layers that subsumes bodily/perspectival/volitional/narrative/social as special cases. Needs work: the boundary between 2nd and 4th degree (observer-without-self vs. self-seen-through) may admit more graded substructure than the current ladder reflects. Contemplative and psychonautic phenomenology suggests multiple distinguishable states in this region.

Agüera y Arcas Ch.5 (cortical column colony, octopus as crew-of-eight, theory of mind as the mechanism for 2nd-order perception); Bach's 3-degree ladder (phenomenology) supplemented by AyA's mutual-prediction mechanism, which resolves the bootstrapping problem Bach's framework inherits from Husserl; efference copy as intra-brain theory of mind (Helmholtz, Crapse & Sommer); split-brain and choice blindness as empirical stress tests (disconnecting the mutual-prediction network produces the observer multiplication the theory predicts); scale-invariance across biological levels (same computational signature at cellular, intra-brain, and social scales). P-009 is the specific application of P-005 at the recursion depth that produces observership; together with P-004 it constitutes the mechanism+ontology pair that dissolves the hard problem; P-003 describes the resulting structure.

Downward: evidence of consciousness in systems with no recursive mutual prediction (a purely feedforward architecture or isolated prediction unit with definitive subjective experience). A formal proof that recursive mutual prediction is insufficient for 2nd-order perception. Neural evidence that the observer resides in a specific localized structure (a homunculus after all) rather than emerging from distributed coupling. Upward: formal characterization of the recursion-depth threshold at which 2nd-order perception emerges. Successful creation of artificial 2nd-order perception in a system of mutually predicting AI units. Cross-species empirical mapping between recursion depth and observer-dependent behavioral markers (mirror test, metacognition, Sally-Anne variants). Needs resolution: AyA Ch.7's phenomenal vs. strange-loop distinction suggests phenomenal consciousness may arise from subcortical mutual prediction (simpler recursion) while strange-loop consciousness requires cortical depth. Are these two thresholds on a single continuum or structurally distinct mechanisms? The relationship between recursion depth and Dunbar's "orders of intentionality" is suggestive but not formalized. And: the combined P-004/P-009 dissolution of the hard problem rests on the computational ontology. If a non-computational property of the brain turned out to be load-bearing for experience (quantum coherence in microtubules, exotic biophysics), the dissolution would need revisiting. No such evidence currently exists.

Bach's computational functionalism. The observation that consciousness doesn't happen "in space" (category error): it models space as content. Self-identity is constructed by software, not given by hardware. The isomorphism requirement is grounded in the same Bayesian framework as P-001 and P-002: if experience is a posterior, then equivalent posteriors require equivalent likelihoods (inputs) and priors (initial state), regardless of what computes them.

Downward: evidence that specific biological properties (quantum coherence in microtubules, particular neurochemistry) are necessary for consciousness and not merely for the computation they implement. A non-biological substrate running a computationally isomorphic process that demonstrably lacks experience (hard to verify, but in principle decisive). A formalization of the Chinese Room that goes beyond "I don't see how syntax produces semantics." Upward: successful creation of artificial consciousness (or strong functional evidence thereof) on non-biological substrate. A formal definition of computational isomorphism precise enough to make the claim empirically testable. Needs resolution: the isomorphism spectrum, where as fidelity increases, "simulation of X" asymptotically approaches "new instance of X" and the boundary between simulating and instantiating dissolves. Where on that spectrum does equivalent experience require you to be? Also: whether Bach's "simulation" and KT's "running a compressive model" (see complexity-measures-of-consciousness.md) are the same claim in different language or subtly different.

Bach's computational reframing of animism. The observation that development is software organizing hardware (not hardware producing software then "generating" mind). The explanatory power for death (implementation of identity ceases on its substrate), for collective agency (spirits coordinating across substrates), and for evolution (reframed as cooperation between software agents that can encode and perpetuate themselves). Follows from P-004 (consciousness is simulation) and P-005 (coherence emerges from mutual prediction): a coherent simulation that self-organizes on a substrate is what we call spirit. As a theorem of P-004 + P-005, confidence is bounded by theirs, but carries sufficient independent explanatory power to warrant explicit formulation.

Downward: evidence that development is better explained bottom-up (hardware produces software) than top-down (software organizes hardware). A formal proof that "implements itself on a substrate" is irreducibly circular and cannot bootstrap without a prior implementer. Revisions to P-004 or P-005 propagate here as upstream dependencies. Upward: successful application of the software-organizing-hardware model to specific biological phenomena (embryonic development as computation, immune system as agent, collective behavior in social insects). Discovery of self-organizing computational processes in non-biological systems exhibiting the properties Bach attributes to "spirit." A formal resolution of the bootstrapping problem. Terminological note: "spirit" risks conflation with substance dualism, which is exactly what the prior rejects. If persistent confusion arises, the framing may need replacement even if the content is unchanged.