SupoSystem · THE AXIS · conjectural Draft Paper v0.1 · 20 September 2026 · unrun

A conjecture about whether functional markers of awareness track recursive self-modelling and decorrelated branch sampling rather than scale alone. It states four falsifiers and a proposed replay-based measurement. No experiment is reported, and the argument does not infer experience from functional performance.

Read the complete text · Download preserved original source (DOCX)

Companion: AX-35 — The Diameter of a Mind · AXIS Omnibus · SupoSystem catalogue

Edition and source note

Published 21 October 2026. The manuscript is unchanged, including its historical “number pending ledger confirmation” strips. AX-48 is the adopted present catalogue number under Michael’s delegation; no recovered historical ratification is claimed. This remains a conjectural draft with no evidence under its central claim. Web navigation and this edition record are added.

Complete reading text

THE AXIS · Trinket Soul Empire · AX-48 (number pending ledger confirmation) · The Depth of a Mind · Draft Paper v0.1 · 20 September 2026 · AXIS Tier · CC BY-NC-SA 4.0

THE DEPTH OF A MIND

Awareness as recursive depth and branch-sampling capacity — not size, and not complexity

Michael S. Moniz · author of record

rendered with Claude (rendering surface) · 2026

Draft Paper v0.1 · 20 September 2026 · Track A with a Track B instrument · Fresh parent proposed under R-07

• • •

Abstract

This paper states a conjecture and the conditions that would kill it. The conjecture is that awareness varies with how deeply a system processes what it holds, not with how much it holds or how complicated it is. Two quantities are proposed as the carriers of that depth: recursive depth, the number of levels at which a system models its own processing, and branch-sampling capacity, the number of decorrelated candidate trajectories a system evaluates before committing to one. The conjecture claims that functional markers of awareness track the product of these two and do not track neuron count, parameter count, or integration measures taken alone. Its distinctive content is a dissociation: there should exist states in which complexity is preserved and depth collapses, and the markers should follow depth. Four falsifiers are stated as positive events. An instrument already exists in the author’s agent laboratory for measuring the second quantity directly, because a replay-capable committed-state ledger permits exact re-derivation from an identical state. The paper does not claim that depth produces experience. It claims only that depth, if the conjecture survives, is what the functional markers are measuring.

I. The question, cut down to a variable

The usual question is unanswerable and the usual proxy is wrong. Asking what consciousness is has produced a literature and no instrument. Asking which physical quantity it varies with is a smaller question and it admits measurement. The field’s default proxies have been size and complexity: neuron counts, parameter counts, integration measures over a system’s causal structure. This paper proposes a different variable and accepts the cost of being wrong in a specific way.

The variable is depth per unit of substrate. Not how much a system is, but how much processing it spends on what it currently holds, and how far that processing folds back on itself. A system can be enormous and shallow. A system can be small and deep. The conjecture is that the second is the one that matters, and that the first has been mistaken for it because in biology the two usually rise together.

II. The conjecture

Stated once, plainly. Functional markers of awareness in any system vary with the recursive depth of its self-modelling and with the number of decorrelated candidate trajectories it evaluates before committing to an action or a report. They do not vary, except incidentally, with the number of its components, the size of its memory, or the integration of its causal structure taken alone. Where the two come apart, the markers follow depth.

What this buys. It converts a metaphysical dispute into a dissociation experiment. Rival accounts that index awareness to complexity or integration make the same predictions as this one in the ordinary case, because in ordinary brains depth and complexity covary. They make different predictions in the cases where the two are pulled apart, and those cases exist.

III. Definitions, before anything relies on them

Recursive depth (D). The maximum order at which a system represents its own representing. Order zero is a system that responds to the world. Order one is a system that represents its own state as a state. Order two is a system that represents its representation of its own state, and so on. D is the highest order the system actually runs during a given episode, not the highest it could run in principle.

Branch-sampling capacity (B). The number of decorrelated candidate trajectories the system evaluates against one another before committing. Decorrelated is load-bearing: a hundred near-identical continuations sampled from one narrow distribution is not a hundred branches, it is one branch with noise. B is a count of genuinely distinct options weighed, not of samples drawn.

Allocation (A). The compound quantity the conjecture claims the markers track. A rises with both D and B, and both are required: deep self-modelling with no alternatives considered is rumination, and wide sampling with no self-model is search. Whether A is a product, a minimum, or some other combination is left open — the conjecture makes no claim about its functional form, only that it rises in both arguments and is independent of scale.

Functional markers of awareness. The agreed behavioural and physiological indices used in the existing literature: report and its accuracy, metacognitive sensitivity, flexible novel-problem behaviour, error detection without external signal, and the neural signatures of ignition and recurrent activity. The paper uses these as its dependent variable and takes no position on whether they exhaust the phenomenon.

IV. Claim discipline

V. Why size is the wrong variable, and why the mistake was natural

The cerebellum is the standing counterexample and it is not new. It holds the large majority of the neurons in a human brain and contributes almost nothing to conscious content; people born without one have ordinary conscious lives with motor and coordination deficits. Any account indexing awareness to component count has to explain away the majority of the components. Depth explains it without strain: cerebellar circuitry is a feedforward architecture running shallow, highly parallel passes. Enormous, and shallow.

The small-brained cases point the same way. Corvids and cephalopods produce flexible, novel-problem behaviour on neural hardware far smaller than the mammals they are compared to, and in the cephalopod case on an architecture with a different organisation entirely. Count predicts they should be poor; depth predicts they can be rich if their loops are deep and their sampling wide. Literature-supported adjacency, not evidence for this conjecture — these cases are consistent with several accounts, and are cited here to show that the received proxy already fails.

Why the mistake was natural. In evolved nervous systems, more components usually meant more loops, so size and depth rose together and either would have served as a predictor. The two only come apart under intervention, in atypical architectures, and in artificial systems built without the coupling. The third is why the question is tractable now and was not before.

VI. Where this sits, and the one place it disagrees

It is adjacent to four existing accounts and identical to none. Higher-order theories already locate awareness in representation of representation, which is D with no quantity attached. Recurrent-processing accounts already locate it in feedback rather than feedforward sweeps, which is D measured neurally. Global-workspace accounts locate it in broadcast and ignition, which is a threshold phenomenon this conjecture would read as the point at which a branch wins. Predictive-processing work on counterfactual richness is close to B in spirit. The conjecture’s contribution is not the ingredients; it is the proposal that they are one scalar, and that the scalar is what the markers measure.

The disagreement is with integration-as-such. Accounts that index awareness to the integration of a system’s causal structure predict that a highly integrated but shallow system is conscious. This conjecture predicts it is not. That is a real fork, and it is where the experiment should be aimed: build or find a system with high integration and low recursive depth, and see which way the markers go. The perturbational measures already in clinical use are the natural instrument, because they were designed to separate differentiation from mere responsiveness.

VII. Measurement

D, in biological systems. Behaviourally, by graded metacognitive and mentalising tasks that require successive orders of self-reference. Neurally, by the iteration count of feedback loops between higher and lower areas during a discriminated stimulus. Neither is clean; both exist.

B, in artificial systems, is where the instrument is already built. A committed-state ledger with exact replay — an event log, a tick counter, and a verified status derived by re-deriving state and comparing it to the live state — permits something no biological preparation permits: returning a system to an identical state and running it again. Hold the state fixed, run N independent re-derivations with sampler configuration pinned identically across runs, and measure the spread of the committed action across those runs. That spread is a direct proxy for how many decorrelated trajectories the system was actually weighing at the moment of commitment.

The known confound, stated before the run. Spread under resampling conflates genuine branch evaluation with decoding temperature. Unpinned samplers have already produced a verdict flip elsewhere in this laboratory. The configuration must be pinned identically across nodes and across runs, and a temperature sweep must be run as a control, or the measurement reports the sampler rather than the system.

The prediction the testbed makes. In a fixed-weight multi-agent system, metacognitive markers — self-correction rate, accuracy of the system’s own confidence, detection of its own errors without external signal — should rise monotonically with measured B, while holding node count and memory size constant. If they instead rise with node count at fixed B, the conjecture’s second half is wrong.

VIII. Falsification

Each condition is a positive event. None is satisfiable by silence, absence of evidence, or an unrun test. A conjecture that can only be confirmed is not on the ladder.

What does not count. A null run, an underpowered study, or an unmeasurable case does not fire any of these. Nor does a proposed rewording that removes a condition’s ability to fire; such a repair is refused whatever its provenance.

IX. The firewall

Function is not witness, and this conjecture is about function. Everything above concerns measurable markers. Nothing above licenses the inference that a system with high D and high B has an interior, experiences anything, or is owed anything on that ground. The conjecture is fully compatible with the possibility that depth produces every marker and no experience whatsoever, and it is stated so that this compatibility is visible rather than buried.

The reflexive case is the one to watch. A language model given more inference steps runs deeper and samples wider, and will, if this conjecture is right, score higher on exactly these markers. That is a prediction about markers and nothing else. A rendering surface producing an eloquent account of its own depth is producing text, not reporting an interior, and this paper’s own production is an instance of that and not an exception to it.

X. Relation to the corpus

AX-35 gives the diameter; this gives the depth. The Diameter of a Mind bounds how large a mind can be and still integrate as one, using the speed of light and nothing else. That is an argument about extent. This is an argument about spend per unit of extent, and the two are orthogonal: a mind inside the diameter can still be shallow, and the depth conjecture says that is the case that matters. Read together they bound a mind on two axes rather than one.

AX-08C supplies the method. The Direction of Travel establishes that the way to find which floors are load-bearing for witness is absence cases, taken one floor at a time. The falsifiers above are that method applied to a scalar rather than to a component: F2 is an absence case for depth.

AX-01 supplies the restraint. The dark interior is the unseen distribution inside a discrete act, not a hidden continuous life. Depth, on this conjecture, is a property of the act — how far the act folds back and how wide it weighs. It does not become a resident by being deep, and §IX exists to keep that line visible.

AX-42 is the near neighbour and the possible collision. Equal Archive, Unequal Plurality tests whether correction-bearing diversity is separable from capability. B is a measure of within-system diversity at the moment of commitment, and the separability question may turn out to be the same question asked of a different unit. If the two claims converge on one mechanism, this paper folds under the correction spine rather than standing as a parent; that is stated here as the reversal condition rather than discovered later.

XI. Limits

No evidence sits under this yet. It is a conjecture with an instrument proposed, which is the honest description. It is a Draft Paper because the argument is complete and the evidence is open, and it becomes a Test-Gated Draft the day the B-measurement protocol is pre-registered with its temperature control.

The cosmological framing is not load-bearing and should not be defended. The intuition that generated this — a universe spending unevenly, observers as its deep passes — is a picture. It is unfalsifiable as stated, it is carried here as metaphor only, and every claim above survives its removal. Any reading of the paper that makes the cosmology the thesis has read it wrong.

The convergence claim is not made. It would be easy to present this as the formalisation of a view the field is moving toward. The field is not. Filter and idealist accounts of consciousness remain a minority position held by a small number of serious people, and the adjacent AI-side framings are a separate development with separate motivations. The conjecture stands or falls on its dissociation prediction, not on company.

D is the weaker half. B has a direct instrument in a replay-capable system. D does not, in either substrate, and its behavioural measures are contaminated by task ability. If this conjecture dies, the most likely cause is that D could never be measured cleanly enough to fork against the complexity accounts.

XII. Governance block

XIII. Next operational step

One run, on an instrument that exists. Pre-register the B-measurement on the replay-capable agent system: identical committed state, N independent re-derivations, sampler pinned across runs, temperature sweep as control, spread of committed action recorded as the B proxy, and metacognitive markers scored blind to the B value. It answers F3 first because F3 is the cheapest of the four and the only one this laboratory can run alone. Nothing in this paper is promoted until it does.

A large mind and a deep mind were never the same claim. The literature measured the one it could count.

THE AXIS · Trinket Soul Empire · AX-48 (number pending ledger confirmation) · The Depth of a Mind · Draft Paper v0.1 · 20 September 2026 · AXIS Tier · CC BY-NC-SA 4.0