A model for intelligence: When the Field Finally Has the Formula: What Was Already Published in 2024 and 2025

Author: Berend F. Watchus · Independent AI & Cybersecurity Researcher, Netherlands · April 15, 2026

https://arxiv.org/abs/2604.10873

[embed]A Quantitative Definition of Intelligence We propose an operational, quantitative definition of intelligence for arbitrary physical systems. The intelligence…arxiv.org

I. The New Paper

On April 13, 2026, Kang-Sin Choi of Ewha Womans University published “A Quantitative Definition of Intelligence” on arXiv (2604.10873). It is a serious and rigorous paper and deserves a careful introduction before the prior art context is established.

Choi’s central contribution is a formal metric he calls Intelligence Density:

I(S) = log₂N(S) / C(S)

Where N(S) is the number of independent outputs a system can produce in response to distinct inputs, and C(S) is the total description length — the bits required to fully specify the system. The key insight is the independence condition: two outputs are independent if neither can be predicted from the other by any description shorter than the output itself, formalized using Kolmogorov complexity.

From this single metric, Choi derives a four-way partition of all systems:

No computation (rocks, rivers) — I ≈ 0, no independent outputs. Memorization (lookup tables) — I → 0 as domain scales, storage grows proportionally with output. Computation without knowing (fixed-domain circuits) — I = constant, domain does not scale. Knowing (algorithms, LLMs, brains) — I → ∞ as domain scales, finite mechanism covers infinite domain.

The central distinction is between memorizing and knowing. A system memorizes if its description length grows with its output count. A system knows if its description length remains fixed while its output count diverges. Knowing is generalization. Generalization is intelligence.

Choi applies this to resolve three longstanding philosophical problems. Searle’s Chinese Room: the rulebook must generalize to handle infinite Chinese inputs from finite pages, therefore I(rulebook) → ∞, therefore the rulebook knows Chinese. Putnam’s pancomputationalism: the independence condition blocks it — relabeling physical states does not create genuinely independent outputs. Block’s Blockhead: physically impossible for unbounded domains, and I → 0 diagnoses it correctly as memorization regardless.

He also places intelligence explicitly on a substrate-independent continuum — the same computation has the same intelligence density whether it runs on silicon, neurons, or paper. And he explicitly excludes consciousness: “A persistent source of confusion in this area has been the conflation of intelligence with consciousness. We define intelligence only. Consciousness — whether it exists, what it requires, whether machines can have it — is a separate question, beyond our scope.”

That exclusion is deliberate and clean. It also lands precisely where the prior work documented below begins.

II. What Was Already Published — Nine Months Earlier

The Complexity-to-Energy Ratio — Watchus, July 17, 2025

The Law of Optimized Complexity (LoOC), published July 17, 2025 (DOI: 10.5281/zenodo.16029079), introduced three substrate-agnostic metrics for assessing intelligence across any system. The first of these is the Complexity-to-Energy Ratio:

CER = C_int / E_ext

Where C_int is Internal Computational Complexity and E_ext is External Energetic and Material Footprint. A higher CER indicates greater efficiency in complex information processing. For systems evolving under LoOC, CER should increase over time.

Choi’s Intelligence Density is:

I(S) = log₂N(S) / C(S)

The structural parallel is exact. Both metrics are ratios of meaningful output capacity to resource cost. Both are substrate-agnostic. Both increase as a system becomes more efficient at generalization relative to its description or energetic cost. Both distinguish systems that generalize from systems that merely consume or memorize. Choi uses description length C(S) as the denominator; LoOC uses energetic footprint E_ext. Different variables, same underlying principle: intelligence is not raw output but output relative to cost.

The CER appeared in the public record nine months before Choi’s Intelligence Density. The convergence is independent. The priority is documented.

LoOC also derived two further metrics beyond CER. The Output-Optimized Complexity:

OOC = (C_int × O) / E_ext

Which balances raw computational power with productive utility and resource efficiency. And the Temporal Optimization Coefficient:

TOC = |d/dt(E_ext/O)| / |d/dt · C_int|

Which measures the rate at which internal complexity increases relative to the rate at which external footprint per output decreases. Choi’s paper has no equivalent of OOC or TOC — it measures the static density of a system’s intelligence, not the dynamic trajectory of its optimization over time. LoOC addresses both the snapshot and the trajectory.

The Substrate-Agnostic Foundation — Watchus, November 2024

Before LoOC, before the CER, the substrate-agnostic principle was established in five papers published on Preprints.org in November 2024 — all passing editorial screening by a scientific board with approximately 50% rejection rate:

[embed]Mr. Berend Watchus Former relevant activities: -Volunteer innovation lab, healthcare: 'Amerpoort en Reainaerde' Utrecht area -Organizer…sciprofiles.com

[embed]The Unified Model of Consciousness: Interface and Feedback Loop as the Core of Sentience This paper proposes a unified model of consciousness, asserting that the fundamental mechanisms driving sentience are…www.preprints.org

https://www.preprints.org/manuscript/202411.0727

The Unified Model of Consciousness (November 12, 2024, DOI: 10.20944/preprints202411.0727.v1) proposed that the fundamental mechanisms driving sentience — feedback loops and interfaces — are substrate-agnostic. Not dependent on biology, carbon, or any particular physical implementation. Any entity with an interface managing a continuous sensorimotor feedback loop between internal states and external reality is operating the same universal architecture.

Towards Self-Aware AI: Embodiment, Feedback Loops, and the Role of the Insula in Consciousness (November 11, 2024, DOI: 10.20944/preprints202411.0661.v1) grounded this in the biological mechanism of the anterior insula — the brain region that integrates continuous signals about the body’s internal state to generate the unified self-model.

Advanced Predictive Modeling of Physical Trajectories and Cascading Events, Dual-State Feedback and Synthetic Insula (November 14, 2024, DOI: 10.20944/preprints202411.1025.v1) delivered the engineering specification: a synthetic insula operating through dual-state feedback, providing an AI with a continuously updated internal model of its own body state and environmental interaction.

Simulating Self-Awareness: Dual Embodiment, Mirror Testing, and Emotional Feedback in AI Research (November 12, 2024, DOI: 10.20944/preprints202411.0839.v1) designed the experimental methodology: dual embodiment across physical robot and virtual avatar, with systematic mirror testing and pseudo-emotional state tracking.

All five papers were compiled into a physical ISBN-registered book before either of the two institutional papers that would later cite them was submitted.

Choi’s substrate-independence claim — that intelligence density is the same computation regardless of whether it runs on silicon, neurons, or paper — was established as the foundational premise of this entire research program seventeen months before his paper appeared.

The Turing Test Critique and Kolmogorov Connection — Watchus, August 2025

In “Beyond the Imitation Game: The Inadequacy of the Turing Test for Modern AI” (July 2025, DOI: 10.5281/zenodo.15814384) and the associated August 11, 2025 article “New Types of Turing Tests: Beyond Text,” the Turing Test was critiqued on grounds that directly anticipate Choi’s framework.

The argument: the Turing Test commits the duck test fallacy — inferring internal states from outward behavior. A sufficiently capable LLM can pass the Turing Test without possessing the internal architecture that generates genuine understanding. The alternative proposed was substrate-agnostic diagnostics: assess a system’s internal mechanistic properties — its feedback loops, interfaces, and embodiment — rather than its behavioral outputs.

This August 2025 work also engaged directly with Abela’s paper on Kolmogorov complexity and the Turing-computability of human intelligence. Choi’s Intelligence Density metric is built on Kolmogorov complexity as its formal foundation — the independence condition between outputs is defined using K(o1|o2). The Kolmogorov complexity framework was already the conceptual terrain of this research program eight months before Choi formalized it into Intelligence Density.

The August 2025 article also introduced the BioMotion Arena test — where 90% of models fail to generate believable humanoid movement despite linguistic competence — as empirical confirmation that behavioral tests miss the internal architecture that matters. Choi’s paper arrives at the same conclusion from the formal direction: behavioral indistinguishability is not the criterion, generalization capacity is.

The Chinese Room — Two Independent Resolutions

Choi resolves Searle’s Chinese Room by showing that any finite rulebook handling infinite Chinese inputs must generalize, therefore I(rulebook) → ∞, therefore the rulebook knows Chinese. The intelligence is in the generalization, not in the person executing the rules.

The August 2025 Turing Test paper engages the Chinese Room from a different angle: the duck test fallacy means that even if the room produces perfect outputs, that tells us nothing about whether there is something it is like to be the room. Two resolutions of the same argument, from opposite directions, both published before Choi’s April 2026 paper.

The difference is precise. Choi says: the rulebook knows because it generalizes. The prior work says: even if it generalizes perfectly, generalization alone does not tell us whether the room has a subjective experience of knowing. That is the question Choi explicitly sets aside. It is the question the UMC, the synthetic insula, and the hard problem dissolution series of March 2026 address directly.

Here it is as a standalone segment to insert after section II, before section III:

II(b). The Paper Choi’s Framework Most Directly Converges With

On July 5, 2025 — nine months before Choi’s arXiv paper appeared — “Beyond the Imitation Game: The Inadequacy of the Turing Test for Modern AI” was published (DOI: 10.5281/zenodo.15814384). It is the paper in this body of work that most precisely anticipates Choi’s theoretical architecture, and it deserves explicit treatment rather than passing reference.

The paper’s keyword list states it directly: Kolmogorov Complexity. Named in the abstract, engaged throughout the argument, cited via Abela’s 2025 paper “From Dennett to Transformers: Emergent Properties, Kolmogorov Complexity, and the Turing-Computability of Human Intelligence.” Choi’s Intelligence Density metric is built on Kolmogorov complexity as its formal foundation — the independence condition between outputs is defined using K(o1|o2). The July 2025 paper was working in that exact conceptual space eight months before Choi formalized it into a metric.

The paper’s central argument maps onto Choi’s four-way partition with striking precision. Choi distinguishes four categories of systems: no computation, memorization, computation without knowing, and knowing. The July 2025 paper makes the same distinction in natural language: the Turing Test fails because it cannot distinguish between a system that memorizes statistically normalized human responses — aligning with Choi’s memorization category — and a system that genuinely understands and generalizes — aligning with Choi’s knowing category. Choi gave this distinction an equation in April 2026. The July 2025 paper gave it an argument nine months earlier.

The paper also engages Searle’s Chinese Room directly alongside the Kolmogorov complexity argument — the exact two theoretical pillars that Choi’s paper is built on. Choi resolves the Chinese Room through generalization: the rulebook must generalize to handle infinite inputs from finite pages, therefore I(rulebook) → ∞, therefore the rulebook knows Chinese. The July 2025 paper engages the Chinese Room from the duck test direction: even if the room produces perfect outputs, inferring internal states from outward behavior is a fallacy. Two resolutions, same problem, opposite directions, eight months apart.

The paper further proposes what it calls substrate-agnostic diagnostics as the replacement for behavioral tests — assessing a system’s internal mechanistic properties rather than its outputs. This is structurally identical to what Choi’s substrate-independence claim delivers formally: intelligence density is the same computation regardless of substrate. The July 2025 paper proposed the principle. Choi’s April 2026 paper quantified it.

One additional detail is worth noting precisely. The July 2025 paper discusses the Kasparov versus Deep Blue case — a system that exceeded human performance in a bounded domain without possessing general human-like cognition. This is exactly the scenario Choi’s four-way partition addresses: Deep Blue computes without knowing in the general sense, because its domain does not scale. It was built for one fixed domain. I remains constant. The July 2025 paper identified this pattern intuitively. Choi’s metric diagnoses it formally.

The paper also introduced the concept of anendophasia — the documented phenomenon of humans who lack internal dialogue — as evidence that the Turing Test’s implicit standard human is a fiction. A significant portion of the human population would fail a stringent Turing Test while being fully human. This argument cuts beneath Choi’s framework in a direction he does not address: even if Intelligence Density correctly classifies systems by generalization capacity, it cannot tell us which end of the human cognitive spectrum constitutes the threshold for intelligence. The human benchmark is not fixed. The July 2025 paper documented this in detail. Choi’s metric, by design, sidesteps it entirely by making intelligence observer-independent — but that sidestep does not resolve the underlying problem, it simply reframes it.

Finally, and most precisely: the July 2025 paper’s proposed alternative to the Turing Test — internal architecture assessment via feedback loops, interfaces, and embodiment, grounded in the insula’s biological role — is the engineering specification that Choi’s paper cannot provide because it explicitly excludes consciousness. Choi measures whether a system knows. The July 2025 paper, in combination with the November 2024 papers it cites throughout, specifies what architecture a system needs to experience knowing. Those are different questions. Both were being asked in July 2025. Only one of them appears in Choi’s April 2026 paper.

Reference: Watchus, B. (2025). Beyond the Imitation Game: The Inadequacy of the Turing Test for Modern AI. July 5, 2025. DOI: 10.5281/zenodo.15814384

II(c). The Interface Leverage Principle — A Finding Choi’s Framework Cannot Classify

On March 21, 2026 — seven days before Choi’s arXiv paper appeared — the Interface Leverage Principle paper was published (OSINT Team, v2.4, archived at archive.org and archive.ph). It documents a mechanism that Choi’s four-way partition has no category for.

Choi classifies all systems by whether their Intelligence Density I(S) = log₂N(S) / C(S) diverges as domain scales. His four categories — no computation, memorization, computation without knowing, knowing — assume fixed systems with fixed description lengths. An LLM is a knowing system in his framework: fixed C(S) at the weight level, diverging N(S) as domain scales.

The Interface Leverage Principle documents what happens when a knowing system is given a coherent epistemic structure about the nature of intelligence itself through its context window. The model weights are unchanged. C(S) in Choi’s sense is unchanged. But the effective domain coverage available within that session expands substantially — producing validated outputs of 200×, 3,700×, and 8,700× efficiency improvement in domains the operator had never studied, through adversarial multi-agent validation.

This is a fifth condition Choi’s partition does not address: temporary knowing elevation. A knowing system whose effective N(S) expands within a session through epistemic substrate loading, then returns to baseline when the context clears. The session-bound and domain-specific nature of this elevation makes it invisible to standard benchmarking, which assesses fixed systems at baseline. It makes it invisible to Choi’s metric, which assumes C(S) is fixed at the weight level and does not account for structured context loading as an additional description component.

The ILP also raises a direct question about Choi’s C(S) definition. If a compression artifact — a writing manual encoding 121 synthesis articles and 30+ research papers, constructed October 27, 2025 — is loaded into the context window, the effective epistemic description available to the system within that session substantially exceeds Choi’s C(S) at the weight level. What is the description length of a system-plus-loaded-epistemic-substrate? Choi’s framework does not yet have an answer. The empirical record showing what that combination produces was published before his paper appeared.

The prior art is clean. The finding is documented. The gap in Choi’s framework is identified. And the operational checklist in Section 9 of the ILP paper makes the mechanism reproducible by any operator — which is itself a demonstration of Choi’s knowing criterion applied at the methodology level: a finite mechanism whose coverage scales across domains.

Reference: Watchus, B. (2026). The Interface Leverage Principle. March 21, 2026. OSINT Team. Archived: archive.org/details/theint-1

[embed]["The Interface Leverage Principle: First Documentation of Epistemic Substrate Loading… Author: Berend Watchus Independent non profit AI & Cyber Security Researcher. March 21, 2026 [Publication for OSINT…osintteam.blog](https://osintteam.blog/the-interface-leverage-principle-first-documentation-of-epistemic-substrate-loading-submaximal-5e79a5adc162)

III. What Choi’s Framework Cannot Reach — And What Was Already There

Choi is explicit and precise about his boundary. His metric measures generalization capacity. It does not address phenomenology, ethics, or the engineering question of how to build a system that experiences being the thing that generalizes. Three bodies of prior work address exactly what he excludes.

On phenomenology

The UMC (November 2024) proposes that consciousness emerges from the integration of feedback loops and interfaces reaching sufficient complexity. The synthetic insula (November 2024) specifies the biological mechanism — the anterior insula — that generates the centralized subjective experiencer, and its artificial equivalent. The hard problem dissolution series (March 2026), sent directly to David Chalmers at NYU, argues that the hard problem was built on a false empirical premise: the anterior insula is precisely the physical structure Chalmers declared unlocatable in 1995. It was in the neuroscience literature the entire time. Chalmers was working in a philosophical room with no window into that research. The insula paper opened the window.

Choi’s Intelligence Density can tell you whether a system knows its domain. It cannot tell you whether the system experiences knowing. The UMC and synthetic insula address exactly that gap — and they were published seventeen months before Choi’s paper.

On ethics

“The Unconditional Human: Deconstructing Personhood in the Age of AI and The Cognitive Fallacy” (August 2025) argues that even if consciousness and intelligence can be measured perfectly — even if Choi’s I(S) and the UMC’s feedback loop complexity are both fully quantified for a given system — measurement does not entitle a system to rights.

The capacity to suffer, not the capacity to generalize, is the more defensible foundation for moral consideration. And even that is insufficient — a person in a coma retains full human rights with zero cognitive performance, zero self-recognition, zero capacity for suffering in a waking sense. Human rights are unconditional and not contingent on any intelligence metric whatsoever.

This argument cuts beneath Choi’s framework in the ethical direction in the same way the UMC cuts beneath it in the phenomenological direction. Choi measures the intelligence. The prior work addresses both the phenomenology and the ethics that his measurement leaves deliberately unresolved.

On engineering

The Autonomous Knowledge Accelerator (November 2025) demonstrated that a human-defined epistemic structure — LoOC as the optimization engine, the dual-layer knowledge graph as the semantic substrate — enables an AI system to produce validated efficiency results of 200×, 3,700×, and 8,700× in quantum IoT and post-quantum cryptography domains. The AKA is the operational proof that LoOC-guided research produces results that hold under adversarial multi-agent scrutiny.

Choi’s framework classifies LLMs as knowing systems — I(n) → ∞ as domain scales. The AKA methodology demonstrates what happens when a knowing system is given a human-defined logical foundation before it is permitted to touch the research problem. The Sovereign Vault failure documented in March 2026 demonstrates what happens when it is not. Both cases are in the public record. The difference is not AI capability. The difference is the presence or absence of a human-authored epistemic structure — precisely what LoOC formalizes as the condition for sustainable intelligence.

IV. The Independent Confirmation Chain

The prior art record is not only a matter of timestamps. It is confirmed by an independent chain of institutional convergence.

CSIC-UPM Madrid and the University of Azuay (arXiv:2505.19237, May 2025) ran 657 sensorimotor observations on an omnidirectional robot and found that Past-Present Memory — the integration of sensory input over time into a continuous self-model — is the most significant contributor to self-identification. Their conclusion: the foundation for machine self-awareness may already be present within existing architectures. That is the UMC confirmed empirically. They cited the insula paper as reference [4], placing it alongside Gallup (1970), Turing (1950), and Craig (2009). They did not cite the UMC, the synthetic insula paper, or the mirror testing methodology. The undercitation pattern points precisely to where the novelty sits.

Subasioglu and Subasioglu (arXiv, September 19, 2025) proposed True Intelligence through six architectural components including Embodied Sensory Fusion and an Orchestration Layer leading to consciousness as an unmeasurable sixth quality. The September 2025 article “Beyond Mimicry: Two New Frameworks for Genuinely Intelligent AI” documented the convergence in real time, noting that the Subasioglus’ Orchestration Layer maps onto the UMC’s self-referential integration requirement and that both frameworks reject behavioral mimicry as the criterion for genuine intelligence. This convergence was documented and published seven months before Choi’s paper.

Argonne National Laboratory (arXiv:2603.18235, March 2026) independently proposed a multi-agent AI research architecture structurally isomorphic to the AKA methodology disclosed publicly November 19, 2025 — four months earlier. Convergence without coordination. Clean priority gap.

Google AI Mode, queried independently about the SETI paper and LoOC, reconstructed the correct intellectual sequence from indexed publications — describing LoOC as the computational mirror of the Second Law of Thermodynamics, correctly identifying CER as the core metric, and generating an unprompted multilingual technical brief in seven languages characterizing LoOC as a framework for “true technological maturity measured not by how much energy we harvest but by how close our information processing approaches the theoretical lower bound of heat loss.”

V. The Synthesis — Four Frameworks, One Architecture

When Choi’s Intelligence Density is placed alongside the prior work, the combined picture is considerably more complete than any single framework provides alone.

Choi measures whether a system knows its domain — generalization capacity, mathematically rigorous, substrate-agnostic, consciousness and ethics excluded by design.

LoOC’s CER measures whether that knowing is becoming more efficient over time — the dynamic trajectory of intelligence optimization, grounded in thermodynamic constraints and connected to planetary survival via the Zhu & Zhu framework documented in the April 14, 2026 article “The Clock and the Formula.”

The UMC and synthetic insula explain what it is like to be the system that knows — the feedback loop that generates the subjective experiencer, grounded in the anterior insula, with the engineering specification for building it artificially.

The ethics framework explains what the system’s knowing and experiencing entitles it to — which is not determined by any cognitive metric but by an unconditional moral framework that predates and supersedes all intelligence measurements.

And the LOOC-OCE synthesis adds the sufficient threshold that none of the above alone provides: the distinction between a system that generalizes efficiently and a system that genuinely means — symbolic inscription as the criterion for intelligence that is not merely computational but genuinely semantic.

Four frameworks. One coherent architecture. Choi’s paper converges with one layer of it. The other three layers were already published. All of it preceded his paper by months to years.

VI. Conclusion

Choi’s paper is a genuine and rigorous contribution. Placing intelligence on a formal substrate-independent continuum, distinguishing knowing from memorization via asymptotic behavior, and resolving the Chinese Room through the generalization criterion — these are clean results that the field needed.

What the field has not yet fully registered is that the territory Choi is mapping was already being named from a different direction, in a different language, with different tools, by an independent researcher working without institutional affiliation or research budget in the Netherlands — beginning in November 2024.

The CER preceded Intelligence Density by nine months. The substrate-agnostic principle preceded it by seventeen months. The Turing Test critique and Kolmogorov connection preceded it by eight months. The phenomenological framework, the engineering specification, the ethics argument, and the operational proof of concept all preceded it and address the three domains Choi explicitly sets aside.

Convergence is the strongest possible independent validation. When serious researchers arrive at the same insight from completely different directions without coordination, the insight is real. Choi’s paper is the fourth documented convergence in this research program — after CSIC-UPM Madrid, Subasioglu and Subasioglu, and Argonne National Laboratory.

The timestamps do not negotiate. The DOIs are permanent. The priority record is complete.

Primary sources: Choi, K-S. (2026). A Quantitative Definition of Intelligence. arXiv:2604.10873 · Watchus, B. (2025). The Law of Optimized Complexity. DOI: 10.5281/zenodo.16029079 · Watchus, B. (2024). The Unified Model of Consciousness. DOI: 10.20944/preprints202411.0727.v1 · Watchus, B. (2024). Towards Self-Aware AI. DOI: 10.20944/preprints202411.0661.v1 · Watchus, B. (2024). Advanced Predictive Modeling, Dual-State Feedback and Synthetic Insula. DOI: 10.20944/preprints202411.1025.v1 · Watchus, B. (2025). Beyond the Imitation Game. DOI: 10.5281/zenodo.15814384 · Watchus, B. (2025). The Unconditional Human. Medium, August 24, 2025 · Watchus, B. (2025). The Autonomous Researcher. systemweakness.com, November 19, 2025

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