A Unified Computational Theory Integrating Finite Machine Hierarchies, Temporal Phenomenology, and Non-Uniform Resource Allocation
Author: Karol Kowalczyk
Date: November 2025
Status: Preprint
This repository contains a comprehensive research framework exploring consciousness through computational theory. The work consists of a foundational 236-page paper plus several companion papers that extend and apply the core theory to specific domains.
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├── README.md # This file
├── main.tex # Main paper entry point (236 pages)
├── preamble.tex # LaTeX configuration and styling
├── bibliography.bib # Complete bibliography (60+ references)
│
├── part1_foundations.tex # Part I: Computational foundations
├── part2_existing_theories.tex # Part II: Integration with existing theories
├── part3_temporal_revolution.tex # Part III: Temporal collapse mechanism
├── part4_mechanisms.tex # Part IV: Neural implementation
├── part5_hard_problem.tex # Part V: Solution to hard problem
├── part6_empirical.tex # Part VI: Testable predictions
├── part7_philosophical.tex # Part VII: Philosophical implications
├── part8_synthesis.tex # Part VIII: Complete synthesis
│
├── appendix_comparisons.tex # Appendix A: Theory comparisons
├── appendix_glossary.tex # Appendix B: Terminology
├── appendix_mathematical.tex # Appendix C: Formal proofs
├── appendix_protocols.tex # Appendix D: Experimental protocols
├── appendix_selector.tex # Appendix E: Selector implementation
├── appendix_toy_model.tex # Appendix F: Toy model examples
│
├── 3papers/ # Extended theoretical papers
│ ├── adjoint_projections.tex # Adjoint functors in hierarchies
│ ├── quantum_measurement.tex # Quantum measurement framework
│ └── [other papers]
│
└── selectors/ # Practical applications
└── Sleep-Wake Orchestration in Hierarchical LLM Cohorts.tex
Length: 236 pages
Entry point: main.tex
PDF: Available on Zenodo
This work presents a unified computational theory of consciousness that integrates insights from Integrated Information Theory (IIT), Global Workspace Theory (GWT), Attention Schema Theory (AST), and quantum consciousness approaches within a novel framework based on non-uniform finite machine hierarchies.
Core Innovation: Consciousness emerges from the collapse of parallel computational explorations across a hierarchy of finite-state machines with exponentially growing resources (M₁, M₂, M₃, ..., Mₙ where Mₙ has 2ⁿ bits of memory). The hierarchy exhibits a generalized non-uniform structure where effective levels follow M_n ⊆ M_{n+f(n)} with variable resource gaps f(n) ≥ 1, representing realistic cognitive resource allocation.
Key Insight: While real computational time includes all parallel attempts, backtracks, and time-reversals, subjective conscious experience perceives only the successful computational path—a smooth, continuous temporal flow that never experiences the failed branches.
- Machine hierarchy with entropic scaling:
I(n) = κ n log n - Non-uniform structure:
M_n ⊆ M_{n+f(n)} - Selector mechanism and non-computability
- Resource allocation with entropic costs
- Detailed comparison with IIT, GWT, AST, Orch-OR
- Integration strategy showing how each theory captures one aspect
- Comparative analysis of strengths and weaknesses
- Computational vs. subjective time distinction
- Parallel exploration and selective memory
- State checkpointing mechanism
- Temporal phenomenology explanation
- Neural implementation considerations
- Cognitive architecture mapping
- Resource allocation patterns
- Biological realization
- Identity solution vs. production solution
- Dissolution of explanatory gap
- Phenomenal character emergence
- Why there is "something it is like"
- Neural signatures of hierarchy levels
- Capacity measurements (realistic: M₁₅ to M₃₅)
- Temporal integration windows
- Testable experimental protocols
- Free will from non-computable selector
- Personal identity as selector continuity
- Qualia as intrinsic collapse patterns
- Consciousness without production relation
- Complete integration of all components
- Cognitive phenomenology of variable gaps
- Individual differences via gap patterns
- Unified explanatory framework
Appendix A: Theory Comparisons (appendix_comparisons.tex)
- Point-by-point comparison with major theories
- Evaluation framework
- Integration strategies
Appendix B: Glossary (appendix_glossary.tex)
- Technical terminology
- Mathematical notation
- Conceptual definitions
Appendix C: Mathematical Formalization (appendix_mathematical.tex)
- Formal definitions and theorems
- Detailed proofs
- Complexity analysis
Appendix D: Experimental Protocols (appendix_protocols.tex)
- Neuroscience experiments
- Behavioral studies
- Implementation guidelines
Appendix E: Selector Implementation (appendix_selector.tex)
- Python implementation of selector mechanism
- Practical demonstrations
- Code examples
Appendix F: Toy Model (appendix_toy_model.tex)
- Simplified examples
- Pedagogical demonstrations
- Conceptual illustrations
File: 3papers/adjoint_projections.tex
Abstract: Develops the categorical structure of hierarchical computation using adjoint functors. Introduces compression/reconstruction as genuine adjunctions with:
- Computable behavioral metrics
- Exact adjunction via linear codes
- Polynomial-time level assignment
- Entropic scaling analysis
Key Contributions:
- Formal category-theoretic framework
- Behavioral distance metrics for machine similarity
- Computational complexity bounds
- Connection to consciousness theory via projection operations
File: 3papers/quantum_measurement.tex
Abstract: Applies the hierarchical framework to quantum measurement, proposing that measurement involves finite-time information processing with entropic scaling.
Main Predictions:
- Projection delay:
τ(m) = τ₀ + γ m ln m(entropic scaling with qubit number) - Born rule corrections: Deviations at O(1/m) for systems with m qubits
Novel Aspects:
- Connects measurement dynamics to computational complexity
- Testable predictions differing from standard QM
- Framework for experimental falsification
Critical Note: Highly speculative but rigorously falsifiable. Physical motivation remains unclear but mathematical structure is well-defined.
File: selectors/Sleep-Wake Orchestration in Hierarchical LLM Cohorts.tex
Abstract: Applies consciousness theory to practical AI systems. Proposes alternating sleep-wake cycles for LLM ensembles where models periodically withdraw for targeted fine-tuning on "gap regions" not covered by similar-capacity peers.
Key Features:
- Gap-based learning: Target regions where models fail but higher-level models succeed
- Resource allocation: Fixed 1/3 training, 2/3 inference budget
- Safe deployment: Canary rollout with automatic rollback
- Theoretical foundation: Formal adjunction between sleep (projection) and wake (collapse)
- Biological inspiration: Computational analog of sleep-dependent memory consolidation
System Components:
- Selector: Routes queries to appropriate model level
- Meta-selector: Monitors performance and triggers escalation
- Sleep scheduler: Manages rotation between active and training states
- Gap detector: Identifies coverage weaknesses in behavioral space
Theoretical Connections:
- Implements adjunction:
Pₙ ∘ Cₙ ≈ id(consolidation preserves information) - Behavioral distance metrics in shared embedding space
- Convergence guarantees under stationarity assumptions
Implementation: Complete Python implementation demonstrates practical feasibility.
- Replaces linear inclusion
M_n ⊂ M_{n+1}with generalizedM_n ⊆ M_{n+f(n)} - Variable gap function
f(n) ≥ 1explains both incremental processing and insight moments - Universality condition:
lim(n→∞) f(n) = ∞ensures asymptotic universality
- Distinguishes computational time (all explorations) from subjective time (collapsed path)
- Explains why consciousness feels unified and forward-flowing
- Connects to memory consolidation and sleep functions
- Consciousness IS collapsed computation experienced from within
- No explanatory gap: computational structure is necessarily experiential
- Dissolves dualism through identity rather than production relation
- Resource allocation follows non-computable optimization
- Natural account of agency and free will
- Top-down causation without violating physical law
- IIT: Integration within each level (Φ > Φ_min required)
- GWT: Global workspace = post-collapse broadcasting
- AST: Attention schema = selector's internal model
- Quantum theories: Classical collapse with similar phenomenology
- Sleep-wake orchestration for LLM ensembles
- Self-optimizing model ecosystems
- Computational homeostasis in production systems
Machine Hierarchy with Entropic Scaling:
M_n ⊆ M_{n+f(n)} where f: ℕ → ℕ⁺, f(n) ≥ 1
Information capacity: I(n) = κ n log n bits
Processing time: τ(n) = τ₀ + γ n log n
Universality: lim(n→∞) f(n) = ∞
Realistic Cognitive Levels:
M₁₅: 32K bits - Basic perception
M₂₀: 1M bits - Object recognition
M₂₅: 32M bits - Working memory
M₃₀: 1G bits - Complex reasoning
M₃₅: 32G bits - Peak consciousness
Collapse Function:
Δ : X_n(T) → P_n
Maps exploration space to phenomenal state
Irreversible: information loss creates arrow of time
Adjoint Structure:
C_n ⊣ P_n : L_{n+1} ⇄ L_n
C_n: Collapse (execution, wake phase)
P_n: Projection (learning, sleep phase)
-
Asymptotic Universality: For any computable function f, ∃n such that M_n can compute f on all inputs of interest
-
Level-wise Decidability: For each fixed n, all properties of M_n are decidable
-
Strict Hierarchy: ∀n, ∃ problems solvable by M_{n+f(n)} but not by M_n
-
Selector Non-Computability: No computable function always returns minimal n for problem solution
-
Agency from Non-Computability: System exhibits genuine agency that resists algorithmic capture
-
Sleep-Wake Duality: Sleep (projection) and wake (collapse) form adjunction with P_n ∘ C_n ≈ id
-
Gap Convergence: Under stationarity, total gap mass converges to ε with probability 1-δ
- Discrete capacity levels at M₁₅, M₂₀, M₂₅, M₃₀ (not smooth gradation)
- Event-related potentials show variable-latency components
- Resource transitions correlate with increased neural synchrony
- Different tasks activate different gap patterns
- Working memory shows discrete jumps, not smooth scaling
- Reaction times cluster at level transitions
- Individual differences in gap patterns predict cognitive style
- Time estimation varies with resource jump magnitude
- Measurement time scales as τ(m) = τ₀ + γ m ln m
- Born rule corrections at O(1/m) for m qubits
- Retrocausal signatures in delayed-choice experiments
- Sleep-wake cycles improve coverage while reducing escalation costs
- Gap-based training outperforms uniform training
- Behavioral distance predicts model performance on queries
- System achieves equilibrium with stable resource allocation
# Compile the main 236-page paper
pdflatex main.tex
bibtex main
pdflatex main.tex
pdflatex main.tex
# Or use latexmk for automatic compilation
latexmk -pdf main.tex# Compile adjoint projections paper
cd 3papers
pdflatex adjoint_projections.tex
# Compile quantum measurement paper
pdflatex quantum_measurement.tex
# Compile LLM orchestration paper
cd ../selectors
pdflatex "Sleep-Wake Orchestration in Hierarchical LLM Cohorts.tex"Required LaTeX packages:
amsmath,amssymb,amsthm,mathtools(mathematics)hyperref,cleveref(cross-referencing)natbib(bibliography)tcolorbox(colored boxes)algorithm,algpseudocode(algorithms)tikz(diagrams)booktabs,longtable(tables)
@article{kowalczyk2025consciousness,
title={Consciousness as Collapsed Computational Time: A Unified Theory
Integrating Finite Machine Hierarchies},
author={Kowalczyk, Karol},
year={2025},
month={November},
publisher={Zenodo},
doi={10.5281/zenodo.17556941},
url={https://zenodo.org/records/17556941},
note={236 pages. Introduces non-uniform machine hierarchy with variable
resource gaps for explaining consciousness, temporal phenomenology,
and cognitive integration}
}Kowalczyk, K. (2025). Consciousness as collapsed computational time:
A unified theory integrating finite machine hierarchies. Zenodo.
https://doi.org/10.5281/zenodo.17556941
@article{kowalczyk2025adjoint,
title={Adjoint Projections on Computational Hierarchies},
author={Kowalczyk, Karol},
year={2025},
note={Formal category-theoretic framework for hierarchical computation}
}
@article{kowalczyk2025quantum,
title={Quantum Measurement as Hierarchical Projection},
author={Kowalczyk, Karol},
year={2025},
note={Application of hierarchical framework to quantum measurement}
}
@article{kowalczyk2025sleepwake,
title={Sleep-Wake Orchestration in Hierarchical LLM Cohorts},
author={Kowalczyk, Karol},
year={2025},
note={Practical application to large language model ensembles}
}This framework builds upon and integrates:
- Integrated Information Theory (Tononi, 2004, 2016)
- Global Workspace Theory (Baars, 1988; Dehaene, 2001)
- Attention Schema Theory (Graziano, 2013, 2019)
- Computational Complexity Theory (Sipser, 2012)
- Kolmogorov Complexity (Kolmogorov, 1965; Chaitin, 1975)
- Conscious Turing Machine (Blum & Blum, 2022)
- Category Theory (Mac Lane, 1971)
- Information Theory (Shannon, 1948)
| Aspect | IIT | GWT | AST | Orch-OR | This Framework |
|---|---|---|---|---|---|
| Hard problem | Assumes identity | Leaves unexplained | Functional only | Quantum needed | Explains identity |
| Temporal structure | Static | Not addressed | Not central | Quantum time | Central feature |
| Agency/Free will | Not addressed | Not addressed | Functional | Quantum | Non-computable selector |
| Resource allocation | Implicit | Capacity limit | Attention | Not addressed | Explicit hierarchy |
| Testable | Difficult (Φ) | Yes (ignition) | Yes (schema) | Very difficult | Yes (multiple) |
| Unifies theories | N/A | N/A | N/A | N/A | ✓ Integrates all |
| Practical AI | No | Limited | Limited | No | ✓ LLM orchestration |
Author: Karol Kowalczyk
Organization: AIRON Games
Email: k.kowalczyk@airon.games
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This work is licensed under Creative Commons Attribution 4.0 International (CC BY 4.0).
You are free to:
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Under the following terms:
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consciousness, computational theory, finite state machines, temporal collapse, machine hierarchy, non-uniform hierarchy, resource allocation, subjective time, computational time, integrated information, global workspace, attention schema, hard problem, qualia, phenomenology, free will, agency, Kolmogorov complexity, non-computability, cognitive architecture, neural correlates, adjoint functors, category theory, quantum measurement, LLM orchestration, sleep-wake cycles, meta-learning
- v1.0 (November 2025): Initial release
- Main paper: 236 pages with complete formalization
- Extended papers: Adjoint projections, quantum measurement
- Applications: LLM sleep-wake orchestration
- 60+ references
- 6 appendices with protocols and comparisons
- Expand experimental protocols in appendix
- Add more worked examples in toy model appendix
- Develop interactive visualizations
- Create summary infographics
- Submit main paper for peer review
- Implement Python demonstrations of core concepts
- Develop neuroscience collaborations for empirical testing
- Create educational materials and tutorials
- Empirical validation of neural predictions
- Test quantum measurement predictions
- Deploy LLM orchestration in production systems
- Extend framework to artificial general intelligence
Status: Open for feedback and collaboration
Last Updated: November 12, 2025