Formal research on consciousness, information, and neural dynamics

This page collects research papers, formal specifications, preprints, and working documents developed within the TUC research programme.

The project is organised into two complementary lines of work:

TUC explores a formal and philosophical framework centred on the mathematical study of consciousness, information, coherence, and phenomenological structure.

TUC-N is the neuroscientific branch of the programme. It develops explicit graph-dynamical models of candidate neural states of consciousness that can be estimated from data, simulated, compared with baseline models, and empirically tested.

The purpose of this archive is to make the mathematical assumptions, derivations, computational methods, and proposed empirical predictions available for critical examination.

Unless explicitly stated otherwise, the documents published here are research manuscripts or preprints. They should not be interpreted as peer-reviewed publications or as empirically validated conclusions. Revisions may be issued when conceptual, mathematical, computational, or empirical issues are identified.

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Article 1

TUC-N: A Graph-Dynamical Multiscale Model of Candidate Neural States of Consciousness

Mathematical Foundations, Computational Architecture, and Falsifiable Neuroscientific Predictions

Author: Alessio De Angelis
Version: 1.0 — Foundational Specification
Date: 28 June 2026
Status: Research manuscript / formal theoretical specification

Abstract

TUC-N is a graph-dynamical framework for the formal study of candidate neural states associated with consciousness. The model represents neural activity as a latent state evolving over time on a weighted neural graph, rather than treating raw measurements such as EEG, MEG, fMRI, or intracranial recordings as directly interchangeable representations of consciousness.

The framework distinguishes a reference neural state, PhiZero, from the deviation of the current neural configuration relative to that reference. It then defines a normalized neural field whose dynamics can be analysed through graph geometry, temporal evolution, structural persistence, and local functional coalitions.

TUC-N combines global and local levels of analysis. At the global level, it specifies measures of deviation from the reference state, spatial differentiation, temporal activity, graph-relative curvature, and structural persistence. At the local level, it identifies candidate neural coalitions and evaluates their internal spatial organisation, temporal coherence, and persistence over time.

The model is designed to be falsifiable. Its proposed descriptors must improve prespecified predictions of independent endpoints, such as conscious access or reported content, relative to appropriate baseline models. The article also defines an observation model, identifiability conditions, synthetic-data verification procedures, and an out-of-sample evaluation framework.

TUC-N is a foundational mathematical and computational proposal. It does not claim completed empirical validation; its scientific value depends on future simulation studies, parameter-recovery tests, preregistered predictions, and comparisons with competing models.

Key features

• Latent neural state-space model rather than direct interpretation of raw neural recordings.
• Weighted neural graph with a canonically normalized graph Laplacian.
• Reference-relative representation based on PhiZero, DeltaPhi, and a normalized neural field.
• Stable input-driven graph dynamics suitable for mathematical analysis and controlled simulation.
• Separate global descriptors for distance, differentiation, temporal activity, and structural persistence.
• Local coalition analysis based on coherence, activity, and structural stability.
• Explicit threshold and margin definitions to avoid informal or post hoc activation criteria.
• Observation model and sampled-data observability conditions for empirical reconstruction.
• Synthetic verification protocol separating formula correctness from recovery under noise.
• Falsifiable empirical predictions evaluated against prespecified baseline models.

Download

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Article 2

A Six-Functional Profile for Structural-Dynamic Coherence in Formal Systems

Internal Definition, Methodological Limits, and a Protocol for Independent External Evaluation

Author: Alessio De Angelis
Version: 1.0 — Methodological Preprint
Date: 11 July 2026
Status: Preliminary methodological preprint / not peer-reviewed / not empirically validated

Abstract

This article presents a formal and methodological proposal for describing technical coherence in formal systems. The proposal introduces the profile $K_{\mathrm{TUC}}$KTUC​, a six-functional vector designed to evaluate structural-dynamic coherence through multiple non-reducible criteria rather than through a single scalar score.

The profile is defined as:$$K_{\mathrm{TUC}}(m;W)=(R_W,D_W,Q_W,N_W,S_W,O_W)(m)$$KTUC​(m;W)=(RW​,DW​,QW​,NW​,SW​,OW​)(m)

where the six components evaluate relational replicability, internal discriminability, structural compositionality, compositional non-collapse, perturbational stability, and non-trivial neutral openness.

The central aim of the article is not to measure consciousness directly, nor to validate the broader TUC-O framework, nor to prove any ontological claim. Instead, it proposes a reviewable formal object for describing whether a system preserves structure, maintains relevant differences, composes without collapse, resists perturbation, and remains open to non-destructive variation.

The article also explains why simpler definitions of coherence, such as stability alone, low variance, high integration, compositional fit, or weighted averages, may be misleading. A system may be stable because it is trivial, differentiated because it is noisy, compositional because the composition law is tautological, or robust because it is insensitive to all inputs.

For this reason, the vector form of $K_{\mathrm{TUC}}$KTUC​ is treated as primary. Scalar summaries and threshold gates are allowed only as secondary decision rules under explicit domain conditions.

A separate supplementary protocol package is associated with the preprint. It specifies a frozen route for future adversarial and independent evaluation, including preregistration, hash verification, role separation, blind handling, constrained outputs, stop rules, and chain of custody. At the time of publication, no empirical validation has been performed and no external evaluation run has been executed.

This document should therefore be read as a preliminary mathematical and methodological proposal, published for critical examination and future adversarial review.

Key features

Six-functional profile for structural-dynamic technical coherence.

Vector-based definition instead of a single scalar coherence score.

Explicit separation between technical coherence, phenomenal consciousness, and ontological claims.

Formal distinction between failure value $0$0 and non-evaluability $\bot$⊥.

Definitions of relational replicability, internal discriminability, structural compositionality, compositional non-collapse, perturbational stability, and non-trivial neutral openness.

Argument against overly simple definitions based on stability, variance, integration, compositional fit, or weighted means.

Worked abstract examples showing constant systems, noisy systems, projective composition, closed stability, and partial evaluability.

Conservative scalarization through the minimum coordinate, avoiding compensatory averages.

Threshold gates and fragility margins defined only under frozen domain conditions.

Explicit non-circularity requirements for windows, thresholds, composition rules, perturbations, and neutral decompositions.

Supplementary external-evaluation protocol with preregistration, hashes, role separation, blind handling, constrained output schemas, stop rules, and chain of custody.

Clear limitation statement: $K_{\mathrm{TUC}}$KTUC​ does not measure consciousness directly, does not prove $\Phi_0$Φ0​, does not validate TUC-O, and does not report empirical results.

Planned procedurally separated AI-assisted adversarial review, whose results may be published independently, including negative or inconclusive findings.

Methodological note

This preprint is published as a working methodological proposal. It is not a peer-reviewed article and should not be cited as empirical evidence for consciousness, neuroscience, physics, or ontology.

The purpose of this public release is to freeze a reviewable version of the $K_{\mathrm{TUC}}$KTUC​ profile and make the associated assumptions, definitions, limitations, and external-evaluation protocol available for criticism.

A future AI-assisted adversarial review may examine the internal mathematical consistency, non-circularity, domain adequacy, redundancy, counterexamples, and claim discipline of the proposal. Such a review, even if positive, would not constitute empirical validation.

Download the external evaluator pre-authorization package

Revisione avversariale assistita dall’IA dell’Articolo 2 della TUC-O

È disponibile la revisione formale e metodologica dell’Articolo 2:

“A Six-Functional Profile for Structural-Dynamic Coherence in Formal Systems”

La revisione è stata condotta mediante una procedura assistita dall’intelligenza artificiale, mantenuta separata dalla fase di elaborazione dell’articolo e impostata secondo un mandato esplicitamente avversariale.

Il revisore è stato incaricato di non assumere la correttezza della TUC-O, di PhiZero, delle sei coordinate funzionali o del protocollo di valutazione esterna. L’analisi ha cercato attivamente errori matematici, definizioni incomplete, problemi di dominio, dipendenze arbitrarie dalla finestra osservativa, circolarità metodologiche, ridondanze tra le coordinate, controesempi e insufficienze nella procedura di preregistrazione.

Esito generale

Il verdetto assegnato è:

FORMALLY_REPAIRABLE

La struttura a sei coordinate non è stata giudicata formalmente incoerente in modo irreparabile. Sono tuttavia emersi problemi sostanziali che richiedono una nuova versione dell’articolo e del protocollo prima di qualsiasi esecuzione esterna.

La revisione ha registrato complessivamente 35 rilievi:

• 17 rilievi maggiori;
• 12 rilievi moderati;
• 5 rilievi minori;
• 1 questione non risolta;
• nessun rilievo classificato come fatale.

Tra i problemi principali figurano la forte dipendenza dei risultati dalle scelte del contratto valutativo, l’insufficiente giustificazione indipendente della finestra osservativa, alcune vulnerabilità degli schemi procedurali e la possibilità che sistemi patologici ottengano profili artificialmente elevati.

Stato della valutazione esterna

La revisione non ha eseguito K_TUC e non ha prodotto risultati empirici o computazionali sulle sei coordinate.

Il pacchetto destinato alla futura valutazione esterna resta nello stato:

READY_FOR_AUTHORIZATION
NOT_AUTHORIZED
NOT_STARTED

Le sei componenti restano quindi:

R = D = Q = N = S = O = NOT_COMPUTED

Nessun obiettivo empirico, dataset, valutatore, ambiente di esecuzione, soglia o risultato è stato inventato o assegnato durante la revisione.

Natura e limiti del documento

Il rapporto pubblicato è una revisione avversariale formale e metodologica assistita dall’intelligenza artificiale.

Non costituisce:

• peer review umana;
• validazione istituzionale;
• certificazione scientifica;
• conferma empirica della TUC-O;
• dimostrazione della coscienza fenomenica;
• conferma di PhiZero;
• validazione neuroscientifica, fisica o ontologica.

Il rapporto valuta esclusivamente la coerenza formale dell’articolo, l’architettura delle sei coordinate e la robustezza del protocollo predisposto per una futura valutazione esterna.

Documento completo

Il rapporto integrale può essere consultato e scaricato qui:

Le correzioni conseguenti alla revisione produrranno una nuova versione dell’Articolo 2. La versione revisionata dovrà essere sottoposta a una nuova analisi avversariale separata prima di procedere alla fase di valutazione esterna.