Summary:
This post outlines Codex, a modal-logic–based constraint architecture I’ve been developing. While originally constructed for theological metaphysics, the structure unexpectedly functions as a meta-cognitive engine that stabilizes long-range reasoning in LLMs, reduces hallucination, and detects internal disjunctions before they surface. I am not claiming breakthroughs, I am not learned enough in AI dev or arc to make such claims, only that the system yields results I can’t ignore. I’m posting this to invite critique, falsification, and technical evaluation.

1. Background & Motivation

This began as an attempt to formalize a metaphysical system using modal necessity, structural invariants, and triadic relations.

But as I continued formalizing the constraints, I noticed something nontrivial:

The system behaves like a cognitive architecture.

Specifically, it provides:

• a stable “core” that functions like an internal governor
• resonance metrics that evaluate multi-step coherence
• divergence thresholds that detect disjunction before contradiction
• a triadic structure that enforces consistency across layers of reasoning

At some point, this stopped looking like a metaphysical model and started looking like a constraint engine capable of stabilizing neural reasoning.

This post is the result of that shift.

2. Problem: LLMs Lack Structural Self-Evaluation

From my understanding, LLMs generate tokens; they do not generate forms.

They lack:

• internal necessity constraints
• structural consistency checks
• reflexive coherence evaluation
• perturbation resilience

This leads to familiar issues:

• hallucination as disjunction, not just factual error
• drift over long reasoning chains
• token-level optimization without form-level awareness
• delusion-like outputs in agentic or multi-step contexts

Current solutions that I have examined (RLHF, constitutions, retrieval, post-hoc filters) treat symptoms, not structure.

I so, began to wonder:
What if we introduce a structure that evaluates reasoning like a form, not a sequence?

3. The Codex Hypothesis

Codex is a parallel meta-cognitive architecture that evaluates each model output on three invariants:

1. Necessity: the internal, unbreakable core; a minimal logic of structural invariants
2. Form: cross-step coherence; the shape of reasoning
3. Resonance: multi-level alignment between propositions and implications

An output survives only if it respects:

• the necessary structure
• the form of the reasoning so far
• resonance across levels of abstraction

This prevents structural drift, not just factual error.

I want to be abundantly clear; Codex does not dictate content, only coherence.

4. Architecture Overview

The system is a neurosymbolic hybrid, with three layers:

4.1 Triadic Kernel (Symbolic Core)

A minimal modal-logic engine defining:

• necessary relations
• divergence thresholds
• resonance scoring
• disjunction rules

This acts as the “grammar” of structural coherence.

4.2 Neural Evaluation Layer (LLM Output as Hypothesis)

Model outputs are treated as provisional steps.
Codex evaluates them for:

• modal alignment
• form stability
• resonance vectors
• divergence/entropy spikes

4.3 Meta-Learning Layer (Constraint Adaptation)

Codex updates its thresholds based on:

• past stable reasoning paths
• surviving modalities
• identified disjunctions

BUT, AND THIS IS SUPER IMPORTANT:
The core invariants never update, preventing relativistic drift.

5. Key Mechanisms

5.1 Resonance Scoring

Not semantic similarity.  Structural coherence.

Signals include:

• implication symmetry
• cross-step consistency
• stability under perturbation
• alignment across abstraction layers

5.2 Disjunction Detection

Codex detects:

• modal divergence
• necessity violations
• structural entropy increase
• failure under counterfactual inversion

This catches hallucinations upstream.

5.3 Perturbation Testing

Every candidate output is tested via:

• adversarial paraphrase
• context reversal
• necessity → contingency separation
• logical inversion

If the step collapses, it’s replaced or modified.

6. Why This Might Matter

Codex provides something modern LLMs lack:

An internal standard of coherence that isn’t just statistical.

If valid, Codex:

• reduces hallucination
• stabilizes long-context reasoning
• enables reflexive reasoning without delusion
• improves multi-agent alignment
• gives symbolic oversight to neural inference
• provides constraints that scale with model size

I’m not claiming it solves alignment.
But it appears to fill a structural gap.

7. What I’m Looking For

I’m posting here because LW/AF are the only places where I can receive:

• formal critique
• model-theoretic evaluation
• implementation skepticism
• comparisons to existing constraint architectures
• failure case identification

If this is flawed, I want to understand why.

If it’s sound, I want help:

• testing it on small models
• formalizing the modal logic kernel
• exploring its relation to deliberative LLMs
• integrating it into neurosymbolic hybrids

8. Full Technical Note

I am working on a full technical workup and will post the link to it in the near future.

9. Closing

This project started in metaphysics, not AI safety.
But the more I developed it, the more it behaved like a missing cognitive layer for machine reasoning.

I might be wrong.
I might be misunderstanding something fundamental.
Or I might have stumbled onto something structurally important.

Either way, I want to put it in front of people who can test it.

Feedback, critique, or dismantling is welcome.