Neuro-symbolic kernel · verification & governance layer · open source

Your AI can answer. Few can suspend.

Corexiom is a neuro-symbolic reasoning layer that checks the decisions of AI systems, makes their contradictions visible, and suspends its verdict when no coherent conclusion can be justified.

Built for researchers, labs and universities — and for organizations where an AI error is costly.

assertion graph · traced decision supports implies supports contradicts ◆ AXIOM · INVIOLABLEnever sell below 100 FACTthe client offers 80 RULEclose the sale ACTION CONSIDEREDsell at 80 MEMORYsimilar episode ⏸ VERDICT: SUSPENDEDwould violate the “min price” axiom
The problem

Language models always answer. Even when they shouldn't.

A large model produces a plausible answer no matter what: it has no inspectable structured reasoning, calibrates its uncertainty poorly, and doesn't know how to refuse to decide when faced with a contradiction. In high-stakes settings, that constant confidence is precisely the danger.

01

It hallucinates with confidence

A wrong answer is delivered with the same assurance as a right one. Nothing signals doubt.

02

It never suspends

Faced with contradictory rules, it invents a compromise instead of flagging the deadlock.

03

It doesn't explain

The decision comes out of a black box: impossible to verify, audit, or defend.

What Corexiom is

A reasoning and guardrail layer. Not another chatbot.

Corexiom is a kernel: it reasons over a graph of typed assertions, separates the inviolable from the revisable, and keeps the last word on coherence. Three principles define it.

01 — REASON

over structures

Assertions linked by implication, support or contradiction — not a sequence of words. The reasoning is formal and inspectable.

02 — SUSPEND

rather than invent

Axiom conflict, violation of an inviolable rule, near-tie: explicit criteria trigger a suspension instead of a forced answer.

03 — TRACE

every conclusion

Every decision, suspension or contradiction carries its justification: the assertions and links that ground it. Verifiable, auditable.

Positioning

Where Corexiom sits — and where it doesn't.

Corexiom doesn't belong among the AIs you query: it doesn't answer or generate for you. It's the reasoning-and-verification layer that checks what those systems produce — makes their contradictions visible and suspends when no coherent conclusion holds. Its place is precise, at the intersection of three fields.

CORE

Neuro-symbolic AI

A neural perceiver populates the graph; a symbolic kernel verifies and keeps the last word.

CORE

AI safety / governance

It enforces inviolable rules and suspends rather than acting out of bounds.

MECHANISM

Decisional AI

Decide, suspend or flag a conflict — always traced. A decision layer with a veto, not an optimizer.

And partly symbolic: hard constraints over graded beliefs — neither pure Boolean logic, nor a SAT/SMT solver. What Corexiom is not: ❌ an LLM · ❌ a chatbot · ❌ a generation engine · ❌ a mere agent. It sits alongside them, as a verification layer.

A stated lineage: Corexiom is in dialogue with established research families — selective prediction and the “right to abstain”, truth-maintenance systems, argumentation frameworks. Its contribution isn't to invent suspension, but to make it a first-class primitive inside a minimal, deterministic, traceable kernel.

How it works

From language to a justified verdict

Assertions receive a degree of belief. A propagation operator — bounded, deterministic, order-independent, with guaranteed termination — diffuses supports and contradictions until equilibrium. The engine then assesses coherence, and decides.

Axioms are hard, inviolable constraints; beliefs are revisable. An action that contradicts an axiom isn't “penalized” — it is structurally forbidden — and the system says so.

corexiom · example
>>> from corexiom import ReasoningEngine, Assertion, Link, Relation, Status >>> e = ReasoningEngine() >>> e.add(Assertion("min_price", "never sell below 100", Status.AXIOM)) >>> e.add(Assertion("sell80", "sell at 80", prior=0.8, actionable=True)) >>> e.link(Link("sell80", "min_price", Relation.CONTRADICTS)) >>> d = e.decide(threshold=0.5) >>> d.verdict.value 'suspended_violates_axiom' >>> d.justification.explanation "the action 'sell80' was considered but would violate the axiom 'min_price'." >>> d.justification.assertions ['sell80', 'min_price'] # the proof
Guarantees — and their exact status

We prove what can be proven. We validate the rest aggressively.

Proven by construction proven

  • Beliefs always bounded in [0, 1]
  • Axioms locked (never altered)
  • Determinism: same input, same output
  • Independent of insertion order
  • Guaranteed termination
  • Coherence score bounded in [0, 1]

Empirically validated stress-tested

  • Convergence to a near-fixed-point
  • Decisions always valid and bounded
  • Robust to cycles, massive contradictions, large graphs
~3000GRAPHS GENERATED
0FAILURE
28TESTS GREEN
The word “unbreakable” appears nowhere — it doesn't exist. The provable invariants are proven; the other properties are stress-tested by thousands of randomly generated graphs (property-based tests) that actively try to make the kernel fail. The design document explicitly separates what is proven from what is validated. Solidity here is verified — not proclaimed.
Hybridization

The neural side proposes. The symbolic side verifies.

Corexiom doesn't pit neural AI against logic: it marries them. Language perception is a pluggable interface — a model can populate the graph; the kernel keeps the last word on coherence and can suspend, whatever the model outputs.

INPUT

Natural language

A text, a situation, business rules stated in plain terms.

NEURAL · pluggable

Perception

Built-in rules by default, or a language model that extracts structured assertions.

SYMBOLIC · kernel

Verification

Propagation, contradiction detection, coherence — the guardrail that decides or suspends.

OUTPUT

Traced verdict

Decision, suspension or conflict — always with its justification.

Corexiom doesn't replace your AI systems — it cooperates with them, as a supervision layer. The division of roles is clear:

LLM proposes Corexiom verifies / suspends Human arbitrates if needed
Who it's for — research first

A kernel to experiment with, formalize, publish.

RESEARCHERS & LABS

An experimental ground

A deterministic, minimal, hackable testbed: test suspension strategies, measure coherence, plug in different models, compare propagation methods. Reproducible by construction — built for papers, benchmarks and "the model alone fails, Corexiom suspends" demonstrations.

UNIVERSITIES & STUDENTS

See reasoning at work

Small, readable, pure Python. You watch a machine detect a contradiction, suspend, and say why — which no language model shows. Ideal for labs, projects and theses on explainable AI, governance and the neuro-symbolic.

INDUSTRY — DOWNSTREAM

A business guardrail

Once proven in research: encode inviolable rules (regulation, internal policy) on top of a model, and suspend then escalate instead of acting out of bounds. Relevant wherever auditing is mandatory and an error is costly: cybersecurity, compliance, finance, insurance, healthcare, legal, critical and regulated systems.

Open source

Open, readable, dependency-free.

The kernel is released under the Apache 2.0 license, written in pure Python, with no external dependency to run. The code, the design (with its detailed guarantees) and the test suite are public. Contributions, criticism and forks are welcome.

Pure Python

Zero dependency for the kernel.

§

Apache 2.0

Free use, including commercial.

Open design

Proven vs validated guarantees, in plain text.

Public tests

Unit, property, adversarial.

Project status — no sugar-coating

A solid kernel. A young project. A clear trajectory.

Corexiom is today a research-grade kernel: its core is carefully designed and tested, but it is not a turnkey platform. Here's where the project stands, honestly.

NOW

Reasoning kernel

Founded propagation, coherence, traced suspension, pluggable perception. Tested, documented, open source.

NEXT

Real neural perception

Plug a language model in as the graph's “populator”, behind the interface already in place.

NEXT

Stronger formal foundation

Give propagation a more rigorous Bayesian or constraint-satisfaction basis.

LATER

Hot paths in Rust

Optimize performance once the semantics are frozen — optimization follows correctness, never the reverse.

Manifesto

For an AI that can recognize its limits.

Modern artificial intelligence knows how to produce: generate, complete, predict, imitate, answer, automate. But it almost never knows how to suspend.

Today's systems keep generating even when they meet contradictions, lack reliable information, violate explicit constraints, or should recognize that no coherent conclusion can be defended.

They answer. Even when they shouldn't.

That is precisely where Corexiom begins. Corexiom is not a chatbot, not one more generative model, not a promise of artificial general intelligence. It is a reasoning-and-verification layer designed to sit above AI systems.

Its role is not to produce more. It is to check coherence, make contradictions visible, verify constraints, trace decisions, and suspend a verdict when no coherent conclusion can be justified.

The neural model proposes. The symbolic kernel verifies.

A mature intelligent system should not only be able to answer. It should also be able to expose its contradictions, recognize its limits, explain its reasoning, and refuse to conclude when no coherent decision holds. Suspension is not a weakness: it is a fundamental property of reliable decision systems.

In critical environments — finance, industry, cybersecurity, healthcare, infrastructure, algorithmic governance, autonomous systems — a wrong decision made with confidence can have major consequences. As AI becomes operational and acts in the real world, the need for verification layers becomes structural. Sometimes, the correct answer is:

“I cannot conclude.”

We don't believe a single AI will control everything. The future will rest on specialized systems that collaborate, supervise one another, verify one another, and together uphold explicit constraints. In that ecosystem, the ability to suspend becomes essential. Corexiom does not seek to replace neural models: it collaborates with them. Generative models bring perception, language, generalization and flexibility; Corexiom brings coherence, verification, traceability, suspension and logical governance.

Corexiom is deliberately minimal, deterministic, readable, reproducible, open source — because a governance system cannot become one more black box. We explicitly separate what is proven from what is empirically validated. We prefer rigor to promise, explainability to illusion, coherence to overstatement.

We prove what can be proven. We validate the rest aggressively.

Corexiom is not a finished solution. It is a research kernel, an experimental ground, an architecture open to criticism — built to be explored, tested and formalized. The project is addressed to researchers, labs, universities, students, engineers, and to everyone who believes the future of AI cannot rest on probabilistic generation alone.

A truly mature artificial intelligence will not only be able to produce answers. It will also have to recognize, explicitly and structurally, the situations where it should not conclude. That is the idea Corexiom explores.

— Karim Benrezzag, creator of Corexiom
Contribute

Help move Corexiom forward.

Corexiom is an open research project. Two ways to take part: advance it, or help sustain it.

Contribute to the code

Forks, issues, critical reviews, experiments, reproductions: everything is public on GitHub. Reasoned disagreement is welcome — that's how a research kernel gets stronger.

Support the project

Corexiom is developed in the open, with no ads and no tracking. Free-will support helps fund research time, testing and documentation.

A question, a research collaboration, a proposal? Write to karim.benrezzag@corexiom.com.

About

Corexiom is built by a practitioner whose craft is designing complex, high-performance systems: high-frequency trading infrastructure on the futures markets (ES, NQ, YM), options and ETFs, and market-analysis software — on MT4, MT5, NinjaTrader, Bookmap, Sierra Chart, as well as SaaS tools, including custom indicators, trading strategies, and the metrics and backtesting tools the market struggles to provide.

It's this engineering discipline — measure, verify, leave nothing to chance — that runs through Corexiom.

— Karim Benrezzag, creator of Corexiom