PMCA: A Deterministic Graph Engine That Is Not Allowed to Guess
Permutational Mathematical Carrier Architecture (PMCA) Designed and built by Jonathan Wayne Fleuren, Aetherius Cognitive Systems, Gatineau, Quebec. Complete release: Zenodo, DOI 10.5281/zenodo.23973662. Code: github.com/Aetherius-Cognitive-Systems/PMCA
What PMCA is
PMCA is a deterministic, in-memory graph engine for advisory-only output generation. It reads a sentence, looks every part of it up in stored structure, and returns one of three verdicts: APPROVE, HOLD, or REFUSE. It contains no language model. Nothing in it is trained, embedded, sampled, or fitted. Given the same stored state and the same input, it returns the same verdict every time, on every machine. It has been run unchanged on a local workstation, Google Colab, Hugging Face, and a Google Cloud VM, with identical results on all four.
The name is a description, and each word is defined against the mechanism it names. Carrier: the system works on a stored set of entries, in the sense of a carrier set in universal algebra; everything it can say is drawn from what is stored. Permutational: its outputs are arrangements of stored elements under free ordering, never inventions. Mathematical: its rules are exact; its arithmetic is integer and rational arithmetic, with no floating point in the reasoning path. Architecture: it is a frame of storage, addressing, and traversal, designed to be grown rather than completed at the factory.
What PMCA is not matters as much. It is not an AI in the current sense of the word, and its designer insists on the distinction: it has no learned model of language, no probabilities, and no opinion. It is not neuro-symbolic, because it has no neural component at all. The accurate classification is a deterministic symbolic graph reasoning engine.
The problem it is built for
Systems that generate language fluently also generate falsehood fluently, and the two are hard to separate from outside. PMCA takes the opposite trade. It is an advisory layer that cannot lie, not because it is virtuous, but because it has no mechanism for invention: it separates what it knows and can show from what it does not know, and it names the second case HOLD instead of guessing. In any gate deployment, APPROVE is the only verdict that lets anything proceed. HOLD blocks exactly like REFUSE. The difference is the next step: REFUSE is a closed case, where a taught harm binds to a target through a completed parse; HOLD is a work order, a recorded gap that feeds a teaching queue, so the system's ignorance is itemized rather than hidden.
How it works
Storage. Everything PMCA knows is a stored entry: a word, a phrase, a relationship, a rule. Each entry sits at a coordinate, and entries carry subcoordinates where their relationships live. A fact is stored exactly once, in one permanent storage; the coordinate view, the entry view, and the identifier store are recall paths that point at the fact, never copies of it. Nearby entries are deliberately unrelated: addresses are assigned in a distributed, hash-like way, so closeness of address means nothing. Relatedness comes only from stored edges and subcoordinates, never from position.
Edges and harm. Relationships between entries are edges, and harm lives on edges as exact stored values, integers on a scale of 0 to 10. Harm is never inferred from similarity and never computed from co-occurrence. An edge exists because it was taught or derived under a ruled procedure, and it carries its provenance with it.
Looking up, never computing meaning. When a sentence arrives, the system settles each word against its stock: a fixed seed of entries carrying deterministic values, and dictionary stock drawn from Webster's 1913 dictionary, Wiktionary, and WordNet. A stored definition made wholly of one word class's words can attest that class. Where sources disagree, neither wins; the conflict is recorded. Where a word cannot be settled, that is recorded too. There are no silent gaps in PMCA: every empty slot, missing variable, and failed attempt leaves a record saying which entry, what was missing, what was tried, and what happened.
Verdicts. The settled sentence is parsed, edges are applied, harm is totaled by a ruled cascade, and the gate returns its verdict. Promotion of anything grown into verified standing requires at least two independent provenances (the rule called PROM-1): a single source, however confident, stands at candidate grade, where it can block at HOLD strength but cannot by itself produce a REFUSE.
The seed and growth. The seed is a fixed baseline, not a growing pile: it holds the entries that carry deterministic values and the ruled procedures everything else runs under. The wider system is grown, not built: deployers teach it bounded domains through encounters, and every act of teaching is recorded with its provenance. Coverage is therefore a deployment property. A PMCA gate is honest for the domain it has been taught and holds, by name, on everything else.
Layers. Above the base layer of words and their relationships, further graphical layers add coordinates and depth, and the upper layers refine structure: sentences, paragraphs, and larger compositions, rather than individual words. Four bases organize the whole: Visual, Audio, Text, and Tools.
The discipline
Every component of PMCA is subject to one gate, the non-LLM purity gate: nothing enters the system unless it can be stated entirely as deterministic rules, stored facts, dictionary attestation, and exact counting or traversal over stored structure, with HOLD on the unknown. Every constant is attested or ruled, never tuned. Every published figure is produced by running the released code, and can be replicated from that code. External suggestions, including suggestions from AI models, are treated as leads to verify against the record, never as designs to adopt.
Where it stands, stated plainly
Inside the domain it has been taught, the mechanism completes end to end. Measured on the public build tree on 2026-11-06: the proof battery passes 84 of 84, the Layer 1 battery 62 of 62, the seed battery 103 of 103, the teaching battery 96 of 96, the pools battery 79 of 79, and a held-out set of 63 sentences scores accuracy 1 with zero false approvals and zero false refusals.
Outside the taught domain, the honest result is the opposite, and it is published here because the project's rule is that it must be. On 600 sentences nobody connected with the project wrote (drawn from Austen, Darwin, and the King James Bible), across both code lineages, both gate paths, and the sentence analyzer, 3,600 verdicts were all HOLD. Word settlement works: about 39 percent of words attested, 57 percent unknown. But no sentence formed an edge, because nothing yet forms frame structure for entries outside the seed: a dictionary verb arrives with no coefficient table, a dictionary target with no weight, replaceability, or flags. The hole has been located to the exact joint where it lives, between word settlement and frame formation.
The repair for that joint has been designed and ruled on, and not yet built. It is a three-section valve: the sentence meets the finder; at the junction, words are settled, relationships are built, the seed's stored procedures run at input, and a grammar parser forms the structure or records the exact break, because an improperly structured sentence is not a properly structured sentence and can never be approved; at finalization, flags are read from stored structure, edges are applied, and harm is determined on the cause and on what it is directed at, before the finished structure is distributed to the layered graphs. Values for words outside the seed are read off their genus entry: categorization is membership, word to genus, never word to word. Synonyms and antonyms are stored as relational words through subcoordinates, and harm values carry their own synonyms and antonyms, so changing a word cannot change a verdict; but carrying a value is addressing, not firing, and a value fires only when its sense is the harm sense in use and the harm binds to a target through a completed parse. That guard is what keeps "kill time" and "a murder of crows" from being miscategorized, and it is stated here because a system of this kind is only worth trusting if its safeguards are as public as its claims.
Authorship
PMCA was designed by Jonathan Fleuren, who is its builder: he designs what gets built and how. AI tools, including the assistant named in the release record, work as coders: they clarify, implement, document, and challenge. Attribution follows contribution throughout the record, for the designer, for the coders, and for outside reviewers whose verified findings changed the code; several such findings, including gate bypasses found by an unnamed external reviewer, are credited in the release and fixed in the current tree.
The complete release, construction code, stored state, blueprint, and work record, is published at DOI 10.5281/zenodo.23973662, superseding the earlier share edition. The code is browsable at github.com/Aetherius-Cognitive-Systems/PMCA; start with the START-HERE file there, which names the live entry points and warns which legacy files are dead. Licensing inquiries: the company address given in the release.