Three public arXiv preprints describe versioned research experiments. In the shipped path, dense candidates use cosine similarity; Fisher-derived terms can inform later scoring. Product behavior is governed by release code, tests, and measured artifacts rather than a component theorem.
Cosine similarity is the shipped dense candidate metric. It measures embedding direction and does not, by itself, encode the confidence stored with an assertion. That limitation does not make cosine invalid; it defines what later scoring stages may add.
Score meanings stay separate. Query-relative relevance, internal ranking utility, stored-memory confidence, trust, and answer confidence are different values. Score Contract v2 preserves those distinctions.
Fisher-derived research terms can influence post-candidate scoring when their required state is available. They do not replace every cosine path, and they do not turn rank into answer probability. Until a held-out calibrator is frozen, answer_confidence remains null.
score_contract_version: "2"Where p and q are probability distributions over memory confidence scores. The sum Σ is taken over all memory dimensions i. The arccos maps the result to angular distance on the unit sphere — the natural geometry of probability distributions under the Fisher information metric.
The preprint studies geometry-inspired forgetting, consolidation, and cognitive quantization. The equations describe the research model evaluated there; they are not a complete specification of every current runtime transition.
The released lifecycle also contains explicit policy, usage, recency, thresholds, and maintenance code. Those inspectable mechanisms—not this equation alone—define shipped behavior.
These are Shannon's fundamental information inequalities. H(X|Y) is the conditional entropy of prompt X given prior context Y — the irreducible information content that cannot be compressed away without information loss. I(X;Y) is mutual information — the quantity of information that X and Y share, which is always non-negative.
These inequalities describe theoretical limits; they do not prove a compression ratio, fidelity result, or provider saving for the shipped implementation. Product claims require a declared corpus, mode, tokenizer, round-trip test, latency measurement, and raw artifact.
Information geometry, developed by Shun-ichi Amari and C. R. Rao, is the study of probability distributions as geometric objects. The key insight: probability distributions do not live on a flat plane. They live on a curved manifold — the statistical manifold — where the natural notion of distance is the Fisher information metric, not Euclidean distance. Amari's 1985 monograph unified differential geometry and statistics into a single framework that lets you reason about distributions the same way classical geometry reasons about shapes.
The research asks whether probability-aware geometry can add useful signals beyond embedding similarity. In the current implementation, dense candidates still use cosine similarity and Fisher-derived terms may modify later scoring. Whether that improves retrieval is an empirical question for a frozen corpus and trace, not an automatic consequence of the theory.
The research claims on this page are traceable to public arXiv preprints. Read the methods, reproduce the results, and cite the work.
Historical information-geometric retrieval experiments. Current dense candidate generation uses cosine; Fisher-derived terms may inform later scoring.
arXiv:2603.14588 →Historical evaluation of trust, privacy, search, graph, and multi-agent memory-poisoning defenses.
arXiv:2603.02240 →Historical forgetting, cognitive quantization, and multi-channel retrieval experiments. Not a generic prompt-compression proof.
arXiv:2604.04514 →