ASIAlgebraic Semantic Index

StatusPatent Pending USPTO ApplicationNo. 64/103,054 FiledJuly 1, 2026

Every natural-language text is mapped to a unique algebraic identifier derived from the geometry of the exceptional Lie group E₈ — the most symmetric structure known in 8 dimensions. The index does not approximate: it computes.

i.The problem

Contemporary semantic retrieval rests on dense embeddings: approximate representations compared by similarity.

Approximation has three structural costs: results that cannot be verified (why two texts are "close" is not provable), retrieval hallucinations (plausible content that was never indexed), and storage that grows with vector dimensionality. In domains where errors carry consequences — contracts, diagnoses, compliance — approximation is not an acceptable trade-off.

ii.The approach

ASI replaces approximate similarity with a geometric assignment: each text is mapped to a unique identifier — the WeylOrbitId — determined by the orbit structure of the Weyl group of E₈, whose 240 roots form the densest known lattice packing in 8 dimensions.

The identifier is a key, not a vector: retrieval is direct access, the match is verifiable by construction, and every result is traceable to the chain of algebraic transformations that produced it. Semantic proximity becomes a property of the lattice geometry — discrete, exact, auditable.

text ⟼ WeylOrbitId(text) ∈ Orbits(W(E₈)) — lookup: O(1)

iii.System properties

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Determinism

Same text, same identifier: indexing is a function, not an estimate. No variability across runs.

O(1) search

The algebraic identifier is a direct access key: retrieval time does not degrade as the corpus grows.

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Hallucination-free retrieval

Designed to return only content that was actually indexed, with an algebraically verifiable match.

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Algebraic audit trail

Every result carries the chain of transformations that justifies it: full traceability, a native requirement of regulated contexts.

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192× compression

Storage footprint reduced by two orders of magnitude versus dense embeddings, at equal indexing capacity.

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Composition

Identifiers compose algebraically: the index of a structured document derives from that of its parts.

Design properties; empirical validation in progress on real corpora of international B2B contracts.

iv.Application domains

The technology has a broad application scope: any domain that requires deterministic semantic indexing and formal control of AI agents.

LawMedicineFinanceRegulatory complianceInternational B2B trade

International B2B vertical. The right of use in the international B2B trade domain (international sales contracts, Incoterms procedures, customs documentation, cross-border payments) is granted on a worldwide exclusive basis to BOS5 S.r.l. — EQUI–BOS5 Technology License Agreement, ref. EQUI-BOS5-2026-001.

v.Intellectual property

Title: ASI (Algebraic Semantic Index)
Application: USPTO Provisional Patent Application No. 64/103,054
Attorney docket: EQUI-ASI-2026-001
Filing date: July 1, 2026 — priority under 35 U.S.C. §111(b)
Assignee: EQUI Technologies International LLC — Delaware, USA (reg. 3958207)
Inventor: Dr. Giovanni P. Barabino