Mathematical & Physical Foundation

Two original research programs.
One protected foundation for BivectorAI.

BivectorAI is not built around a statistical language model as the authority for correctness. Its architecture grows from two original foundational research programs developed by Dam Van Vi through independent work spanning mathematical physics, relational geometry, formal computation, structured reasoning and machine-checkable verification.

Public materials describe the research scope, public record and evidence boundaries. Protected mathematical constructions, derivations, implementation primitives and trade-secret mechanisms remain private.

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Two Research Programs

One relational bivector foundation. Two complementary research directions.

These foundational programs are active research programs supported by public preprints, formal audit records and protected invention work. Public descriptions remain intentionally high level.

Protected Physics Program

Relational Information Quantum Gravity

An original mathematical-physics program underlying BivectorAI's physical and information-theoretic research. Its public scope includes spacetime, gravitation, quantum information, particle physics, cosmology and testable physical questions.

Protected constructions and implementation methods are not disclosed on the public website.

Mathematical physics Quantum information Gauge structure Cosmology Information structure

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Protected Mathematical Program

Relational Bivector Foundation

An original mathematical research program supporting structured reasoning, formal verification, evidence completeness and machine-checkable audit.

The research record includes work addressing major open mathematical problems through formal branch-ledger, witness and audit disciplines. Public pages do not disclose protected primitives or derivations.

Formal reasoning Verification Audit protocols Witness structures Structured evidence

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From Research to Architecture

BivectorAI extends the research toward verifier-first intelligence.

The architectural principle is simple: probabilistic systems may propose candidates, explanations or intermediate work, but correctness and customer-facing authority are bounded by deterministic verification, evidence contracts and explicit decision gates.

Foundational research

Mathematical and physical research supporting structured evidence, relational reasoning and bounded computation.

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BivectorAI architecture

Protected verification mechanisms operating behind customer-safe inputs, outputs and evidence boundaries.

Formal audit discipline

Claim boundaries, evidence completeness, branch auditing, witness records and reviewable acceptance conditions.

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Customer evidence system

Structured verdicts, reports, rankings, bounded evidence objects and controlled review workflows.

Technology & Products

Protected technology behind four clear buyer paths.

BivectorAI does not sell access to its internal mathematical core. Customers buy a bounded workflow: defined inputs, defined outputs, evidence, deployment boundaries and commercial terms.

Civilian Commercial Products

Industrial, scientific, software, security, compliance, materials, chemistry, biomedical, infrastructure and physical-system assessment workflows.

Products expose customer-safe assessments, rankings, reports, evidence packages or review states — not protected algorithms.

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Integrated AI Agent

One integrated Agent product combining instruction screening, policy controls, PII handling, content-safety checks and software/workspace assurance context.

The Agent is a commercial interface around controlled verification and evidence workflows; it does not expose the protected core.

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Defense & National Technology

Private, local and air-gapped technology acquisition for mission resilience, sensing, communications, data continuity, autonomy, sustainment, trusted hardware, critical infrastructure and space systems.

No public Defense API and no automated Defense checkout. Controlled technical information is handled under transaction-specific diligence and NDA boundaries.

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Discovery Licensing

Bounded licensing and evaluation path for computational drug and material candidate portfolios included in Application E.

Public materials describe portfolio inventory, evidence boundaries and commercial structure while candidate-generation and internal screening methods remain protected.

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Public technology boundary. Product pages describe what the customer provides, what BivectorAI returns, what the result means, what it does not mean, and how the commercial engagement works. Source code, mathematical mechanisms, protected hardware architecture, internal candidate-generation logic and trade-secret implementation are not public deliverables.

Public Research Record

The work is public and traceable where disclosure is appropriate.

ORCID

Public researcher identity and research-work index.

Zenodo

Public preprints and research records where released by the author.

Patent Pending

Six public U.S. provisional application identities: the Part 1 foundation filing and Applications A–E.

Public research visibility does not imply disclosure of the private mathematical core or implementation. Research publication, patent disclosure and commercial product exposure are separate boundaries.

Protected Invention Portfolio

Six public U.S. provisional application identities.

BivectorAI's public filing architecture is organized around one foundation filing and five additional subject-matter-specific provisional applications. Historical technical disclosure labels are not separate filed applications.

Foundation Filing · Part 1

64/129,790

Patent Pending
Official filing date: April 9, 2026.

High-level coverage includes foundational computation, quantum-information systems, communications, processor/repeater architectures and related physical-computation embodiments.

Application A

64/150,249