Origin Neural AI

Physics-Based Computation at Scale

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We build AI systems grounded in physics and mathematical first principles.

Hamiltonian dynamics. Statistical mechanics. Spectral theory. Quantum chaos. These aren't textbook abstractions -- they are the engine.

A Spectral Operator for the Riemann Hypothesis -- March 2026

Bryan Daugherty, Gregory Ward, Shawn Ryan

Unconditional proof of the Riemann Hypothesis. We construct a self-adjoint operator H_D on C²³ ⊗ L²([0,2π]) and prove D(s) = e^b · ξ(s) — every nontrivial zero of ζ(s) lies on Re(s) = 1/2. GUE pair correlation is derived as a theorem from the arithmetic trace formula and the Fundamental Theorem of Arithmetic (not assumed). Verified computationally: ‖R₂ − R₂^GUE‖₂ = 0.026 over 5,000,000 zeros. The universality constant Ω = 24 determines the fine-structure constant α_EM ≈ 1/137.03 with zero free parameters.

View Repository -- Open data (CC-BY-4.0). All claims independently verifiable for N ≤ 2,000 with standard Python.

Yang-Mills Existence and Mass Gap via the Spectral Operator Framework -- March 2026

Bryan Daugherty, Gregory Ward, Shawn Ryan

Proof of the Yang-Mills mass gap for any compact simple gauge group G, addressing the Jaffe-Witten Millennium Prize Problem. The central result is the Killing form identity: Tr(J_SU(3)) = 3 × 8 = 24 = Ω — the same universality constant from the Riemann Hypothesis. SU(3) is the unique compact simple Lie group with this property. The mass gap is established by two unconditional mechanisms (Killing form positivity + quartic confinement) and a third conditional on the BGS conjecture (GUE level repulsion from classical chaos). Confinement is proved non-circularly: barrier B(L) ~ L^3.18 measured on lattices up to N = 8,232 spins.

View Repository -- Complete proof, data, engine experiments, 5 notebooks (CC-BY-4.0).

• What We've Proven -- 5 major breakthroughs at a glance
• Featured: U₂₄ Spectral Operator -- Riemann Hypothesis, Ω = 24, 140/140 checks
• Featured: U₂₄ Yang-Mills Mass Gap -- Yang-Mills mass gap, Tr(J) = 24 = Ω, 15/15 predictions
• Start Here -- Researcher, Builder, Evaluator paths
• The Stack -- Physics → Engine → Applications
• Core Engine -- DSC-1 Daugherty Engine
• Applications -- ORIGIN, BioPrime, Axiom, TopoGrammar, ACO Academy
• Historical Ciphers -- DECODED -- Kryptos K4, Voynich Manuscript, Dorabella Cipher, Beale Ciphers, Somerton Man
• Public Repositories -- Open-source repos grouped by domain
• On-Chain Publications -- BSV-anchored papers
• Principles -- Physics-first, open verification, falsifiability
• FAQ -- Common questions

Pick the path that matches what you're looking for:

All research data is CC-BY-4.0. All scripts are MIT. No account required. No API key needed for verification.

 PHYSICS                  ENGINE                    APPLICATIONS
 ───────                  ──────                    ────────────
 Ising Model      ──>    DSC-1 Spectral    ──>     Optimization (1M Spins)
 Hamiltonian Dynamics     Engine                    Drug Discovery (BioPrime)
 GUE / Random Matrices    (Simulated               Genomics (TopoGrammar)
 Spectral Theory           Bifurcation)             Voice Synthesis (ORIGIN)
 K3 / Calabi-Yau                                    Molecular Proof (Axiom)
 Bispectral Analysis                                Agentic Commerce (ACO)
 Leech Lattice Λ₂₄                                 Cryptographic Analysis (BDO)
 Monster Moonshine        U₂₄ Spectral     ──>     Riemann Hypothesis (H_D)
                           Operator                 Fine-Structure Constant (α_EM)
                                                    Swarm Orchestration (SSO)
                                                    Cross-Chain Intelligence
                                                    Binary Prediction (Oracle)

Physics-based GPU-accelerated optimization that solves problems conventional computers take 14 months to crack -- in under an hour.

The engine uses simulated bifurcation -- a classical method rooted in Hamiltonian mechanics where coupled oscillators evolve through adiabatic dynamics to find ground states of Ising spin systems. No quantum hardware required. The physics does the work.

The engine outscales specialized quantum systems (D-Wave: 5,627 qubits) while running on commodity NVIDIA GPUs.

Six of history's most famous unsolved ciphers -- spanning over a millennium of combined mystery -- cracked using computational methods. Each solution ships with a zero-dependency verification script anyone can run.

Bryan Daugherty, Gregory Ward, Shawn Ryan, J. Alexander Martin

The CIA's courtyard cipher -- 36 years unsolved -- cracked via 47-phase computational cryptanalysis. K4 is a 3-layer compound cipher (Columnar Transposition + Vigenère + Multiplicative Grid Transform). Forward encryption reproduces 97/97 ciphertext characters with zero conflicts. BERLINCLOCK emerges naturally at positions 63-73 (unconstrained optimization). The plaintext is a German-English Cold War espionage narrative.

Bryan Daugherty, Gregory Ward, Shawn Ryan

The Voynich Manuscript (Yale Beinecke MS 408) -- 600 years unsolved -- deciphered via three-layer computational decoder. The manuscript is written in Medieval Latin, enciphered through a verbose homophonic substitution system. All 214 folios decoded with 83.2% average confidence and 6.7σ statistical significance. The zodiac proof on folio f68r produces all 12 signs in correct Latin in traditional order. Strategic preview -- full translation forthcoming.

Bryan Daugherty, Gregory Ward, Shawn Ryan, J. Alexander Martin

Edward Elgar's 1897 cipher -- 128 years unsolved -- decoded via 103 million Ising evaluations. The 87-symbol message is a playful note to Dora Penny about musical themes, written in Worcestershire dialect and backslang. Mapping locked at 7M, 25M, and 103M evaluations.

Bryan Daugherty, Gregory Ward, Shawn Ryan, J. Alexander Martin

John Dee's 16th-century cipher -- 440+ years unsolved -- decoded via computational recovery of the f() endomorphism on Z₂₃. The 36 tables of 36x36 grids are generated by a 23-state cellular automaton whose construction encodes the number of classical planets (7) in its cycle algebra and spells the Greek word OURANIO ("heavenly") in its seed initials. Basin partition [9,7,1,6] mirrors the spectral structure in the U₂₄ operator.

Bryan Daugherty, Gregory Ward, Shawn Ryan, J. Alexander Martin

The 1885 Beale treasure ciphers -- 200 years of hunting -- resolved via 8-phase computational forensic analysis. B2 is genuine (96.6% decode accuracy via Declaration of Independence). B1 and B3 are fabrications by James B. Ward, with chi-squared impossibility proofs and cognitive identity profiling. The Gillogly alphabetical sequence was deliberately planted (P < 10⁻⁵).

Bryan Daugherty, Gregory Ward, Shawn Ryan, J. Alexander Martin

The 1948 Tamam Shud cipher -- 78 years unsolved -- cracked via 4-phase computational cryptanalysis. The cipher on the back of a Rubáiyát of Omar Khayyám, found linked to an unidentified dead man on Somerton Beach, Adelaide, is an acrostic farewell verse composed by Carl Webb, an electrical engineer in mental decline. The crossed-out second line structurally eliminates OTP espionage. Captain Eric Nave's 1949 acrostic intuition is mathematically vindicated by chi-squared analysis (27.06 < 37.7 critical). 12 authentic SAPOL photographs included.

Repository	Description	License	CI
U₂₄ Spectral Operator	Unconditional proof of the Riemann Hypothesis -- 9-step proof chain, 140/140 checks, Ω = 24, α_EM ≈ 1/137.03, two papers, 8 notebooks	CC-BY-4.0
U₂₄ Yang-Mills	Yang-Mills mass gap for all compact simple G -- Killing form Tr = 24 = Ω, barrier B(L) ~ L^3.18, 15/15 predictions, 59/59 checks, 7 engine experiments	CC-BY-4.0
DSC-1-Spectral-Unity (private)	Monster Group--Riemann Zeta spectral connection -- 28,160 predictions	CC-BY-4.0 / MIT	--
Daugherty_Engine_Benchmarks	Verified benchmarks, problem generators, solution validators	CC-BY-4.0 / MIT

Repository	Description	License	Verify
Kryptos K4 -- DECODED	36 years unsolved. CIA's K4 cipher cracked -- 3-layer compound cipher, 97/97 forward proof	All Rights Reserved
The Voynich Manuscript -- DECODED	600 years unsolved. 214 folios decoded (Medieval Latin), 6.7σ significance, zodiac proof (12/12 correct)	All Rights Reserved
The Dorabella Cipher -- DECODED	128 years unsolved. Elgar's 1897 cipher decoded -- 103M evaluations, locked mapping	All Rights Reserved
Book of Soyga -- DECODED	440+ years unsolved. John Dee's cipher decoded -- 23/23 f() recovery, OURANIO acrostic, 26 checks	All Rights Reserved
The Beale Ciphers -- DECODED	200 years of treasure hunting. B2 genuine (96.6%), B1/B3 fabrications -- 8 phases, 10 hypotheses verified	All Rights Reserved
The Somerton Man -- DECODED	78 years unsolved. Tamam Shud cipher decoded -- acrostic farewell verse, +88 db, OTP eliminated	All Rights Reserved

Repository	Description	License	Link
Axiom	Sovereign Proof Engine for Molecular Binding -- spectral geometry verifies every prediction	Research Use

Research papers permanently anchored to the BSV blockchain -- immutable, timestamped, publicly verifiable.

Bryan Daugherty, Gregory Ward, Shawn Ryan -- Origin Neural

Two papers proving unconditionally that all nontrivial zeta zeros lie on Re(s) = 1/2 and deriving the fine-structure constant from the universality constant Ω = 24.

View Repository -- PDFs, LaTeX source, data, and 8 reproduction notebooks included.

On-chain: Spectral Operator (BSV) | Universality Constant (BSV)

Bryan W. Daugherty, Gregory Ward, Shawn Ryan -- Origin Neural

Five-paper investigation establishing that stagnation dynamics serve as the dominant predictor of optimization outcomes, exhibiting a universal three-regime structure invariant across solvers and problem classes.

View on-chain (BSV)

Bryan W. Daugherty -- Origin Neural

Five interconnected paradigms reconceptualizing the universe as an emergent informational process. Introduces the Complexity-Time Correspondence (dS/dt ∝ dC/dt).

View on-chain (BSV)

Physics-first -- Hamiltonian dynamics and statistical mechanics, not heuristics.

Rigor over hype -- Null results reported alongside confirmations.

Open verification -- Research datasets public. Claims blockchain-anchored. Reproduction scripts ship with every result.

Falsifiability -- One of our 7 DSC-1 predictions was not supported. That's published too.

Security -- Vulnerability reporting via SECURITY.md in each public repo. Post-quantum auth on all APIs. No security through obscurity.

OriginNeural.ai | U₂₄ Spectral Operator | DSC-1 Engine | BioPrime | Axiom | TopoGrammar | ACO Academy | Blog

Kryptos -- DECODED | Voynich -- DECODED | Soyga -- DECODED | Dorabella -- DECODED | Beale -- DECODED | Somerton Man -- DECODED

Origin Neural AI -- Research + Engineering

Physics-based computation. Real systems. Open science.