Applied Neurosymbolic AI
We focus on AI that can be used in practice. Our architectures are designed to bring neural and symbolic techniques together so that systems can both interpret complex inputs and reason over them in a structured way.
Company Overview
Practical AI for real-world work
What We Are Working On
Our work is grounded in the practical deployment of advanced AI, with a continuing interest in the next generation of computational methods.
Workflow and Spreadsheet Understanding
These methods are being applied to general workflows and to the understanding of spreadsheets, where interpretation, structure, and operational intent all need to be handled together.
Research Direction
Quantum Computing in View
We also have a theoretical research interest in quantum computing, although this is not yet mature enough to apply within our applications.
We see it as part of the mid-term future rather than something ready for present-day deployment.
Quantum Mechanics explained in 8 easy pieces
With grateful acknowledgement to the genius of Richard Feynman and John Wheeler.
- 1. The Jar of Nothing That Contains Everything Why empty space isn't empty — and why physics has no idea what's in it →
- 2. The Most Successful Failed Theory in Science The Standard Model of particle physics gets everything right — and explains nothing →
- 3. Wheeler's Dream and Why Nobody Could Build It The forty-year quest to build the universe from information — and the one thing everyone was missing →
- 4. What If Particles Are Just Error-Correcting Codes? An 8-qubit register, three Boolean rules, and every known fermion in the Standard Model →
- 5. The Shape That Builds Itself How identical qubits, with no instructions and no blueprint, spontaneously crystallise into the geometry of space → Watch the crystallisation animation
- 6. Why Quarks Can't Escape Colour charge as spatial direction, gluons as binary arithmetic, and confinement as an unbreakable rubber band made of geometry →
- 7. The Numbers That Fall Out Six fundamental constants derived from counting faces, bridges, and constraints — with zero fitted parameters →
- 8. Fourteen Predictions and Everything We Don't Know The specific, falsifiable claims of the information lattice — and an honest inventory of its unsolved problems →
- 9. The Paradoxes Dissolve Ten quantum mysteries that aren't mysterious anymore →
- 10. The Universe's Firewall: Black Holes, Hawking Radiation, and the Walk Operator Why space and time swap inside a black hole — and what the walk operator reveals about Hawking radiation, the firewall, and information loss →
Our Papers
We have a strong interest in AI, especially in using it in ways that produce reliable results that can be trusted. We have developed a novel "blackboard" architecture that combines opportunistic reasoning with robust truth maintenance and efficient use of the LLM resource. We also have a theoretical interest in quantum computing and the algorithms that it supports. This has led us to study the underlying nature of quantum physics, and we have been able to derive much of the Standard Model of physics from an information-theoretic base.
Methodology — a sound protocol for using AI in research
The Rigid Ground Truth Framework: A Protocol for Catching AI Confabulation in Speculative Research
A working methodology for using large language models in serious research without falling into their characteristic failure modes — fluent confabulation, sycophantic over-validation, pattern-matching enthusiasm, off-task generation. Six interlocking artifacts (a versioned canonical ANCHOR.md, a DRIFT.md retraction ledger, a three-tier locked / proposition / open epistemology, Bayesian search-space accounting with formal foundation in standard model-comparison theory, a growing anti-pattern catalogue, and a project-instructions file codifying required AI behaviour) convert the LLM from a creative collaborator into a constrained calculator whose errors get caught and retracted faster than they accumulate. The paper defines a measurable convergence property — the headline-derivation gap G(t) — shows it decreases monotonically under the protocol, and documents the catalogue of overclaims the protocol has caught and the "D-pile" of papers it caused to be retracted across a six-month physics collaboration. It also proposes a system-level "Adversarial Auditor" mode for AI developers and provides a paste-ready adoption template portable to any speculative-research domain where quantitative claims can be tested against external data.
The failure mode the protocol is built to prevent.
Methodology — the runnable tool (companion to the framework above)
Relocating Trust to the Verifier: A Truth-Maintenance System for an AI-Generated Theory of Everything
The runnable operationalisation of the methodology above. The manual protocol works but is enforced by a human reading every diff — which does not scale and has documented mechanical failures. PTMS mechanises the consistency discipline as a truth-maintenance system that enforces consistency, not truth: it treats every AI-supplied justification as untrusted until it binds to checkable evidence — a cited script that exits 0, a retired claim's signature flagged at every surviving site, a cross-reference that resolves. Three commands of increasing cost — check, verify, and graph — run over a machine-readable sidecar of the canon without ever editing the human-facing ANCHOR.md / DRIFT.md prose. Reported against a six-month AI-assisted physics corpus (~250 claims, ~120 self-asserting scripts), it mechanically catches un-propagated retractions, evidence regressions, seductive numerical coincidences, and live claims standing on retracted foundations. The paper is explicit about the limit: the system makes such research auditable and constrained, not correct — only forward prediction closes the remaining gap.
Framework index · ground truth
The Holographic Circlette — Substrate Predictions Index
Tier-classified index of the framework's substrate-derived claims, brought through a methodology audit (29 retraction-ledger entries, search-space accounting, anti-pattern catalogue). Includes: qualitative structural reproductions of the Standard Model (anomaly cancellation, three generations, CPT, proton stability) which are Locked; quantitative spectroscopy and cosmology results at Proposition tier with named-mechanism formulae and 3 ppb to few-% precision; recent papers with Zenodo DOIs; falsifiable forward predictions for DESI Y3/Y5, CMB-S4 / LiteBIRD, and LHCb heavy-baryon spectroscopy. Several previously-headlined precision claims have been retracted or recharacterised under the audit; the audit-status banner on the index page details the changes.
Open the framework index
Interactive synthesis
The Geometric Shadow of the Vacuum
A short visual tour through the framework: how the Standard Model — gauge couplings, electrodynamics, the ρ(770) meson mass, the Hartman tunnelling effect and the CKM mixing hierarchy — emerges from the topology of a discrete 4.8.8 Archimedean lattice and an [8,4,4] quantum error-correcting code. Five interactive charts, no equations to chase down.
Open the synthesis
Major result — four cosmological observables from one code
One Code, Three Cosmologies: Parameter-Free Derivations of η, n_s, N, and r from the [8,4,4] Code on Z³ ⊗ Q₃
A single combinatorial value — the spectral gap Δ₁ = 1/28 of the [8,4,4] extended-Hamming code on the Z³ ⊗ Q₃ substrate — is identified as a common source for four cosmological observables. Numerical positions: η = (3/14)α⁴ + (1/3)α⁵ ≈ 6.145 × 10⁻¹⁰ (0.6σ Planck 2018); n_s = 27/28 ≈ 0.9643 (0.14σ Planck); the inflationary e-fold count N = 56 follows from the slow-roll relation 1 − n_s = 2/N; the tensor-to-scalar ratio r ≈ 0 at leading substrate order, with subleading r ~ α⁴ ≈ 2.8 × 10⁻⁹ falsifiable by CMB-S4 / LiteBIRD. Audit status: the α⁴ scaling is structurally identified with the [8,4,4] minimum-weight bypass; the 3/14 prefactor is at Proposition tier pending formula-freedom audit. The r ≈ 0 / r ~ α⁴ prediction is the headline falsifiable forward claim. The structural mechanism (Sakharov conditions as substrate-structural consequences, dissolution of the horizon/flatness/monopole problems, graph-theoretic impossibility of a pure-photon universe) is the qualitative-structural core; the numerical matches are tier-classified consistency checks.
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Hypothesis framework — derivation conditional on K_eff = 205 computation (audit 2026-05-30)
Holographic Dilution and the Emergence of Gravity: Deriving the Planck Mass from the Z³ ⊗ Q₃ Error-Correcting Vacuum
A proposed derivation of Newton's gravitational constant G via holographic dilution on the discrete substrate (0.02% numerical match conditional on a specific subspace-reduction conjecture). The paper proposes that the vacuum is a discrete, UV-finite Z³ ⊗ Q₃ topological tensor network maintained by the [8,4,4] extended Hamming QEC code. Anchoring the lattice spacing to the hadronic chiral scale (Λ_QCD ≈ 332 MeV) gives a bare Planck mass of exactly Λ_QCD; macroscopic gravity is proposed as an emergent E_g transverse metric shear, holographically diluted across the ~2.77 × 10⁴¹ discrete nodes spanning the static de Sitter causal horizon (R_dS = √(3/Λ)). The continuous Euclidean loop factor 1/16π² is replaced by a discrete Feshbach resolvent trace over the 208-dimensional invalid error-correction subspace; the paper proposes this reduces to K_eff = 205 via three "structurally decoupled virtual states," yielding M_P ≈ 1.2207 × 10¹⁹ GeV vs CODATA 1.2209 × 10¹⁹ GeV. Audit status (2026-05-30): the paper has been re-scoped from "derivation" to "hypothesis framework awaiting computational verification." The K_eff = 205 reduction is asserted but not yet derived; the explicit Brillouin-zone matrix-trace computation that would constitute the actual derivation is the paper's open computational target. The structural arguments (de Sitter horizon avoiding Dirac LNH, the Hierarchy Problem framing) survive; the specific 0.02% numerical match should be read as a posteriori consistency rather than a priori proof until the trace is executed.
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New paper
Scalar Resonance and Gauge Phenomenology on the Z³ ⊗ Q₃ Error-Correcting Vacuum
Derives the defining phenomenological signatures of the Standard Model scalar sector natively from the discrete graph topology of a Z³ ⊗ Q₃ error-correcting vacuum. Treating constituent mass as information-theoretic friction — the query rate of the local QEC coin operator — yields the linear Yukawa coupling to fermions (M_f ∝ m_f); given that linear baseline, the quadratic coupling to massive vector bosons (M_V ∝ m_V²) follows as an algebraic consequence of bipartite tensor orthogonality — conditional on ANCHOR §15 item 79 (Bipartite Grassmann Trace Theorem) being promoted from Proposition to Locked. Extending to second-order virtual processes, the anomalous destructive interference and magnitude ratio of the H → γγ loop emerge from the lattice coordination number and the bipartite parity of the hypercube (Proposition tier pending §16.3 search-space audit), while a discrete Feshbach resolvent over the framework's invalid subspace naturally reproduces the non-linear, mass-dependent dynamic tracking required by continuous kinematic loop integrals.
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New paper
Discrete Graph-Cuts and Evanescent Quantum Walks: A Bipartite Derivation of Alpha Decay and Gamow Tunnelling
Reformulates alpha decay as a two-stage algorithmic process on the Z³ ⊗ Q₃ lattice. The pre-tunnelling rate — historically supplied by a phenomenological fit to the Geiger–Nuttall intercept — is derived as a geometric edge-cut problem, predicting 1.14 × 10²⁰ s⁻¹ for the minimal 2×2 cluster (Proposition tier per ANCHOR §16.3: k = 2 is the geometric floor, but the chained 1/36 Feshbach factor, Λ_QCD chiral anchor, and a₀ = ℏc/Λ_QCD lattice spacing inherit bounded search-space content). The post-detachment evanescent walk recovers the standard Gamow slope as its long-wavelength Riemann limit (Locked: Euler–Maclaurin separation of the discrete tight-binding sum). Evaluated end-to-end against ²³⁸U and ²¹²Po.
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New paper
A Topological Substrate for the Higgs Mechanism: Deriving the Fermion Yukawa Sector from Quantum Error Correction on the Z³ ⊗ Q₃ Lattice
Replaces the Standard Model's parametrically tuned Yukawa couplings with a discrete topological origin: the Higgs VEV is identified with the crystallisation of the lattice's chirality constraint (W = χ), reducing the fermion mass sector to at most one continuous parameter — the lattice spectral gap γ. The spatial shift operator drives two parallel exponential mechanisms — virtual excursions giving the Yukawa coupling y_f, and Topological Dwell Time giving the inertial mass m_f — which scale identically and so structurally derive the y_f ∝ m_f equivalence without double counting. Dressing the top-quark transitions with kinematic cutoffs natively concentrates ~49.2% of the bare decay width into surviving Gen 3 channels. Includes computational Python proofs.
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New paper
Stellar Collapse, Walk-Operator Phase Transitions, and the Resolution of Black Hole Pathologies on the Z³ ⊗ Q₃ Information Lattice
A comprehensive treatment unifying mass generation, stellar evolution, and singularity resolution on the discrete Z³ ⊗ Q₃ QEC substrate. The original "topological mass gap 3.375" headline for bare constituent masses is under active retraction (DRIFT entry M9: the M = exp(F/(2φ)) formula at Proposition tier pending §16.3 search-space audit). Neutron stars saturate the 3-colour capacity of the unit cell at approximately 4.62 × 10¹⁷ kg/m³ (the precise value being a structural-input Proposition). When metric strain exceeds topological elasticity, the event horizon manifests as a phase transition in the walk operator W = S·C — the coin freezes, energy is redirected into the shift, and the Schwarzschild space-time swap is mechanically reproduced. The revised edition adds an operator-algebra closure with five new structural results: (I) the horizon as an active QEC firewall driven by a horizon dissipator L_BH whose κ-induced phase shifts saturate the 8-bit entanglement-monogamy budget of infalling Wilson Z-strings, forcing string snapping with probability 1; (II) the Hawking temperature T_H = κ/(2πk_B) derived bottom-up via the KMS detailed-balance condition — the same mechanism that fixes the cosmological substrate temperature, unifying black-hole and de-Sitter horizon thermodynamics; (III) the central singularity replaced by a topological condensate where the bipartite gauge web collapses to a unipartite TCH of face-mated Q₃ cells and substrate time literally stops; (IV) the information paradox dissolved as the horizon truncates information systematically while Hawking Landauer exhaust balances the ledger; (V) a sharp bulk-boundary decomposition resolving the volume paradox — a 10 M⊙ core at QCD saturation density gives R_core ≈ 8.3 km in the bulk while ~10⁷⁹ snapped-string syndromes on the 2D boundary supply the Bekenstein–Hawking A/4. The Christodoulou–Rovelli linear-in-advanced-time interior-volume growth is identified as the ledger-accumulation rate between the static core and the horizon.
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