Neuro-Symbolic is dedicated to the practical application of advanced AI to real-world problems.
We have developed advanced reasoning architectures that combine the capabilities of neural and symbolic computing, and we are applying these to general workflows and to understanding spreadsheets.
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.
LLMs can generate plausible research claims faster than anyone can check them — the real damage is state corruption in a living research corpus: confidence promoted without support, retired results resurfacing, scripts that merely print a number passing as tests. ClaimLedger is an open-source architecture in which a generative agent may propose claim-state transitions, a deterministic evidence-bound verifier checks admissibility against six executable invariants, and only a human-controlled commit path applies them. All eight seeded failure classes are caught by their assigned verifier layers, with zero false findings on the clean corpus.
Our work is grounded in the practical deployment of advanced AI, with a continuing interest in the next generation of computational methods.
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.
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 in
one accessible account
With grateful acknowledgement to the genius of Richard Feynman and John Wheeler.
A plain-language introduction
An Accessible Account of an "It from Bit" Quantum Theory
The eleven short "easy pieces" trace the discrete-substrate programme in plain language — from the quantum vacuum and the Standard Model to Wheeler's "It from Bit" dream, the 8-qubit code, the shape that builds itself, why quarks cannot escape, the numbers, the predictions, how the paradoxes dissolve, the emergent mass hierarchies, and black holes — brought into line with the current canon. Read them piece by piece, or as one combined account. No equations to chase down.
Reality Is Built, with Inescapable Logic, from Bits
Quantum mechanics isn't a pile of bizarre rules to accept on faith — it's the only way a universe that can remember anything could possibly work. The essay climbs the argument one honest step at a time: grant only that the world can keep a record, and you are pushed, rung by rung, into complex numbers, error correction, the Born rule, and a thermodynamic arrow. The twist is the ending — quantum "weirdness" looks strange only because we live in the over-copied classical limit, where facts are so cheap to copy that we never meet the rules that govern a single, uncopied one.
The "It from Bit" Metaphor: A Graduate Introduction to the Finite QEC Substrate
The intuition layer for the finite quantum-error-correction substrate programme, written for a reader who already knows some quantum mechanics, special relativity, and the Standard Model but is new to this framework. It does not replace the equations — it supplies the picture behind them: physical objects read as stable quantum records, particles as protected patterns in a finite code, interactions as operations on those records, and the classical world as the part of the quantum world that has become robust enough to remember itself. The paper deliberately separates three levels — the standard physics it uses (Hilbert space, amplitudes, decoherence, gauge fields, relativistic propagation), the coding-theoretic claims it argues (why the minimal balanced protected record cell must be the unique self-dual doubly-even [8,4,4] code — a byte of eight qubits), and the speculative bridges to particle spectra, the dark sector, gravity, and cosmology that remain under construction. Along the way: colour read as spatial orientation, the electron as the colourless ground cell, wave–particle duality as the difference between how a possibility propagates and how a record is written, and a closing field guide that, for each hard question, states what the Standard Model says, why that answer is conceptually incomplete or technically hard, and what the framework offers instead.
A consolidated, self-contained account of what dark matter could be in the finite-QEC substrate: not a new particle but crystallisation debris — defects left behind when the lattice ordered too quickly to heal. The June 2026 canon narrows the claim: this K04 fossil is a pinned dark-sector component and falsification target, not the dominant mobile dark matter and not the CMB-third-peak carrier (that budget moves to a separate R4 zero-mode / sterile branch). Four questions answered for a graduate reader. Taxonomy: a defect is permanently locked only if it winds the system, so the smallest indestructible object is a one-dimensional string, not a point particle — every finite defect can heal. Mobility: the locked objects are extended and frozen, ruling them out as a collisionless particle gas but exactly what large-scale structure should do. Energy scale: the two defect tensions are computed exactly (a string costs w₄+4w₆ per step, a frustrated domain wall 2w₄+12w₆ per cut cell), and the cell crystal is hugely degenerate so most walls cost nothing. Abundance: a Kibble–Zurek picture gives the clean, falsifiable relic density ρ_dark ∼ (4/7) σ_wall/ξ(R), the 4/7 share of energy-costing walls being exact; the remaining unknowns reduce to the cooling law that fixes ξ(R) and the lattice-to-physical unit conversion. Every numerical claim is reproduced by a short self-checking program.
A Finite-QEC Substrate Program for Particle Physics and Cosmology: Current Canon and Audit Methodology
The shortest map of the current canon. Particle physics and cosmology are modelled as consequences of a finite quantum-error-correcting register geometry rather than fields on a pre-assumed continuum: an eight-bit local code crystallises into a register-bearing cubic phase with a finite service ledger for boundary and bulk correction events. The load-bearing themes are a now-canonical 28 = 2×14 service clock, a proton-primary route in which the measured proton mass fixes the chiral scale and the framework predicts G, M_P and H₀, a dynamic dark-energy branch w(a) = −1 + a/28, and the n_s = 27/28 inflationary tilt. The paper states plainly what is exact finite arithmetic, what is computed, what is conditional, and what has been retired — including its own standing falsification targets.
Foundations and Methodology for a Finite-QEC Substrate: Code, Crystallisation, Ledgers, and Audit Protocol
The rules of construction and the audit protocol. A finite register system whose ordered crystalline phase supplies the visible substrate and whose correction, strain, and boundary ledgers decide which quantities become physical observables. The eight-bit cell is now derived rather than assumed — the self-dual doubly-even [8,4,4] code is forced as the unique minimal balanced record-cell — and the bare service rate α₀ = 1/137 is derived from the symmetric record-pair alphabet (Sym²(16) = 136, plus the idle channel). Defines the bi-cubic crystallisation, the syndrome/strain distinction, the 28 = 2×14 service clock, and the locked / computed / conditional / retired / open classification that makes every later coefficient auditable.
Matter, Gauge Structure, and Spectroscopy in the Finite-QEC Substrate
The matter-sector companion. Exact finite identities — charge bookkeeping, anomaly cancellation, the separation of spatial, colour, generation and repair-axis roles, and the chiral charge-cube identity ∑Q_L³ = −2/9 — sit alongside more conditional continuum and spectroscopy results. The paper states clearly which parts are exact finite arithmetic, which are reproducible computations, and which remain continuum-lift or operator-definition frontiers.
Gravity, Horizons, and Black Holes in the Finite-QEC Substrate
The gravity and horizon canon, now proton-primary: the measured proton mass fixes Λ_P = m_p/(2√2) and the QEC/horizon chain predicts G, M_P and H₀ (with H₀ cancelling from the final input ledger). The Bekenstein severing-channel factor sharpens from a loose O(1) number to C = 55/8; the black-hole sector gains a finite-cell isometry, a Schwarzschild radial shell-channel form, and a finite Hawking-ladder verification. Falsifiable: H₀ = 67.27 km s⁻¹ Mpc⁻¹ and Ω_Λ = 12π/55 = 0.6854.
Dark Matter, MOND, and K04 Debris in the Finite-QEC Substrate
The dark sector resolves into three separated carriers — boot-frozen K04 domain-wall fossils that gravitate but are pinned (a durable relic, not the mobile halo); a scheduler-clocked R4/MOND line-current route reproducing the cubic AQUAL action and the baryonic Tully–Fisher relation; and a conserved R4 zero-mode reservoir plus the 17.7 keV sterile-neutrino branch, which carries the pressureless CMB and halo budget. The earlier island-floor abundance is now archival (K04-as-halo is killed by pinning). Each branch carries a stated kill condition — the MOND branch on its scheduler premise and the Tully–Fisher normalisation, the zero-mode/CMB completion on behaving as pressureless dust without double-counting R4/MOND, and cluster-scale lensing offsets that discriminate pinned from collisionless wall debris.
Cosmology, Dark Energy, and Inflation in the Finite-QEC Substrate
Cosmology, dark energy, and inflation under stricter labels than the historical papers used — these sectors were the main source of earlier overclaims. The dark-energy equation of state reduces to w(a) = −1 + a/28 (positive activation excludes phantom behaviour); the inflationary tilt has a conditional scalar-clock route to n_s = 27/28; and the cosmological constant splits into a horizon/Dirac scale relation and a newer generation-vertex computation landing at ρ_Λ ≈ 1.0019 ρ_obs. A sharper program, not a closed one.
Special and General Relativity from the Finite-QEC Substrate
How relativity, in both its forms, is recovered as an emergent property of the substrate. Special relativity is the universal reversible propagation clock — the invariant speed c is one lattice step per service tick, so internal observers infer Lorentz symmetry even though the microscopic update has a preferred order. General relativity is the coarse-grained covariance of that clock under strain: the metric perturbation is the strain field, and the linearised Bianchi identity and the substrate's strain-ledger conservation become one statement, making G_μν = 8πG T_μν a consistent field equation rather than an imposed one. The equivalence principle follows once gravity couples to the full energy (kinetic plus confinement/Yukawa mass), and the program's four horizon objects — Bekenstein area law, Hawking ladder, firewall isometry, gravitational source — turn out to be one register-syndrome read four ways.
Going Deeper into a Black Hole: The Horizon as a Quantum-Error-Correcting Record
A deep-dive companion to the gravity & black-hole paper: the horizon as a finite quantum-error-correcting record governed by one object, the three-cube coboundary δ. The Bekenstein area law turns out to be exactly equivalent to a microscopic records rate — each horizon node carries ~10³⁸ nats while an eight-bit cell holds at most 8 ln 2 ≈ 5.5, so the area entropy cannot be stored (it fails by 37–45 orders of magnitude) and must instead flow. The area coefficient is fixed at C = 55/8 by 56 directed monogamy incidences modulo one blind slot under AGL(3,2) covariance, predicting Ω_Λ = 12π/55 = 0.6854 and a discrete Hawking line spectrum with gap F_min = 3. (An earlier ≈0.31-Eddington horizon-bandwidth reading is now withdrawn — the horizon is a post-service record-writing channel, not a real-time bottleneck, so super-Eddington accretors are not a falsifier.)
Baryogenesis as a Quantum-Error-Correction Residue
A focused companion that reads the matter–antimatter asymmetry off the code itself — not a fine-tuned initial excess but an error rate. At the cosmological boot the QEC engine prunes a chaotic state onto the [8,4,4] code and Landauer-dumps the corrected bulk as the photon bath; almost all matter and antimatter are erased back to radiation, and the surviving baryon number is the residue of weight-4 logical faults that slip past the stabilizers undetected. The minimum undetectable fault has weight equal to the code distance d = 4, giving an α₀⁴ suppression, and a colour-singlet veto over the 14 weight-4 channels fixes a 3/14 branching — so η = (3/14)α₀⁴ = 6.08×10⁻¹⁰, a 0.9σ match to the Planck baryon-to-photon ratio with no free parameter once α₀ is fixed. The three Sakharov conditions map onto three intrinsic features of the substrate; the absolute matter label remains a discrete geometric convention, as in any CPT-respecting theory.
Short companion notes (June 2026) that each develop a single thread of the canon — measurement, expansion, the constant ledger, holography, the past hypothesis, and an adversarial falsification sheet.
Working note
The Born Rule as a Closed Record Pair: Measurement, Objectivity, and the Arrow of Time
A measurement is not primitive — it is the substrate recording a syndrome. The current canon now closes the Born rule inside the accepted complex-QEC substrate, two complementary ways: repeatable syndrome readout gives orthogonal, non-contextual projectors, so Gleason-type uniqueness fixes pᵢ = Tr(ρPᵢ); and the Naimark/Stinespring record map makes measurement an isometric copying of syndrome facts whose closed forward/backward history leaves the surviving diagonal |A|². What remains open is no longer the Born measure itself but the deeper reconstruction floor — why nature is a complex, locally tomographic, record-writing QEC system at all.
Expansion as Boundary Printing: One Printer for Inflation, Dark Energy and Dark Matter
Cosmic expansion reframed not as a stretching metric but as Holographic Boundary Crystallization — printing fresh zero-entropy cells at the horizon to stay under the Bekenstein bound, with inflation and dark energy the same printer at different clock rates. The scalar sector (A_s, n_s, e-folds, w₀) follows from two printer parameters and lands within 1σ of Planck; the tensor sector gives a primordial-tensor null, r ∼ 2×10⁻⁹ (no observable B-modes). Falsifiable by any B-mode detection at r ∼ 10⁻³–10⁻¹·⁴.
The Constant Ledger: Physical Constants as Crystallisation Readouts
Turns into a ledger the expectation that the “fundamental constants” are readouts of one frozen scale and a discrete code. A single anchor — Λ_QCD, fixed by the proton mass — yields every other dimensionful constant (lattice spacing, Planck mass, G, dark-energy density, a 17.7 keV sterile-neutrino mass) to between 0.02% and a fraction of a sigma; the dimensionless readouts are fixed code integers and fractions (137, 55/8, 12π/55, 27/28, 1/28, T = 9); a short live list (H₀, ρ_Λ, w(a)) are horizon-service rates. Sharp corollary: the frozen constants (G, α) must not drift, while w(a) = −1 + a/28 must evolve.
A Falsification Sheet for the Finite-QEC Substrate Programme
A deliberately adversarial map of the simplest empirical ways to kill, demote, or constrain the framework. Near-term kill switches: a confirmed primordial tensor signal at r ≳ 10⁻³; a dark-energy reconstruction excluding w(a) = −1 + a/28; a scalar tilt excluding n_s = 27/28; a secular drift in G or α; a neutron EDM far above 10⁻³¹ e·cm with no extra CP source; or dark matter shown to be a freely streaming particle gas. Several tests are branch-level (the 17.7 keV sterile neutrino, the R4/MOND line law, the K04 debris walls) and would retire a branch without collapsing the matter sector.
A Holographic Error-Correcting Code in de Sitter Space: Relation to AdS/CFT
A graduate-level bridge between the substrate and AdS/CFT holographic error correction. A three-part verdict: they share a deep principle (bulk-in-boundary error correction) and a deep law (entanglement entropy = geometric area), but differ in two checkable ways — the substrate's code is not a HaPPY perfect tensor, and its spacetime is flat with a de Sitter cosmology, not anti-de Sitter. The natural bridge is therefore de Sitter / cosmological-horizon holography, where the substrate offers a concrete microscopic holographic code with explicit boundary dynamics; the Ryu–Takayanagi area law is verified directly on the lattice.
The Past Hypothesis as Substrate Boot: Why the Universe Began Ordered, and Is Not a Boltzmann Brain
The Second Law holds only because the universe began in a low-entropy state that standard cosmology must simply posit. Here the posit is not needed: entropy is carried by recorded error-syndrome bits, and before the error-correcting machinery switches on there are none, so entropy is zero by construction. The same mechanism defuses the Boltzmann-brain objection — such brains can only dominate in eternal equilibrium, which this driven, continuously self-minting substrate (w(a) = −1 + a/28 ≠ −1) never reaches. The reframe is firm; the Boltzmann-brain suppression is new and conditional.
Quantum Darwinism as Syndrome Broadcast: A Finite-QEC Reconstruction of Objective Records
Why does the everyday world look objective — the same for every observer? Quantum Darwinism already answers that classical facts are information about einselected pointer states copied redundantly into many fragments of the environment; this note reconstructs that mechanism from the single premise of stable local records. Repeatable records force orthogonal sectors; finite noise forces an error-correcting code; syndrome extraction selects the pointer basis; syndrome fan-out supplies the redundant environmental copies; and finite, reusable registers make the irreversible part of measurement a Landauer reset. In the ideal syndrome-broadcast limit the characteristic Darwinist plateau is immediate — any non-empty proper fragment of the environment carries the full classical syndrome entropy, while the extra quantum phase information lives only in the whole. Deliberately modest: it does not replace decoherence theory, derive the Born rule, or solve the measurement problem; it closes by mapping the programme's older geometry-first language (cells, strain, defects) onto the finite-QEC vocabulary (code, syndrome, ledger).
Methodology — the runnable tool that audits the canon
Relocating Trust to the Verifier: A Truth-Maintenance System for an AI-Generated Theory of Everything
The runnable operationalisation of the Rigid Ground Truth methodology that produced the canon 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 (296 registry records, 477 cited scripts), it mechanically catches un-propagated retractions, evidence regressions, seductive numerical coincidences, and live claims standing on retracted foundations; at the latest refresh the read-only check reports 0 hard findings and 27 soft contamination flags. The paper is explicit about the limit: the system makes such research auditable and constrained, not correct — only forward prediction closes the remaining gap.
Earlier framework papers (the Holographic Circlette series and its
companion notes) have been retired to an archive pending revision under
the audit methodology. The six papers above plus the methodology tool
below are the current canon.
