RECOGNITIONJournal articles, preprints and preliminary manuscripts from Recognition Science. Select a title to read the work.
The Journal of Chemical Physics · 165(7):074903 · 2026 · Published · Matter and molecules
Studies rod-shaped particles confined to a curved surface with their orientation fixed. Curvature forces a tilted layered packing that does not arise in the corresponding flat geometry.
The Journal of Chemical Physics · 2026 · Accepted · Matter and molecules
Maps where rod-shaped particles sit on a sphere when their orientation is locked at a chosen tilt. The tilt sets how wide the bare region around each pole is. How uniform the coverage can be made is limited by the rod length, the rod diameter and the sphere radius, and tilt cannot remove that limit.
Journal of Statistical Mechanics: Theory and Experiment · 2026(8):083204 · Published · Dynamics
Derives Boltzmann probabilities and free energy for a finite set of states weighted by recognition cost, connecting the construction to equilibrium statistical mechanics.
Mathematics (MDPI) · 14(15):2672 · 2026 · Published · Comparison and foundations
Shows how the stated consistency rules for a conserved comparison ledger determine its scale, cost and internal ratio. Counterexamples establish why each rule matters.
Mathematics (MDPI) · 14(12):2157 · 2026 · Published · Comparison and foundations
Classifies comparison costs that treat a ratio and its reciprocal equally under the stated conditions. It identifies the family in which the canonical RS cost lies.
Foundations (MDPI) · 6(2):17 · 2026 · Published · Comparison and foundations
Connects coherent comparison to paired records, discrete events and an eight-step cycle in the stated three-dimensional construction.
Mathematics (MDPI) · 14(8):1386 · 2026 · Published · Comparison and foundations
Establishes that the d’Alembert composition rule is selected by the paper’s consistency conditions. This supplies a route from combining comparisons to the canonical cost.
Mathematics (MDPI) · 14(6):935 · 2026 · Published · Comparison and foundations
Proves that the stated composition and calibration conditions uniquely select J(x) = ½(x + 1/x) − 1. Reciprocal comparisons therefore receive the same cost.
Axioms (MDPI) · 15(2):151 · 2026 · Published · Comparison and foundations
Finds where a reciprocal convex cost assigns equal cost to two matches: at their geometric mean. It also derives rules for combining matched pairs.
Advances in Pure Mathematics · 16(9):705–739 · 2026 · Published · Arithmetic
Derives arithmetic from repeated distinction under explicit formation rules and proves that faithful counting systems have the same arithmetic up to the unique map preserving their start and successor. The construction tracks the additional logical commitments used for richer number systems.
Mathematics (MDPI) · 14(14):2483 · 2026 · Published · Geometry
Derives golden-ratio and related metallic structures from the geometry generated by the reciprocal cost.
Axioms (MDPI) · 15(5):378 · 2026 · Published · Geometry
Compares several quantities at once and derives the resulting geometry. Although the comparison has several coordinates, its cost depends on one underlying direction.
Axioms (MDPI) · 15(2):90 · 2026 · Published · Geometry
Develops a geometry from acts of distinction and the relations between them, then examines the structure those relations generate.
Entropy (MDPI) · 28(11):1167 · 2026 · Published · Geometry
Asks whether a completed recognition stays distinguishable from its reversal. A closed run balances its debits and credits, so the state record alone cannot tell it from its reverse; a phase account on the complement of the recognized path can, and nonzero winding there is the same condition that selects three dimensions. With additive tally costs and one ledger posting at a time, a loop costs exactly eight units to traverse, and every higher-dimensional process in the admissible class costs more.
Mathematical and Computational Applications (MDPI) · 31(5):211 · 2026 · Published · Dynamics
Shows that the calibrated cost cosh v − 1, evaluated at log-velocity, makes the action on positive paths strongly convex with a unique closed-form minimizer. The excess action of any computed path then bounds that path’s error, and the paper derives the Newtonian limit and a cosh-dual Hamiltonian.
Mathematics (MDPI) · 14(17):3134 · 2026 · Published · Dynamics
Constructs a reversible shift on an assumed eight-sample register. A further half-cycle condition selects a four-dimensional complex sector. The remaining physical question is what selects those inputs.
Mathematics (MDPI) · 14(15):2726 · 2026 · Published · Dynamics
Finds a unique lowest-cost configuration on a finite graph when the mean and flux conditions are fixed. It also proves a stability gap controlling departures from that configuration.
Entropy (MDPI) · 28(4):477 · 2026 · Published · Gravity
Recovers Newtonian gravity with a small correction in a discrete informational model. The paper compares the model with galaxy rotation without fitting a separate parameter for each galaxy.
Symmetry (MDPI) · 18(6):962 · 2026 · Published · Particle masses
Derives charged-lepton mass ratios within a recognition composition construction with no continuously adjustable dimensionless parameters. The construction retains discrete structural inputs and the externally fixed fine-structure constant; the electron mass supplies the SI calibration.
Molecules (MDPI) · 31(15):2701 · 2026 · Published · Matter and molecules
Organizes liquid water’s hydrogen-bond timescales and terahertz bands on a golden-ratio ladder. One measured timescale anchors the ladder, and a measured participation law connects it to the physical system.
Symmetry (MDPI) · 18(7):1087 · 2026 · Published · Matter and molecules
Organizes within-period atomic-property trends on a coordinate centered on noble gases, using the golden ratio to set the progression.
Advances in Pure Mathematics · 2026 · Accepted · Geometry
Shows why transition counts cannot recover the order of a closed walk on a cube. The shortest walk with zero signed cycle counts and nonzero degree-two commutator information has 14 edges. An unbounded stack recovers every reduced loop word; no fixed finite-state reader can.
AIP Advances · 2026 · Accepted · Matter and molecules
Determines when measured spectra can distinguish molecular conformations at finite resolution. The criteria include explicit uncertainty and tests on audited quantum-chemistry ensembles.
arXiv · 2610.30146 · 2026 · arXiv preprint · Comparison and foundations
Shows that the complete equilibrium-location map on a two-site graph identifies a reciprocal cost generator with positive log curvature up to scale; unit-curvature calibration fixes the scale. A finite synthetic sweep tests how well selected generators can be distinguished under noise.
arXiv · 2608.12418 · 2026 · arXiv preprint · Comparison and foundations
Classifies reciprocal costs on positive rational numbers. A regular extension to real numbers requires all prime weights to follow a common multiple of log p.
arXiv · 2603.20205 · 2026 · arXiv preprint · Comparison and foundations
Provides a finite-window procedure for certifying exact neutrality under reciprocal cost. The stated reconstruction and projection rules are sound and locally maximal on the certifiable cases.
arXiv · 2603.13553 · 2026 · arXiv preprint · Geometry
Expresses local matching rules as cocycle conditions and connects them to a global conservation law.
Preprints.org · 202609.1990.v1 · 23 September 2026 · Preprints.org preprint · Geometry
Asks why space has three dimensions. A recognizer with finitely many binary distinctions traces a circle through all of its states. Requiring a second recognition path to stay linked with that circle, in a way no deformation undoes, holds exactly in dimension three for closed, connected, orientable substrates with vanishing first homology; the paper proves the converse and shows that closedness and the homology condition cannot be dropped.
arXiv · 2604.17775 · 2026 · arXiv preprint · Geometry
For finite connected simple graphs and even, twice-differentiable, strictly convex, nonquadratic edge costs, the nonlinear minimum-cost selector agrees with the linear Hodge projection for every edge field exactly when each edge lies on at most one simple cycle.
arXiv · 2606.07922 · 2026 · arXiv preprint · Dynamics
Tests reciprocal cost as a lattice action. The continuous version meets a proved obstruction, while a finite-valued version satisfies a key consistency condition.
arXiv · 2506.12859 · 2025 · arXiv preprint · Particle masses
Extends the recognition composition construction to the full fermion mass spectrum. The peer-reviewed charged-lepton paper gives the narrower published result for electron, muon and tau.
arXiv · 2609.02930 · 2026 · arXiv preprint · Matter and molecules
Tests a noble-gas coordinate in charge equilibration for 52 molecules. It identifies cases where one shared coordinate gives zero dipoles and shows how period-specific scales restore polarity.
arXiv · 2607.02784 · 2026 · arXiv preprint · Matter and molecules
Uses reciprocal cost to audit whether reversible enzyme-kinetics measurements obey thermodynamic consistency. The work includes curated two-sided data and a labeled error benchmark.
arXiv · 2608.18153 · 2026 · arXiv preprint · Photonic experiments
Reports eight complete, sequential CHSH passes on a commercial cloud photonic processor, each scoring above 2. Each fixed-order pass is an experimental unit. The analysis examines readout imbalance; the scores do not certify entanglement.
arXiv · 2606.18408 · 2026 · arXiv preprint · Photonic experiments
Tests nested parity-check filters for an eight-slot balance structure on a commercial cloud photonic processor.
Recognition, Necessity, and Physical Prediction
Technical book manuscript · 24 October 2026 · 140 pages
Every measurement needs distinguishable events, a physical comparison and a record that survives. This technical book follows those requirements through arithmetic, comparison cost, the golden hierarchy, space, physical sources and records, and scientific predictions.
Early manuscripts shared for discussion. These works have not been peer reviewed.
Physical Structure, Agency, and the Conditions of Living Together
Preliminary book manuscript · Not peer reviewed · 2026 · 357 pages · Ethics and economics
Develops ethics as the physical structure of relations, actions and their consequences. Love's conserving repair connects fourteen virtues to care, consent, authority, resources and shared life. Worked examples and formal propositions retain the conditions of each result and identify the connections still to be completed.
Preliminary preprint · Not peer reviewed · 24 October 2026 · 22 pages · Consciousness and physical records
Derives an exact criterion relating finite joint containment of felt occurrences to the closure of subject profiles. Under a further realization condition, an experiencing whole can contain distinct local subjects. Physical results establish matter–photon correlation and coherent record capture and retention under stated interactions. Recognition’s experiential identity, actual finite subject composition and realization of the whole-subject limit remain open connections.
Preliminary preprint · Not peer reviewed · 24 October 2026 · 9 pages · Matter and radiation
Derives energy-bearing field emission from a localized vacuum input for the native one-electron source on the infinite cubic lattice. An exact energy balance identifies the source terms that fund the emitted photon energy. The same charged hopping reads displaced field arms through a different matter current. The derivations retain the full transverse bosonic field, all four eight-state registers and the original operator domain.