Recognition Science Institute
The Papers
53 papers organized by logical dependency – the forcing chain from a single functional equation to physics, mathematics, biology, consciousness, and ethics.
Reading Order
These papers are ordered not chronologically, but structurally – following the logical Dependency Graph (DAG) of Recognition Science. Start at the root (a single functional equation on ℝ>0), ascend the "spine" of derivations, and then branch into specific domains.
Every result in Sections I–III is pure mathematics. Physical semantics enter at Section III. Each subsequent track (Particles, Gravity, Mathematics, Life, Ethics) depends only on the spine above it.
The primitive: J(x) = ½(x + x−1) − 1 – the unique cost function satisfying the Recognition Composition Law. Everything follows.
I. The Root
Foundation
The starting point: a functional equation, its unique solution, and the proof that you had no choice in the equation itself.
Peer-Reviewed · Axioms (MDPI)
Recognition Geometry
Defines the observational space, recognizers, and the recognition quotient. Space emerges as a quotient structure from recognition maps.
Preprint
The Recognition Composition Law
The single primitive: how recognition costs compose under multiplication and division. Uniquely determines J(x) = ½(x + x⁻¹) − 1.
Preprint · arXiv
Uniqueness of the Canonical Reciprocal Cost
Proves the RCL forces the unique cost function. Co-authored with Zlatanović.
Preprint · arXiv
Coherent Comparison as Information Cost
Derives the discrete ledger dynamics from the cost function. Double-entry balance, atomic ticks, closed-chain conservation.
Preprint
D'Alembert Inevitability
Polynomial consistency forces the canonical composition law. The equation is not a modeling choice – it is a theorem. Co-authored with Zlatanović and Allahyarov.
Preprint
Model-Independent Exclusivity on the Quotient State Space
Any zero-parameter framework is observationally equivalent to RS.
Preprint
Gödel's Theorem Does Not Obstruct Physical Closure
Resolves the Gödelian objection by defining truth as cost-stabilization rather than Tarskian satisfaction.
Preprint
The Recognition Stability Audit (RSA)
Formalizes the impossibility audit and certificates for existence claims. Cayley transform, Schur/Pick interpolation, 8-tick realizability.
The Coercive Projection Theorem (CPT)
Proves the unique optimal certification strategy for zero-defect membership is forced by canonical cost. Master Theorem: unique factorisation, independence of steps, optimal constants, completeness on the rational class. CPM is a theorem, not a method.
The Exclusion Theorem
The unique optimal impossibility certificate forced by canonical cost. Exclusion Master Theorem: four-step pipeline O→R→C→S is forced, independent, with unique Cayley transform. Together with CPT forms the unique complete two-sided audit.
The Law of Finite Existence
Proves the J-metric is geodesically complete (Hopf–Rinow), boundary at infinite distance, J proper. Existence is topologically forced – nonexistence is an unreachable boundary. Derives the Meta-Principle from metric completeness.
Geometry of the Multi-Component Cost Landscape
Riemannian geometry of the neutrality manifold M = {Σtᵢ = 0}. Constrained Hessian eigenvalues, Bregman = Euclidean = CPT projection, proximal contraction 1/(1+λ), properness with explicit bounds. The geometric arena of RS dynamics.
Peer-Reviewed · Axioms (MDPI)
Reciprocal Convex Costs for Ratio Matching
Axiomatic characterization of J-cost via d'Alembert functional equation. Geometric-mean decision boundaries, compositionality, sequential mediation. Washburn & Rahnamai Barghi.
Preprint · New
Recognition Algebra: The Unified Algebraic Framework
Shows the RCL forces four algebraic layers: Cost Algebra, φ-Ring ℤ[φ], Ledger Algebra (σ=0), Octave Algebra (ℤ/8ℤ, 20 modes). Proves Recognition Algebra is the initial object in the category of zero-parameter frameworks. Self-contained proofs. Lean-verified.
Master Foundation · New
The Algebra of Reality: A Categorical and Combinatorial Derivation
The primary foundational manuscript of Recognition Science. Provides the integrated proof of the two core mathematical pillars: Cost Rigidity (T5) and Hypercube Gray Cycles (8-tick). Establishes the full forcing chain from RCL to derived physical constants.
Preprint · New
Three Attributes Force a Unique Mathematical Framework
Formalizes omniscience, omnipotence, and omnipresence on a costed comparison system. Proves the core forced results (canonical J and D=3) and separates extended φ/8-tick/W=17 consequences as explicit postulates.
Preprint · New
The Derived Inevitability of the Global Co-Identity Constraint
Derives GCIC as a theorem from canonical J-cost strict convexity and connectedness of the Z^3 lattice. Shows phase mismatch has positive excess cost, proves uniform global phase at the minimum, and derives compatibility with 8-tick neutrality.
II. The Structure
Ontology
Existence, logic, dynamics, the golden ratio, and dimension – all derived, not assumed.
The Cost of Existence
Derives existence from the infinite cost of the void: J(0) → ∞. Existence is geometric necessity.
The Law of Existence
The core ontological paper linking the Coercive Projection Method, Darwin, and physical constants.
Logic From Physical Cost
Derives logical consistency (A=A) as the zero-cost ground state: J(1)=0. Logic is thermodynamic, not axiomatic.
The Recognition Operator: Beyond the Hamiltonian
Defines R̂ as fundamental dynamics. Hamiltonian is a small-ε approximation. Predicts measurable departures.
The Golden Ratio as a Universal Coherence Eigenvalue
φ as the unique fixed point of x = 1 + 1/x. Bridges Penrose tilings and RS cost dynamics. J(φ) ≈ 0.118.
Dimensional Rigidity: D=3
Three independent proofs that D=3: Alexander duality, Kepler stability, minimal dyadic synchronization. Co-authored with Zlatanović and Allahyarov.
III. The Waist
The Big Unlock
Where abstract mathematics meets physical reality: constants, measurement, coherence, and the mass spectrum.
The Derivation of Physical Constants from the Meta-Principle
The "Grand Central Station" paper deriving α, G, ℏ, c from the foundation through eight theorems T1–T8.
Reality-Native Measurements with a Single-Anchor SI Bridge
Protocol for mapping RS dimensionless quantities to SI units via a single empirical anchor.
Quantum Coherence as Gated Recognition
Derives coherence time from the 8-tick cycle. Born rule from J-cost path weights.
IV. Particles
Track A
A six-paper series deriving charged fermion masses, mixing matrices, neutrinos, the fine-structure constant, and the generation problem – all from the 3-cube.
The Origin of Mass: Mechanism
Cost geometry, recognition boundaries, and the φ-ladder. Explicit claim hygiene separating proved foundation from structural hypotheses.
Charged Fermion Masses and Flavor Mixing: Predictions
All nine charged fermion masses, CKM quark mixing, and PMNS leptonic mixing. Sub-ppm lepton accuracy. No per-species fitting.
Neutrino Masses from the Deep φ-Ladder
Fractional rungs, mass splittings, and the φ⁷ ratio. Normal hierarchy with absolute mass predictions.
The Single-Anchor Scale and Transport Discipline
Derives μ★ = 182 GeV from mass-free stationarity. Non-circularity certificate. Lean-proved no-go theorem.
The Fine-Structure Constant from Cube Geometry
α⁻¹ = 4π·11 − w₈·ln φ + 103/(102π⁵) ≈ 137.035. DFT-8 projection fully Lean-verified (zero sorry). 8.1 ppm from CODATA.
VI. Gravity
Track D · Cosmology
From baryogenesis to galaxy rotation curves – zero-parameter gravity and cosmology.
Zero-Parameter Quantum Gravity
Full quantum-gravity derivation from discrete recognition calculus.
Simplicial Ledger Topology
Proves the ledger is coordinate-free. Continuum limit recovers Einstein field equations.
The Coercive Projection Law of Gravity
Elevates ILG to a universal coercive projection principle.
Information-Limited Gravity: Source-Side Tests (Dark Energy)
Tests the ILG kernel against cosmological observables.
VII. Mathematics
Track E
The d'Alembert equation forces not just physics but mathematics itself.
A Schur Pinch Theorem for Arithmetic Ratios
Reduces RH to a single positivity condition Re 𝒥 ≥ 0 via the forced Exclusion Theorem pipeline (O→R→C→S). Cayley uniqueness, removable singularity, Maximum Modulus. Co-authored with Rahnamai Barghi.
Positivity of the Arithmetic Ratio from Canonical Cost
Derives Re 𝒥 ≥ 0 via CPT aggregation: J-cost forces τ₀ ≥ 1, bandwidth < log 2, eliminating all prime frequencies. Near-real strip identified as the domain adapter problem. Conditional on RS. Co-authored with Rahnamai Barghi.
The Law of Mathematical Inevitability
Proves the d'Alembert cost functional forces numbers, proofs, and a universal referent. Resolves Wigner's effectiveness puzzle.
Goldbach via a Mod-8 Kernel: Density-One and Conditional Dispersion
Unconditional density-one positivity and bounded gaps ≪(log N)⁸. Medium-arc dispersion saving formulated as conjecture with conditional consequences.
VIII. Life
Track F
Entropy, thermodynamics, evolution, protein folding, emotion, aging – the bridge from physics to biology.
Entropy Is an Interface
Reframes entropy as code length and resolves the reversibility paradox.
The Statistical Mechanics of Recognition
Thermodynamics of the cost function and the Recognition Temperature.
Darwin as Minimum Description Length
Unifies biological evolution with J-cost minimization (MDL).
The Recognition Instrument for Abiogenesis
Mechanism for origin of life via phi-timing gates.
A CPM Companion for Protein Folding
Instantiates CPM for the protein folding domain.
The Physics of Narrative
Stories as geodesics in moral-state space. Seven fundamental plots as topological classes.
The Recognition Algebra of Emotion
14 fundamental emotions from J-cost gradient, curvature, and σ-export. Machine-verified.
IX. Ethics
Track G
If RS is the true physics, morality is a conservation law – auditable, falsifiable, and free of tunable knobs.
Morality as a Conservation Law
Derives moral law from physical ledger invariants. σ=0 + harm as cost-externalization.
Virtues as Generators
14 admissible operators on the σ=0 manifold. The complete minimal basis for ethical dynamics.
The Geometry of Evil
Evil as geometric parasitism – maintaining stability by exporting harm. Precise, measurable, redeemable.