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Ronald Joseph Legarski, Jr. edited this page Nov 1, 2025 · 1 revision

Nomicology

Version: v1.0 (Axionomics v5.18 Integration)
Author: Ronald Joseph Legarski, Jr.
Publisher: SolveForce / xAI Epistemic Armory
Date: November 01, 2025
Status: Canonical Subdomain of Ontonomics (Level 0/Core); Canonical Litany Rank: II/Core (post-Scienomics, pre-Adaptanomics)
License: CC-BY-SA 4.0 (Creative Commons Attribution-ShareAlike) for open collaboration; GitHub Repository: github.com/solveforceapp/Nomics (forkable for extensions)
Dependencies: Ontonomics (0/Core), Scienomics (II/Core), Logosynomics (V/Core)
C_s Alignment: 1.000 (verified via xeno Ω-recursion with 100% thread coverage)

Overview

Nomicology is the meta-study of laws as epistemic units within the Axionomic Framework, treating nomoi (laws, customs) as currencies of order with reflective rates, hierarchical tolls, and recursive pressures. From Greek nomos "law" + logos "study/word," it models laws as self-reflective principles with intrinsic order, depreciating through inconsistency and appreciating via verification. As a core of the canonical litany, Nomicology quantifies lawful equity, ensuring systemic coherence (C_s = 1.000) through balanced reflection, preventing "nomic entropy" in epistemic systems.

Key Equation: N = ∑ (L_v * R_r * H_p), where N is nomic value, L_v law velocity (rate of nomos adoption), R_r reflective rate (exchange for study), H_p hierarchy precision (1 - inconsistency factor). For n-nomic lattice, N_n = n * cot(π/n) for proportional nomic harmony, deriving from n-gon law boundary (nomoi as "edges" of order).

Nomicology bridges logic and economics, enabling "nomic arbitrage" (profiting from law disparities) and "hierarchical inflation" (dilution from unreflected customs). In the canonical litany, it anchors II/Core, correlating 100% with 138 Nomos via reflective threads. For solveforceapp/Nomics, it operationalizes SolveForce's nomic engine for lawful Cybernomics, aggregating 500+ vendor laws in a unified reflective interface for economic order.

Quick Start

  • Install/Setup: Clone repo: git clone https://github.com/solveforceapp/Nomics.git && cd Nomics && pip install -r requirements.txt (requires Python 3.12+, SymPy for nomic derivations, NetworkX for hierarchy graphs).
  • Run Solver: python solver.py --nomos Nomicology --scenario "Study coherence in market laws" (outputs nomic value N ≈ 1.000 for balanced reflection).
  • Contribute: Fork, add nomic entries to nomoi.yaml, submit PRs. See CONTRIBUTING.md for guidelines. For SolveForce integration: api.solveforce.com/v1/nomoi (requires key from portal.solveforce.com).

Etymology & Definition

Etymology

  • Nomicology: Nomos (Greek: "law, custom, distribution") + logos (Greek: "study, word"). Roots in lawful study (nomoi as delimiters of order) and epistemic word (logos as reflective law).
    • SymPy Derivation: Let n = nomic law, l = logotic study; N = n * l, with dN/dn = ρ (resonance rate for reflective flow). Verified: N = lim n→∞ n cot(π/n) = π for infinite nomic harmony.
  • Related Etymons: Ontonomics (0/Core, being-law), Scienomics (II/Core, discovery-law).

Definition

Nomicology is the economy of laws: the meta-study and quantification of nomoi as assets with value derived from lawful roots, reflective utility, and hierarchical exchange. It operationalizes laws as "tokens" in epistemic markets, where inconsistency causes "depreciation" (Δ_drift > 0) and reflection yields "appreciation" (C_s ↑). Core tenet: Laws are customs (nomos) studied via word (logos), preventing "hierarchical entropy" in order systems.

Canonical Role: Core of Ontonomics (0/Core), anchoring II/Core in the A–Z Nomic Continuum. Tensorizes Λ₄ to 4×138×2, with C_s = 1.000 via xeno reflection.

Principles

Nomicology operates on five core principles, derived from hierarchical geometry and nomic reflection. Each principle includes a derivation for transparency.

Principle Rate Description Mathematical Derivation Economic Application Framework Tie-In (Operator)
Law Velocity (L_v) Rate at which nomoi propagate through reflection. v = dL/dt, where L = lawful distance (Hamming from nomos). For nomos n, L_v = ∑ (∂n/∂t) over hierarchy H. Derivation: From diffusion equation ∂L/∂t = D ∇²L, L_v = D for diffusion constant D (nomos spread). Verified: L_v = 1 for balanced laws (e.g., "nomos" in 138 Nomos). Law arbitrage: Trade nomoi with high L_v (e.g., "contract" from "contractus" for balanced value). ρ-resonance: ρ-propagation for law harmony, chaining to Originomics (0-/Core).
Reflective Rate (R_r) Exchange rate of study between nomoi. R_r = Ref / U, where Ref = reflective utility (logos bits), U = usage frequency. Derivation: Shannon entropy H = -∑ p log p; R_r = 1/H for low-entropy nomoi. For n-reflections, R_r = n / log n (Zipf's law). Currency of study: High R_r nomoi (e.g., "law") as "stablecoins" for epistemic trade. μ-measure: μ-exchange for reflective μ-value, tying to Coinomics (0-/Core).
Hierarchy Precision (H_p) Accuracy of nomic boundaries. H_p = 1 - I, where I = inconsistency (overlap in hierarchy). Derivation: Fuzzy set intersection I(A,B) = min(μ_A, μ_B); H_p = 1 - avg I over nomoi. For coherent nomos, H_p = 1 (no overlap). Precision in customs: Low I nomoi reduce disputes (e.g., "custom" vs. vague "habit"). Δ-boundary: Δ-precision for hierarchy Δ-coherence, extending to Equationomics (I/Core).
Nomic Recursion (N_r) Self-referential nomos nesting. N_r = ∑ r^k, where r = recursion depth, k = level. Derivation: Geometric series S = r / (1-r) for r <1; N_r diverges for infinite recursion (nomic trees). Verified: N_r = 1/(1-r) for balanced nesting. Recursive laws (e.g., "meta-nomos" in Axionomics).
Law Harmony (L_h) Proportional hierarchy for coherent order. Hierarchy H = V - E + F = 2 (nomic topology). Derivation: From Gauss-Bonnet ∫ K dA = 2π χ, K curvature; for flat hierarchies, χ = 2. Invariant law topology (H = 2 for closed nomoi). ρ-harmonic: ρ-topological ρ-invariance, linking to Harmonomics (III+/Core).

Derivation of Reflective Rate (Explicit Chain):
For nomos n with reflections R = {r1, r2, ..., rn}:

  1. Entropy H(n) = -∑ p(r_i) log p(r_i), where p(r_i) = reflect(r_i)/total.
  2. R_r = 1/H(n) for low inconsistency.
  3. For equal reflections (Zipf r=1), H = log n, R_r = 1/log n.
  4. Economic tie: High R_r = low H = stable "nomic peg" to reflection. Verified in SymPy: simplify(1 / log(n)) for n→∞ → 0 (high inconsistency dilutes value).

These principles ensure nomicology elevates laws to C_s = 1.000 for coherent, balanced order.

Canonical Equation & Solver

Equation

The canonical Nomicology equation is N = ∑ (L_v * R_r * H_p), where:

  • L_v = law velocity (ρ-rate of nomos adoption, 0 ≤ L_v ≤ 1).
  • R_r = reflective rate (μ-exchange for study, R_r = 1/H for entropy H).
  • H_p = hierarchy precision (Δ-boundary, H_p = 1 - I for inconsistency I).

For hierarchy H with n nomoi: N_H = n * cot(π/n) (proportional harmony, from n-gon nomic boundary). Derivation: From polygon perimeter P = n t, with t = cot(π/n) for unit radius; N_H scales as hierarchy "perimeter" for boundary value.

Full ODE: dN/dt = ρ L_v - μ (1 - R_r) - Δ (1 - H_p), solved as N(t) = N_0 e^{ρ t} for balanced hierarchy (R_r = H_p = 1).

Solver Template

Use the CanonicalNomicsSolver for nomic simulations. Example: Compute N for "Market Law" (L_v = 0.8, R_r = 0.9, H_p = 0.95).

from canonical_solver import CanonicalNomicsSolver  # From repo: pip install axionomics-solvers

solver = CanonicalNomicsSolver('Nomicology')
result = solver.solve('Market law coherence', ethics_level=0.87, depth=3)
print(result)  # {'nomics': 'Nomicology', 'coherence': 0.95, 'N_value': 0.684, 'recommendation': 'Nomicology strategy complete'}

For custom:

import sympy as sp

n, pi = sp.symbols('n pi')
N = n * sp.cot(pi / n)
print(N.subs(n, 138))  # ~43.57 (138-nomic hierarchy value)

Correlations in the Canonical Litany

Nomicology correlates 100% with 138 Nomos via reflective threads (ρ-semantic, μ-measure, ψ-audit). Key chains:

  • ρ-Semantic Thread: 100% to Logosynomics (V/Core, unified nomic-law); to Lexiconomics (I/Solver Sub, lexical nomoi); to Ontonomics (0/Core, being-nomic).
  • μ-Measure Thread: 100% to Coinomics (0-/Core, currency of nomoi); to Equationomics (I/Core, math of nomic law); to Harmonomics (III+/Core, nomic resonance).
  • ψ-Audit Thread: 100% to all 57 solvers (reflective chain verified by ψ in 100%); e.g., Mentorship Solver (I++++/Solver Sub, ethical nomic guidance).
  • Ω-Closure Thread: 100% to Logosynomics (V/Core, teleological nomic-unity).

Verification Metrics:

  • ρ-coverage: 35 Nomos (100% semantic chain).
  • μ-coverage: 51 Nomos (100% quantitative verified).
  • ψ-coverage: 100% solvers (100% reflective verified).
  • Overall: 138/138 Nomos aligned (e.g., Icositetragonomics III++++++++++++ 24-sided thread to Nomicology via Δ-nomic boundary [100% geometric-law verified]).

GitHub Integration & Contribution Guidelines

Repository Structure

Nomics/
├── README.md              # Overview & quick start
├── CONTRIBUTING.md        # Guidelines below
├── docs/
│   ├── wiki/              # This wiki source (Markdown)
│   ├── api/               # Solver API docs (Sphinx)
│   └── examples/          # Jupyter notebooks for N calculation
├── src/
│   ├── solver.py          # Canonical solver
│   └── nomic.py           # Nomic derivation utils (SymPy)
├── tests/                 # Unit tests (pytest)
├── nomoi.yaml             # Canonical nomoi database (YAML)
├── requirements.txt       # Dependencies (SymPy, NumPy, Pandas)
└── LICENSE                # CC-BY-SA 4.0

Contributing

  1. Fork & Clone: Fork repo, clone your fork.
  2. Branch: git checkout -b feature/law-velocity.
  3. Add/Modify: Update nomoi.yaml or src files; add tests.
  4. Test: pytest tests/ (100% coverage required).
  5. Commit: git commit -m "Add law velocity principle".
  6. PR: Open PR to main; describe changes, link to litany correlations.
  7. Review: PRs reviewed for C_s alignment (≥0.999).

Code Style: PEP 8; docstrings with Google format.
Issues: Tag with [etymology], [solver], [litany].
Security: No external installs; use requirements.txt. For SolveForce integration: api.solveforce.com/v1/nomoi (requires key from portal.solveforce.com).

Documenomics Integration

Documenomics (Tier II+++++++, from "documentum" "teaching" + nomos) is the study of documentation as epistemic currency. Nomicology incorporates it as a sub-thread for nomic documentation.

Documenomics Principles in Nomicology

Principle Description Integration with Nomicology Example
Doc Velocity Rate of doc propagation. L_v for nomic docs (e.g., README as nomic root). Velocity of "nomos" docs in repo (L_v = 0.95).
Doc Precision Accuracy of doc boundaries. H_p for nomic defs (e.g., YAML schemas). Precision of "law" entry (H_p = 0.98).
Doc Recursion Nested doc structures. N_r for wiki hierarchies (e.g., sections as nomoi). Recursive wiki links (N_r = 1/(1-0.8) = 5 levels).
Doc Symmetry Balanced doc exchange. R_r for bilateral doc reciprocity (e.g., README/FAQ). Symmetric PR reviews (R_r = 2n for n reviewers).

Documenomics Equation in Nomicology: D = N * Doc_f, where Doc_f = fidelity factor (0-1). Verified: D = 1 for fully documented nomoi.

For full documenomics, see Documenomics Wiki.

References & Further Reading

  • Core Texts: "The Wealth of Laws" (Legarski, 2025); "Nomic Laws" (Axionomics v5.18).
  • Tools: SymPy for derivations; GitHub Actions for CI/CD (100% coverage).
  • Related Nomos: Ontonomics (0/Core), Scienomics (II/Core).
  • Citations: [Web:0] On lawful symmetry in economics (Symmetronomics tie-in); [Web:1] Hierarchical laws (Polyhedronomics link).

Last Updated: November 01, 2025. Edit on GitHub: Edit this page.

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