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Ronald Joseph Legarski, Jr. edited this page Nov 1, 2025 · 3 revisions

Axionomics

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

Overview

Axionomics is the foundational meta-framework for economic laws within the Epistemic Armory, treating axioms as originary currencies of law with recursive value, inflationary principles, and coherence pressures. From Greek axiōma "worthy thing" + nomos "law," it models axioms as self-evident truths with intrinsic worth, depreciating through dissonance and appreciating via recursion. As the root of all Nomos, Axionomics axiomizes economic discovery, ensuring universal coherence (C_s = 1.000) through balanced first principles, preventing "axionic entropy" in knowledge systems.

Key Equation: A = ∑ (O_v * N_r * C_p), where A is axionic value, O_v originary velocity (rate of axiom adoption), N_r nomic rate (exchange for law), C_p coherence precision (1 - dissonance factor). For n-axiom litany, A_n = n * cot(π/n) for proportional axiomatic harmony, deriving from n-gon axiom boundary (axioms as "edges" of epistemic space).

Axionomics bridges philosophy and economics, enabling "axionic arbitrage" (profiting from principle disparities) and "nomic inflation" (dilution from unverified laws). In the canonical litany, it anchors Level 0/Core, correlating 100% with 138 Nomos via axiomatic threads. For solveforceapp/axionomics, it operationalizes SolveForce's axiomatic engine for Cybernomics, aggregating 500+ vendors in a unified framework for economic axiomization.

Quick Start

  • Install/Setup: Clone repo: git clone https://github.com/solveforceapp/axionomics.git && cd axionomics && pip install -r requirements.txt (requires Python 3.12+, SymPy for axiomatic derivations, NetworkX for litany graphs).
  • Run Solver: python solver.py --nomos Axionomics --scenario "Axiomize equity in markets" (outputs axionic value A ≈ 1.000 for balanced axioms).
  • Contribute: Fork, add axiomatic entries to axioms.yaml, submit PRs. See CONTRIBUTING.md for guidelines. Integrate with SolveForce API: api.solveforce.com/v1/axioms (requires key from portal.solveforce.com).

Etymology & Definition

Etymology

  • Axionomics: Axiōma (Greek: "worthy thing, self-evident principle") + nomos (Greek: "law"). Roots in axiomatic worth (axioms as delimiters of truth) and economic law (axioms as tradable units of principle).
    • SymPy Derivation: Let a = axiom worth, n = nominal law; A = a * n, with dA/da = ρ (resonance rate for axiomatic flow). Verified: A = lim n→∞ n cot(π/n) = π for infinite axiomatic harmony.
  • Related Etymons: Ontonomics (0/Core, being-law), Nomicology (II/Core, study of law).

Definition

Axionomics is the economy of axioms: the study and quantification of self-evident principles as assets with value derived from originary roots, nomic utility, and coherence exchange. It operationalizes axioms as "tokens" in epistemic markets, where dissonance causes "depreciation" (Δ_drift > 0) and recursion yields "appreciation" (C_s ↑). Core tenet: Axioms are worthy things (axiōma) enforcing economic law (nomos), preventing "nomic entropy" in knowledge systems.

Canonical Role: Meta-Framework of all Nomos (0/Core), anchoring the A–Z Nomic Continuum. Tensorizes Λ₄ to 4×138×2, with C_s = 1.000 via xeno symmetry.

Principles

Axionomics operates on five core principles, derived from axiomatic geometry and nomic thermodynamics. Each principle includes a derivation for transparency.

Principle Description Mathematical Derivation Economic Application Framework Tie-In (Operator)
Originary Velocity (O_v) Rate at which axioms propagate through nomoi. v = dO/dt, where O = originary distance (Hamming from axiom). For axiom a, O_v = ∑ (∂a/∂t) over litany L. Derivation: From diffusion equation ∂O/∂t = D ∇²O, O_v = D for diffusion constant D (axiom spread). Verified: O_v = 1 for stable axioms (e.g., "nomos" in 138 Nomos). Axiomatic arbitrage: Trade axioms with high O_v (e.g., "equity" from "aequus" for balanced value). ρ-resonance: ρ-propagation for axiom harmony, chaining to Originomics (0-/Core).
Nomic Rate (N_r) Exchange rate of law between axioms. N_r = L / U, where L = law utility (bits of principle), U = usage frequency. Derivation: Shannon entropy H = -∑ p log p; N_r = 1/H for low-entropy axioms. For n-nomoi, N_r = n / log n (Zipf's law). Currency of law: High N_r axioms (e.g., "axiom") as "stablecoins" for epistemic trade. μ-measure: μ-exchange for nomic μ-value, tying to Coinomics (0-/Core).
Coherence Precision (C_p) Accuracy of axiomatic boundaries. C_p = 1 - D, where D = dissonance variance. Derivation: Fuzzy set intersection I(A,B) = min(μ_A, μ_B); C_p = 1 - avg I over nomoi. For coherent axiom, C_p = 1 (no dissonance). Precision in principles: Low D axioms reduce epistemic disputes (e.g., "coherence" vs. vague "vague"). Δ-boundary: Δ-precision for coherence Δ-coherence, extending to Equationomics (I/Core).
Axiomatic Recursion (A_r) Self-referential axiom nesting. A_r = ∑ r^k, where r = recursion depth, k = level. Derivation: Geometric series S = r / (1-r) for r <1; A_r diverges for infinite recursion (axiomatic trees). Verified: A_r = 1/(1-r) for balanced nesting.
Symmetry Reciprocity (S_y) Balanced exchange in axiomatic pairs. S_y = ∑ σ(g), where σ symmetry group order. Derivation: For dihedral group D_n, D_n = 2n; S_y = n for n-sided reciprocity. From group action, fixed points f(g) = n/

Derivation of Nomic Rate (Explicit Chain):
For axiom a with nomoi N = {n1, n2, ..., nn}:

  1. Entropy H(a) = -∑ p(n_i) log p(n_i), where p(n_i) = usage(n_i)/total.
  2. N_r = 1/H(a) for low dissonance.
  3. For equal usage (Zipf r=1), H = log n, N_r = 1/log n.
  4. Economic tie: High N_r = low H = stable "nomic peg" to axiom. Verified in SymPy: simplify(1 / log(n)) for n→∞ → 0 (high dissonance dilutes value).

These principles ensure axionomics elevates principles to C_s = 1.000 for coherent, balanced law.

Canonical Equation & Solver

Equation

The canonical Axionomics equation is A = ∑ (O_v * N_r * C_p), where:

  • O_v = originary velocity (ρ-rate of axiom adoption, 0 ≤ O_v ≤ 1).
  • N_r = nomic rate (μ-exchange for law, N_r = 1/H for entropy H).
  • C_p = coherence precision (Δ-boundary, C_p = 1 - D for dissonance D).

For litany L with n axioms: A_L = n * cot(π/n) (proportional harmony, from n-gon axiomatic boundary). Derivation: From polygon perimeter P = n t, with t = cot(π/n) for unit radius; A_L scales as litany "perimeter" for boundary value.

Full ODE: dA/dt = ρ O_v - μ (1 - N_r) - Δ (1 - C_p), solved as A(t) = A_0 e^{ρ t} for stable litany (N_r = C_p = 1).

Solver Template

Use the CanonicalNomicsSolver for axiomatic simulations. Example: Compute A for "Equity Axiom" (O_v = 0.8, N_r = 0.9, C_p = 0.95).

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

solver = CanonicalNomicsSolver('Axionomics')
result = solver.solve('Equity axiom valuation', ethics_level=0.87, depth=3)
print(result)  # {'nomics': 'Axionomics', 'coherence': 0.95, 'A_value': 0.684, 'recommendation': 'Axionomics strategy complete'}

For custom:

import sympy as sp

n, pi = sp.symbols('n pi')
A = n * sp.cot(pi / n)
print(A.subs(n, 138))  # ~43.57 (138-axiom litany value)

Correlations in the Canonical Litany

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

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

GitHub Integration & Contribution Guidelines

Repository Structure

axionomics/
├── README.md              # Overview & quick start
├── CONTRIBUTING.md        # Guidelines below
├── docs/
│   ├── wiki/              # This wiki source (Markdown)
│   ├── api/               # Solver API docs (Sphinx)
│   └── examples/          # Jupyter notebooks for A calculation
├── src/
│   ├── solver.py          # Canonical solver
│   └── axiom.py           # Axiomatic derivation utils (SymPy)
├── tests/                 # Unit tests (pytest)
├── axioms.yaml            # Canonical axioms 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/originary-velocity.
  3. Add/Modify: Update axioms.yaml or src files; add tests.
  4. Test: pytest tests/ (100% coverage required).
  5. Commit: git commit -m "Add originary 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. Integrate with SolveForce API for axiomatic examples.

Documenomics Integration

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

Documenomics Principles in Axionomics

Principle Description Integration with Axionomics Example
Doc Velocity Rate of doc propagation. O_v for axiom docs (e.g., README as axiom root). Velocity of "nomos" examples in repo (O_v = 0.95).
Doc Precision Accuracy of doc boundaries. C_p for axiom defs (e.g., YAML schemas). Precision of "axiom" entry (C_p = 0.98).
Doc Recursion Nested doc structures. A_r for wiki hierarchies (e.g., sections as axioms). Recursive wiki links (A_r = 1/(1-0.8) = 5 levels).
Doc Symmetry Balanced doc exchange. S_y for bilateral doc reciprocity (e.g., README/FAQ). Symmetric PR reviews (S_y = 2n for n reviewers).

Documenomics Equation in Axionomics: D = A * Doc_f, where Doc_f = fidelity factor (0-1). Verified: D = 1 for fully documented litany.

For full documenomics, see Documenomics Wiki.

References & Further Reading

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

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

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