| _version_ | 1866901383191461888 |
|---|---|
| author | Simpson, Brian |
| author_facet | Simpson, Brian |
| contents | <p>This paper introduces Coherence-Merge Algebra (CMA) — a new, commutative, idempotent but generally non-associative algebra that models how coherence and phase combine under geometric constraints.<br>The operation</p> <p>(TB1,L1) ⊕ (TB2,L2) = (√(TB1·TB2) · exp[–γ·dL(L1,L2)], (L1+L2)/2)</p> <p>is derived from six axioms requiring closure, symmetry, and consistency in the zero-strain limit.<br>Non-associativity in CMA corresponds to curvature in the phase-strain metric dL; associativity is restored exactly when this geometry is flat.<br>By projecting quaternionic (H) and octonionic (O) structures into CMA space, the work reveals a continuous bridge between associative and curved composition laws, extending the classical real–complex–quaternion–octonion sequence into a new coherence-geometric domain.<br>The dataset includes the full technical document, reviewer revisions, and explanatory examples for dL, λ₂, and the octonion-curvature link.</p> |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_17460059 |
| institution | Zenodo |
| language | |
| publishDate | 2025 |
| publisher | Zenodo |
| record_format | zenodo |
| spellingShingle | Coherence-Merge Algebra (CMA)- Axioms, Curvature, and the Bridge to H and O Simpson, Brian <p>This paper introduces Coherence-Merge Algebra (CMA) — a new, commutative, idempotent but generally non-associative algebra that models how coherence and phase combine under geometric constraints.<br>The operation</p> <p>(TB1,L1) ⊕ (TB2,L2) = (√(TB1·TB2) · exp[–γ·dL(L1,L2)], (L1+L2)/2)</p> <p>is derived from six axioms requiring closure, symmetry, and consistency in the zero-strain limit.<br>Non-associativity in CMA corresponds to curvature in the phase-strain metric dL; associativity is restored exactly when this geometry is flat.<br>By projecting quaternionic (H) and octonionic (O) structures into CMA space, the work reveals a continuous bridge between associative and curved composition laws, extending the classical real–complex–quaternion–octonion sequence into a new coherence-geometric domain.<br>The dataset includes the full technical document, reviewer revisions, and explanatory examples for dL, λ₂, and the octonion-curvature link.</p> |
| title | Coherence-Merge Algebra (CMA)- Axioms, Curvature, and the Bridge to H and O |
| url | https://doi.org/10.5281/zenodo.17460059 |