Coherence: Mathematical Framework for the Taiji–Skyrme Theory — Technical Document Suite

This suite of eleven technical documents provides the mathematical framework accompanying Coherence: A Philosophy of the Breathing Universe. The framework formalises a coherence-based ontology using SU(2) Skyrme field theory with a Taiji spinor parametrisation. The Potential Field (Ψ) and Excitation (Φ) are encoded as components of a unified spinor, with coherence defined as a renormalised quantum operator whose classical limit serves as the order parameter across all subsequent applications. The documents are ordered by logical dependency: Coherence Dictionary — canonical symbol definitions governing all subsequent documents Mathematical Framework — SU(2) field, Taiji spinor, topological sectors Lagrangian and Hamiltonian — dynamics and energy-momentum tensor Vacuum Structure — effective potential, branch minima, domain walls Unified Particle Structure — soliton profiles and parameter scaling Quantum Coherence — operator quantisation, fluctuation spectrum, entanglement Coherence Normalisation — scaling, reference scales, calibration Coherence and Gravity — stress-energy tensor, gravitational coupling Galaxy Rotation Curves — phenomenological application Friedmann Cosmology — FRW background with coherence field Collapse and Catastrophe — branch transition dynamics Throughout, gravity is treated strictly within general relativity, with the total stress-energy tensor as the unique gravitational source. No independent coherence force is introduced. The framework is not derived from first principles; it is constructed to be internally consistent and compatible with known physics at the scales where comparison is possible. Known limitations — including the absence of fundamental fermions, the externally added Maxwell sector, and the lack of a first-principles derivation — are documented explicitly. This work was developed through sustained collaboration with AI systems, as described in the accompanying philosophical text. It is presented to be tested, challenged, and extended by those with the formal training to do so.