Subjectivity Intersection Mathematics: A Pointed-Braid Source for Quantum History, Lorentzian Geometry, and Reciprocal Backreaction

Version 0.5 integrates the fixed-finite pointed-braid quantum-geometry construction with three later advances. First, one fixed crossing generates a nonterminal tower of full matrix algebras at all finite stages; matched flip and non-Yang-Baxter controls show that growth alone is not Braid-specific, and a stage-compatible map to the finite 87-coordinate response space remains open. Second, state admissibility is separated from state selection: a unique Braid-clock Hadamard state is refuted, while an all-order matrix-block Hadamard construction is obtained under explicit smooth elliptic-slab and fixed state-of-low-energy assumptions. Exact PBM-centre, local a6, and leading-energy results sharpen the stress problem, but the absolute renormalized stress and its higher-jet majorant remain open. Third, the effective relation-polarization law receives a minimum twelve-dimensional Gaussian CPTP completion, while its microscopic Braid origin remains open. An independent Observer-Braid continuation adds a finite relational 1+3 null carrier and an exact source-specific 4+5 geometry-memory balance with reciprocal block response, but does not identify memory with physical matter or yield Einstein dynamics. The results are conditional and mathematical; they do not establish physical infinity, a physical continuum, quantum gravity, general relativity, natural-data validation, SIC/O3, subjectivity, or consciousness.