C05.2 · Prior art

| Result | Classification | Predicate and exact scope | Source | |---|---|---|---| | T1 | STANDARD | Artin braid relations and the central full twist; polynomial manipulation of a quadratic relation and ordinary matrix functional calculus. | [BB] §1.2 and §5.1; [LL] §3. These references do not identify the programme matrices. | | T2 | PROGRAMME | The frozen active-module multiplicity, registered hyperbolic word and selected positive-spectrum square root. | LIB2-014 and LIB2-015; Appendix H p.198 and Appendix T pp.312–313. | | T3 | PROGRAMME | The universal registered carrier-map Gram law and the nonscalar central image on the full carrier. | LIB2-194 and LIB2-195; Appendix T §14 p.313. The conditional proof below states the transpose hypotheses explicitly. | | T4 | STANDARD | The displayed two-dimensional unipotent matrices provide a direct exact example satisfying the Artin presentation; the trace-three root identities are polynomial consequences, not an origin of the golden unit. | [BB] §1.2 for the presentation; [LL] §3 for matrix functions. All entries and identities of this example are separately computed below. | | T5 | PROGRAMME | The registered tick, cylinder-condition failure, winding-census scale class and NS/R parity-pattern reading. | LIB2-054, LIB2-055, LIB2-056 and LIB2-084; Appendix P pp.268–270. Their original generator/census payloads are not re-executed here. | | T6 | UNRESOLVED | Alignment of the example with the frozen carrier, verification of its Frobenius transpose convention, and the missing braid-to-winding and Spin-bundle maps. | The necessary frozen arrays, metric/intertwiner and geometric maps are not supplied. | | T7 | STANDARD | Frobenius Grams are quadratic forms in the carrier map and depend on the chosen transpose/metric; the explicit non-orthogonal-similarity example is an elementary countercontrol. | [BV] Chapter 3, quadratic forms and their Hessians; the displayed exact matrices and output key give the complete elementary calculation. |

The Clifford Braiding Theorem in [KL] is useful prior context for constructing braid operators from Clifford generators. Its Majorana representation is not the split-real unipotent representation used in this article. No equivalence is asserted between those two constructions.