Pre-registration — Complete classification of the well-posed subsets of the Rao (1998) Śrīyantra constraint system (unchanged from v1.0/v1.1)
Key Points
This work aims to classify well-posed subsets of the Rao Śrīyantra constraint system more effectively.
Implemented certified real-box enumeration using affine-arithmetic interval-Newton methods.
Applied a queue-exhaustion completeness criterion with outward-rounded arithmetic.
Validated methods on an eight-subset exploratory pilot.
Amendment-01's method was found computationally intractable for completeness.
New invariants and provisions were introduced in Amendment-02, enhancing the classification process.
Tooling freeze actions were documented to ensure methodological consistency.
Abstract
Version 1.2 adds Amendment-02, which supersedes Amendment-01 in full. Amendment-01's coefficient-parameter family homotopy for plane-form Tier-2 completeness is recorded as computationally intractable (an exploratory negative result). Amendment-02 installs in its place certified real-box enumeration via rigorous affine-arithmetic interval-Newton (AA-Krawczyk) over the registered box, with a queue-exhaustion completeness criterion under outward-rounded arithmetic, new recorded invariants, Gate-1 and Gate-M provisions, and a tooling freeze. The method was validated on an eight-subset exploratory pilot (recorded; not confirmatory). Filed before any confirmatory subset run and before the tooling freeze. The engine under test is unchanged at v0.1.0.
Pre-registration — Complete classification of the well-posed subsets of the Rao (1998) Śrīyantra constraint system (unchanged from v1.0/v1.1) | Synapse