Pre-registration — Complete classification of the well-posed subsets of the Rao (1998) Śrīyantra constraint system

Version 1.1 of the pre-registration for the confirmatory enumeration and classification of the well-posed subsets of C. S. Rao's (1998) Śrīyantra constraint system. This version adds Amendment 01 (amendment-01.md). The original pre-registration (preregistration.md, version 1.0, DOI 10.5281/zenodo.20630790, registered 2026-06-10) is included unchanged. Amendment 01 supersedes only the method and completeness certificate of the plane-form Tier-2 step (§6): the per-subset polyhedral "all paths tracked" criterion is replaced by a coefficient-parameter family homotopy — one generic monodromy solve per degree type, certified complete by the trace test (yielding the generic solution count N*), followed by parameter continuation to each subset. A subset's negative is completeness-bearing only if its degree-type family passed the trace test and its own continuation had zero genuine path failures; otherwise, it is downgraded to a Tier-1 "no solution found," exactly as in the original clause. The amendment additionally registers N* as a recorded invariant (a confirmatory raw count; any interpretation of it remains exploratory), registers the family-level trace-test dependency (a trace-test failure downgrades every subset of that degree type), and adds a mandatory pre-run validation (Gate M): re-verification of the lifted system's equivalence to the frozen v0.1.0 engine, and a two-way cross-check of subset {1,2,3,4,8} solved both ab initio and by the family homotopy. Everything else is unchanged: the scope (enumeration and classification only; optimisation deferred), the confirmatory research question, the confirmatory/exploratory demarcation, validation Gates 1–4, the Tier-1 procedure, the equivalence metric and τ sweep, and the reporting schema. The §8 amendment protocol — in particular, no retroactive reclassification — governs Amendment 01 and is reaffirmed: no result obtained before this amendment's timestamp is confirmatory under it, and the amendment expands the registered procedure prospectively only. The amendment is GPG-signed and OpenTimestamps-stamped, provably dated before any confirmatory run. Files in this version: preregistration.md (unchanged), amendment-01.md, each with a detached GPG signature (.asc) and OpenTimestamps stamp (.ots). Frozen engine under test: Sri Yantra Constraint Engine v0.1.0 (DOI 10.5281/zenodo.20617730).

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Publication Details

Journal
Zenodo (CERN European Organization for Nuclear Research)
Published
2026-06-12
DOI
https://doi.org/10.5281/zenodo.20672072
Primary Topic
Homotopy and Cohomology in Algebraic Topology
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article
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article

Pre-registration — Complete classification of the well-posed subsets of the Rao (1998) Śrīyantra constraint system

Salah-Eddin Gherbi
Zenodo (CERN European Organization for Nuclear Research)
Homotopy and Cohomology in Algebraic Topology
article

Pre-registration — Complete classification of the well-posed subsets of the Rao (1998) Śrīyantra constraint system

Salah-Eddin Gherbi
article en

Abstract

Version 1.1 of the pre-registration for the confirmatory enumeration and classification of the well-posed subsets of C. S. Rao's (1998) Śrīyantra constraint system. This version adds Amendment 01 (amendment-01.md). The original pre-registration (preregistration.md, version 1.0, DOI 10.5281/zenodo.20630790, registered 2026-06-10) is included unchanged. Amendment 01 supersedes only the method and completeness certificate of the plane-form Tier-2 step (§6): the per-subset polyhedral "all paths tracked" criterion is replaced by a coefficient-parameter family homotopy — one generic monodromy solve per degree type, certified complete by the trace test (yielding the generic solution count N*), followed by parameter continuation to each subset. A subset's negative is completeness-bearing only if its degree-type family passed the trace test and its own continuation had zero genuine path failures; otherwise, it is downgraded to a Tier-1 "no solution found," exactly as in the original clause. The amendment additionally registers N* as a recorded invariant (a confirmatory raw count; any interpretation of it remains exploratory), registers the family-level trace-test dependency (a trace-test failure downgrades every subset of that degree type), and adds a mandatory pre-run validation (Gate M): re-verification of the lifted system's equivalence to the frozen v0.1.0 engine, and a two-way cross-check of subset {1,2,3,4,8} solved both ab initio and by the family homotopy. Everything else is unchanged: the scope (enumeration and classification only; optimisation deferred), the confirmatory research question, the confirmatory/exploratory demarcation, validation Gates 1–4, the Tier-1 procedure, the equivalence metric and τ sweep, and the reporting schema. The §8 amendment protocol — in particular, no retroactive reclassification — governs Amendment 01 and is reaffirmed: no result obtained before this amendment's timestamp is confirmatory under it, and the amendment expands the registered procedure prospectively only. The amendment is GPG-signed and OpenTimestamps-stamped, provably dated before any confirmatory run. Files in this version: preregistration.md (unchanged), amendment-01.md, each with a detached GPG signature (.asc) and OpenTimestamps stamp (.ots). Frozen engine under test: Sri Yantra Constraint Engine v0.1.0 (DOI 10.5281/zenodo.20617730).

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Homotopy and Cohomology in Algebraic Topology
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