The Geometry Generation Theorem (GGT) Explanatory Census (Version 1.0): A Dependency-Origin Audit of Classical Mathematical Objects

The Geometry Generation Theorem (GGT). A versioned research artifact containing a dependency-origin census of classical mathematical objects, constructed using a four-stage documented methodology (search → candidate generation → five-test filter → adversarial review) and a three-level confidence system (A / B / C). The census contains 49 retained dependency-origin records across three parts: (I) canonical classical objects, (II) classical objects with new genealogy, and (III) GGT-native objects. 12 candidates were discarded and documented. Each entry specifies a parent object, construction origin, what standard presentations leave implicit, what the framework reveals, logical dependence in the framework, and a one-sentence explanatory gain. This is Version 1.0 of a living research artifact. Entries and confidence ratings are expected to evolve with expert feedback. Future revisions will be released as Version 1.1, 1.2, etc.

Authors

Publication Details

Journal
Zenodo (CERN European Organization for Nuclear Research)
Published
2026-07-25
DOI
https://doi.org/10.5281/zenodo.21560156
Primary Topic
Mathematics Education and Teaching Techniques
Type
preprint
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preprint

The Geometry Generation Theorem (GGT) Explanatory Census (Version 1.0): A Dependency-Origin Audit of Classical Mathematical Objects

Ashish Atri
Zenodo (CERN European Organization for Nuclear Research)
Mathematics Education and Teaching Techniques
preprint

The Geometry Generation Theorem (GGT) Explanatory Census (Version 1.0): A Dependency-Origin Audit of Classical Mathematical Objects

Ashish Atri
preprint en

Abstract

The Geometry Generation Theorem (GGT). A versioned research artifact containing a dependency-origin census of classical mathematical objects, constructed using a four-stage documented methodology (search → candidate generation → five-test filter → adversarial review) and a three-level confidence system (A / B / C). The census contains 49 retained dependency-origin records across three parts: (I) canonical classical objects, (II) classical objects with new genealogy, and (III) GGT-native objects. 12 candidates were discarded and documented. Each entry specifies a parent object, construction origin, what standard presentations leave implicit, what the framework reveals, logical dependence in the framework, and a one-sentence explanatory gain. This is Version 1.0 of a living research artifact. Entries and confidence ratings are expected to evolve with expert feedback. Future revisions will be released as Version 1.1, 1.2, etc.

Zenodo (CERN European Organization for Nuclear Research)
Mathematics Education and Teaching Techniques
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