erdos-ant-verification: An Executable Verification Artifact for the Sawin et al. Lower Bound on the Erdős Unit-Distance Exponent
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| Natura: | Recurso digital |
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Zenodo
2026
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| _version_ | 1866902166154772480 |
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| author | Flamehaven Labs |
| author_facet | Flamehaven Labs |
| contents | An open-source Python implementation that computationally verifies the finite, checkable parts of the 2026 OpenAI/Sawin disproof of the Erdős planar unit-distance conjecture. Reproduces equation (2.2) of the remarks PDF (delta >= ~6.24e-38 for the explicit construction with T = {3,5,7,11,13,17}, S = {101, infinity}, L_T = Q(sqrt 5, sqrt 13, sqrt 17, sqrt 21, sqrt 33)) to within 0.014% relative error using mpmath at 200-bit precision. The artifact does NOT contain a new mathematical proof, does NOT construct the infinite Golod-Shafarevich tower, and has NOT been peer-reviewed. It is intended as a citable reproducibility artifact for the published numerical lower bound. |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_20366884 |
| institution | Zenodo |
| language | |
| publishDate | 2026 |
| publisher | Zenodo |
| record_format | zenodo |
| spellingShingle | erdos-ant-verification: An Executable Verification Artifact for the Sawin et al. Lower Bound on the Erdős Unit-Distance Exponent Flamehaven Labs erdos-unit-distance algebraic-number-theory golod-shafarevich class-field-tower discrete-geometry combinatorics reproducibility executable-verification mathematical-verification mpmath openai-research sawin-construction An open-source Python implementation that computationally verifies the finite, checkable parts of the 2026 OpenAI/Sawin disproof of the Erdős planar unit-distance conjecture. Reproduces equation (2.2) of the remarks PDF (delta >= ~6.24e-38 for the explicit construction with T = {3,5,7,11,13,17}, S = {101, infinity}, L_T = Q(sqrt 5, sqrt 13, sqrt 17, sqrt 21, sqrt 33)) to within 0.014% relative error using mpmath at 200-bit precision. The artifact does NOT contain a new mathematical proof, does NOT construct the infinite Golod-Shafarevich tower, and has NOT been peer-reviewed. It is intended as a citable reproducibility artifact for the published numerical lower bound. |
| title | erdos-ant-verification: An Executable Verification Artifact for the Sawin et al. Lower Bound on the Erdős Unit-Distance Exponent |
| topic | erdos-unit-distance algebraic-number-theory golod-shafarevich class-field-tower discrete-geometry combinatorics reproducibility executable-verification mathematical-verification mpmath openai-research sawin-construction |
| url | https://doi.org/10.5281/zenodo.20366884 |