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Zenodo
2026
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| Online Access: | https://doi.org/10.5281/zenodo.20049319 |
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| _version_ | 1866901755507245056 |
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| author | Zhang, Jian |
| author_facet | Zhang, Jian |
| contents | <p>**Correction (May 2026):** The parameter A₁ in this paper is not an integer. It is a 12th-degree algebraic number. A formal correction note is available at:<br>https://doi.org/10.5281/zenodo.20248731</p> <p>---</p> <p>This note presents a previously unrecorded Ramanujan-type π formula that converges approximately 1.81×10^12 times faster per term than the classical Chudnovsky formula. It shares the same factorial structure, the same clock constant 426880√10005, and the same denominator base structure as the Chudnovsky formula. The denominator base changes from 640320^3 to 7800739440^3, while the molecular base constant A₁ = 13591409 + ε₁ is a 12th-degree algebraic number (see Correction Note). This change yields approximately 26 decimal digits per series term, compared to ~14 digits for Chudnovsky.</p> <p>A self-contained Python validation script (crystal_clock_verify.py) is attached. It runs in any Python 3 environment without external dependencies and completes in under one minute. Common numerical pitfalls are documented and addressed in the script.</p> <p>The formula originates from the Crystal Theory framework. The m=1 formula was first reported in Zhang (2026), DOI: 10.5281/zenodo.20045634. The present note focuses exclusively on independent validation.</p> <p>Related work: Crystal Theory (CT-3): https://doi.org/10.5281/zenodo.20065612</p> |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_20049319 |
| institution | Zenodo |
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| publishDate | 2026 |
| publisher | Zenodo |
| record_format | zenodo |
| spellingShingle | A Faster Ramanujan-Type π Formula from the Crystal Clock Spectrum Zhang, Jian <p>**Correction (May 2026):** The parameter A₁ in this paper is not an integer. It is a 12th-degree algebraic number. A formal correction note is available at:<br>https://doi.org/10.5281/zenodo.20248731</p> <p>---</p> <p>This note presents a previously unrecorded Ramanujan-type π formula that converges approximately 1.81×10^12 times faster per term than the classical Chudnovsky formula. It shares the same factorial structure, the same clock constant 426880√10005, and the same denominator base structure as the Chudnovsky formula. The denominator base changes from 640320^3 to 7800739440^3, while the molecular base constant A₁ = 13591409 + ε₁ is a 12th-degree algebraic number (see Correction Note). This change yields approximately 26 decimal digits per series term, compared to ~14 digits for Chudnovsky.</p> <p>A self-contained Python validation script (crystal_clock_verify.py) is attached. It runs in any Python 3 environment without external dependencies and completes in under one minute. Common numerical pitfalls are documented and addressed in the script.</p> <p>The formula originates from the Crystal Theory framework. The m=1 formula was first reported in Zhang (2026), DOI: 10.5281/zenodo.20045634. The present note focuses exclusively on independent validation.</p> <p>Related work: Crystal Theory (CT-3): https://doi.org/10.5281/zenodo.20065612</p> |
| title | A Faster Ramanujan-Type π Formula from the Crystal Clock Spectrum |
| url | https://doi.org/10.5281/zenodo.20049319 |