The Erdős Discrepancy Problem under the Rei D-FUMT8 Lens: Numerical Confirmation that Every Tested ±1 Sequence Has Unbounded Discrepancy
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2026
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| _version_ | 1866901722219151360 |
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| author | Fujimoto, Nobuki |
| author_facet | Fujimoto, Nobuki |
| contents | Phase 2.5 attack target #4. Re-interprets Tao 2016 Erdős discrepancy proof through Rei D-FUMT8 lens. Empirical verification on 5 sequences (Liouville, Möbius±1, Thue-Morse, alternating, random) at N up to 1500 confirms Erdős conjecture: every sequence has growing discrepancy. Surface-trivial 'alternating' (-1)^(n-1) achieves D=750=N/2 via d=2 progression — sharp counter-intuition. Liouville smoothest growth (D≈√N, ratio 5.74) explains Tao's choice of λ. Rei D-FUMT8 classification: BOTH for paraconsistent ±1 (Liouville, Möbius), FLOWING for Thue-Morse / random / revised alternating. Liouville is canonical multiplicative ±1 anchor in Paper 78 p-adic FLOWING family. No new math, but coherent framework re-positioning of Tao's result. |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_19599940 |
| institution | Zenodo |
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| publishDate | 2026 |
| publisher | Zenodo |
| record_format | zenodo |
| spellingShingle | The Erdős Discrepancy Problem under the Rei D-FUMT8 Lens: Numerical Confirmation that Every Tested ±1 Sequence Has Unbounded Discrepancy Fujimoto, Nobuki Erdős-discrepancy Tao-2016 Liouville-function Möbius Thue-Morse paraconsistent-logic BOTH D-FUMT8 p-adic-FLOWING Rei-AIOS Phase-2.5 Phase 2.5 attack target #4. Re-interprets Tao 2016 Erdős discrepancy proof through Rei D-FUMT8 lens. Empirical verification on 5 sequences (Liouville, Möbius±1, Thue-Morse, alternating, random) at N up to 1500 confirms Erdős conjecture: every sequence has growing discrepancy. Surface-trivial 'alternating' (-1)^(n-1) achieves D=750=N/2 via d=2 progression — sharp counter-intuition. Liouville smoothest growth (D≈√N, ratio 5.74) explains Tao's choice of λ. Rei D-FUMT8 classification: BOTH for paraconsistent ±1 (Liouville, Möbius), FLOWING for Thue-Morse / random / revised alternating. Liouville is canonical multiplicative ±1 anchor in Paper 78 p-adic FLOWING family. No new math, but coherent framework re-positioning of Tao's result. |
| title | The Erdős Discrepancy Problem under the Rei D-FUMT8 Lens: Numerical Confirmation that Every Tested ±1 Sequence Has Unbounded Discrepancy |
| topic | Erdős-discrepancy Tao-2016 Liouville-function Möbius Thue-Morse paraconsistent-logic BOTH D-FUMT8 p-adic-FLOWING Rei-AIOS Phase-2.5 |
| url | https://doi.org/10.5281/zenodo.19599940 |