Shranjeno v:
| Glavni avtor: | |
|---|---|
| Format: | Recurso digital |
| Jezik: | angleščina |
| Izdano: |
Zenodo
2026
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| Teme: | |
| Online dostop: | https://doi.org/10.5281/zenodo.20114315 |
| Oznake: |
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- <p><strong>PCF-2 v1.4</strong> — minor amendment to v1.3, recording the resolution of one forward-pointed Open Problem (<code>op:j-zero-amplitude-h6</code>, the <em>j=0</em> amplitude / Chowla–Selberg closure) in the soft branch.</p> <p><strong>Version changelog (v1.4)</strong>:</p> <blockquote> <p>v1.4 (May 2026): Records the resolution of Open Problem <code>op:j-zero-amplitude-h6</code> (j=0 amplitude / Chowla–Selberg closure) in the soft branch via Prompt 014 <code>PASS_A_EQ_6_ONLY</code> (T25D-RETRY-13PARAM, SIARC bridge SHA <code>e857172</code>, 2026-05-02); ratified at M7 V0 cascade <code>T1-SYNTH-M7-V0-CLOSURE-CASCADE-123</code> (bridge SHA <code>7f93b9e</code>, 2026-05-09; aggregated MEDIUM-HIGH; annotation <em>(SOFT-BRANCH; HARD-BRANCH-PENDING)</em>). Hard-branch stretch goal |δ| < 10<sup>-30</sup> forward-pointed under Q22 path-(b). All other v1.3 content unchanged.</p> </blockquote> <p><strong>Numerical content of the closure (inherited from M7 V0 cascade <code>7f93b9e</code>)</strong>: max |δ<sub>lin</sub>| = 3.09 × 10<sup>-23</sup> across the four j=0 cubic families (Q_30..Q_33, dps = 25,000, N ≤ 1200, 11-parameter LIN refit at K_FIT = 7); PSLQ on the 17-member deduplicated H6 Chowla–Selberg basis B19+ at maxcoeff = 10<sup>50</sup>, tolerance = 10<sup>-40</sup> returns no Γ(1/3) relation in any of the 4 families.</p> <p><strong>Q23 PSLQ basis hygiene</strong>: the closure runs in the deduplicated 17-member basis, NOT the literal 18-basis (which contains the ℚ-redundant pair {√3, Γ(1/3)Γ(2/3)/(2π)} via Γ-reflection identity).</p> <p><strong>Cascade-132 deposit-ordering note</strong>: deposited FIRST in the M-axis V0 closure-series Zenodo session, before umbrella v2.2 and picture-chain v1.20+, per cascade-132 unanimous Option α (path: PCF-2 v1.4 → umbrella v2.2 → picture-chain v1.20+).</p> <p><strong>Companion documents</strong>:</p> <ul> <li>PCF-1 v1.3 (concept DOI <code>10.5281/zenodo.19931635</code>) — degree-2 progenitor.</li> <li>Umbrella v2.2 (forthcoming, deposited second per cascade-132 Option α).</li> <li>Picture-chain v1.20+ (forthcoming, deposited third per cascade-132 Option α).</li> </ul> <p><strong>M1–M12 program-axis coverage (snapshot at PCF-2 v1.4 deposit time):</strong></p> <table> <tbody><tr> <th>Axis</th> <th>Status</th> <th>Primary substrate</th> </tr> </tbody><tbody> <tr> <td>M1</td> <td>external</td> <td>D2-NOTE concept <code>10.5281/zenodo.19996689</code></td> </tr> <tr> <td>M2</td> <td>tabled (RULE 1)</td> <td>—</td> </tr> <tr> <td>M3</td> <td>tabled (RULE 1)</td> <td>—</td> </tr> <tr> <td>M4</td> <td>closed (V0; folded)</td> <td>bridge cascade <code>5f9db69</code> (cascade 106)</td> </tr> <tr> <td>M5</td> <td>tabled (RULE 1)</td> <td>—</td> </tr> <tr> <td>M6.CC</td> <td>closed (retired into Channel Theory)</td> <td>Channel Theory concept <code>10.5281/zenodo.19941678</code></td> </tr> <tr> <td>M7</td> <td>closed (V0; folded)</td> <td>bridge cascade <code>7f93b9e</code> (cascade 123)</td> </tr> <tr> <td>M8a</td> <td>closed (V0; folded)</td> <td>bridge cascade <code>cb429e1</code> (cascade 127R)</td> </tr> <tr> <td>M8b</td> <td>closed (V0; folded)</td> <td>bridge cascade <code>74c5630</code> (cascade 130R; d≥3 caveat in Umbrella v2.3 Appendix C iii)</td> </tr> <tr> <td>M9</td> <td>partial</td> <td>bridge cascade <code>b9aa881</code> (slot 136 picture v1.20+)</td> </tr> <tr> <td>M10</td> <td>partial</td> <td>Lean sorry discharge work-stream; SAFE phrasing in Umbrella v2.3 Appendix C ii</td> </tr> <tr> <td>M11</td> <td>tabled (RULE 1)</td> <td>—</td> </tr> <tr> <td>M12</td> <td>tabled (RULE 1)</td> <td>—</td> </tr> </tbody> </table> <p>The axis-coverage table follows the SIARC v1 schema locked by slot 160 verdict (siarc-relay-bridge cascade <code>012736f</code>); status vocabulary and atomic listing are normative. Bridge cascade SHAs are content-addressed persistent identifiers; URLs may decay if the <code>siarc-relay-bridge</code> repository is renamed but SHAs remain recoverable from any clone.</p>