Vertical Non-Injectivity and the Stability of the Observable Rank: Closing the Unconditional Transfer cχ → δpair → β∗
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| Natura: | Recurso digital |
| Lingua: | inglese |
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2026
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| _version_ | 1866901221747458048 |
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| author | Beau, Jérôme |
| author_facet | Beau, Jérôme |
| contents | <div> <div> </div> <p>O18 established the minimal fibre condition: Born-Infeld parity is the only global symmetry of $S_{\mathrm{BI}}[\chi]$, ensuring that each fibre of the non-injective projection $\Pi$ is exactly $\{\chi, -\chi\}$. O22 proved the shell-alignment conjecture of O21, and O23 derived the threshold condition $\Sigma_c(n_3) = 3$ from the quaternionic maximality of the admissible neutral traceless sector. Together, these results show that the integer $3$ in $\Sigma_c(n_3) = 3$ is a property of $\operatorname{Im}\Pi \cap \mathcal{N}_{\mathrm{trl}}$, not of the cardinality of the fibres. The condition of O18 is therefore stronger than necessary: the programme requires only that any symmetry of $S_{\mathrm{BI}}$ acts <em>vertically</em> with respect to $\Pi$, i.e. does not enlarge the real rank of the admissible neutral traceless sector. The present paper proves this <em>verticality condition</em> directly from Born-Infeld admissibility and the quaternionic maximality established in O23, without requiring a classification of $\mathcal{C}_{\mathrm{eff}}$. As a corollary, the transfer chain<br>\[<br>c_\chi \;\longrightarrow\; \delta_{\mathrm{pair}} \;\longrightarrow\; \beta^* = \frac{1}{\delta_{\mathrm{pair}} + \tfrac{1}{2}} \approx 0.126<br>\]<br>is established unconditionally with respect to the fibre structure of $\Pi$. Non-injectivity may increase microscopic multiplicity, but cannot enlarge the admissible observable structure.</p> </div> |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_19386581 |
| institution | Zenodo |
| language | eng |
| publishDate | 2026 |
| publisher | Zenodo |
| record_format | zenodo |
| spellingShingle | Vertical Non-Injectivity and the Stability of the Observable Rank: Closing the Unconditional Transfer cχ → δpair → β∗ Beau, Jérôme Cosmochrony Spectral admissibility Non-injective projection Verticality condition Observable rank stability Quaternionic maximality Born-Infeld constraint Fibre structure Cascade exponent β∗ <div> <div> </div> <p>O18 established the minimal fibre condition: Born-Infeld parity is the only global symmetry of $S_{\mathrm{BI}}[\chi]$, ensuring that each fibre of the non-injective projection $\Pi$ is exactly $\{\chi, -\chi\}$. O22 proved the shell-alignment conjecture of O21, and O23 derived the threshold condition $\Sigma_c(n_3) = 3$ from the quaternionic maximality of the admissible neutral traceless sector. Together, these results show that the integer $3$ in $\Sigma_c(n_3) = 3$ is a property of $\operatorname{Im}\Pi \cap \mathcal{N}_{\mathrm{trl}}$, not of the cardinality of the fibres. The condition of O18 is therefore stronger than necessary: the programme requires only that any symmetry of $S_{\mathrm{BI}}$ acts <em>vertically</em> with respect to $\Pi$, i.e. does not enlarge the real rank of the admissible neutral traceless sector. The present paper proves this <em>verticality condition</em> directly from Born-Infeld admissibility and the quaternionic maximality established in O23, without requiring a classification of $\mathcal{C}_{\mathrm{eff}}$. As a corollary, the transfer chain<br>\[<br>c_\chi \;\longrightarrow\; \delta_{\mathrm{pair}} \;\longrightarrow\; \beta^* = \frac{1}{\delta_{\mathrm{pair}} + \tfrac{1}{2}} \approx 0.126<br>\]<br>is established unconditionally with respect to the fibre structure of $\Pi$. Non-injectivity may increase microscopic multiplicity, but cannot enlarge the admissible observable structure.</p> </div> |
| title | Vertical Non-Injectivity and the Stability of the Observable Rank: Closing the Unconditional Transfer cχ → δpair → β∗ |
| topic | Cosmochrony Spectral admissibility Non-injective projection Verticality condition Observable rank stability Quaternionic maximality Born-Infeld constraint Fibre structure Cascade exponent β∗ |
| url | https://doi.org/10.5281/zenodo.19386581 |