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2026
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| Acceso en línea: | https://doi.org/10.5281/zenodo.19019184 |
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| _version_ | 1866901356722257920 |
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| author | Okada, Masaki |
| author_facet | Okada, Masaki |
| contents | <p>This preprint develops the first parity-synthesis layer of the hierarchy-compressed line in the \kappa-theory series. The B-line is governed by the unified local hierarchy law</p> <p>\kappa=\frac{m}{2},</p> <p>where m is the local order of vanishing at a turning point. Earlier notes established the canonical odd-branch crossing datum</p> <p>\mathcal C_m=(\Phi_m,A_m),</p> <p>together with its extraction mechanism, and later identified the canonical even-branch barrier datum</p> <p>\mathcal B_{2k}.</p> <p>The purpose of the present note is to synthesize these results into one structural statement about the B-line.</p> <p> </p> <p>The main claim is that hierarchy-compressed transport is unified at the index level but split at the canonical-object level. Odd and even local orders belong to the same hierarchy through</p> <p>\kappa=\frac{m}{2},</p> <p>but they do not carry the same canonical local object. Odd local order yields a crossing-type canonical datum, while even local order yields a barrier/coalescence-type canonical datum. The note therefore establishes that the B-line is best read as a parity-split canonical-object theory built over one common hierarchy law.</p> <p> </p> <p>The treatment is local and architectural rather than semi-global. The note does not derive explicit formulas for all odd crossing data, does not fix a fine-grained coefficient package for all even barrier data, and does not yet address application-facing or A-line/C-line matching questions. Its role is more specific: to reorganize the local object layer of hierarchy-compressed transport as one parity-split theory rather than a collection of separate branch-specific notes.</p> |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_19019184 |
| institution | Zenodo |
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| publishDate | 2026 |
| publisher | Zenodo |
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| spellingShingle | Parity-Split Canonical Local Objects in Hierarchy-Compressed Transport Okada, Masaki • hierarchy-compressed transport • parity split • canonical local objects • turning point • crossing datum • barrier datum • local singularity hierarchy • odd branch • even branch • κ-theory <p>This preprint develops the first parity-synthesis layer of the hierarchy-compressed line in the \kappa-theory series. The B-line is governed by the unified local hierarchy law</p> <p>\kappa=\frac{m}{2},</p> <p>where m is the local order of vanishing at a turning point. Earlier notes established the canonical odd-branch crossing datum</p> <p>\mathcal C_m=(\Phi_m,A_m),</p> <p>together with its extraction mechanism, and later identified the canonical even-branch barrier datum</p> <p>\mathcal B_{2k}.</p> <p>The purpose of the present note is to synthesize these results into one structural statement about the B-line.</p> <p> </p> <p>The main claim is that hierarchy-compressed transport is unified at the index level but split at the canonical-object level. Odd and even local orders belong to the same hierarchy through</p> <p>\kappa=\frac{m}{2},</p> <p>but they do not carry the same canonical local object. Odd local order yields a crossing-type canonical datum, while even local order yields a barrier/coalescence-type canonical datum. The note therefore establishes that the B-line is best read as a parity-split canonical-object theory built over one common hierarchy law.</p> <p> </p> <p>The treatment is local and architectural rather than semi-global. The note does not derive explicit formulas for all odd crossing data, does not fix a fine-grained coefficient package for all even barrier data, and does not yet address application-facing or A-line/C-line matching questions. Its role is more specific: to reorganize the local object layer of hierarchy-compressed transport as one parity-split theory rather than a collection of separate branch-specific notes.</p> |
| title | Parity-Split Canonical Local Objects in Hierarchy-Compressed Transport |
| topic | • hierarchy-compressed transport • parity split • canonical local objects • turning point • crossing datum • barrier datum • local singularity hierarchy • odd branch • even branch • κ-theory |
| url | https://doi.org/10.5281/zenodo.19019184 |