সংরক্ষণ করুন:
| প্রধান লেখক: | |
|---|---|
| বিন্যাস: | Recurso digital |
| ভাষা: | |
| প্রকাশিত: |
Zenodo
2026
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| বিষয়গুলি: | |
| অনলাইন ব্যবহার করুন: | https://doi.org/10.5281/zenodo.19019184 |
| ট্যাগগুলো: |
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সূচিপত্রের সারণি:
- <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>