{"schemaVersion":1,"publication":{"id":"spectral-ratios","title":"Cross-Domain Spectral Ratio Structure: Refined Recurrence, Robustness and Diagnostic Limits","subtitle":"Refined Recurrence, Robustness and Diagnostic Limits","description":"Ordered spectral-ratio profiles recur across several hydrogen and image readouts, with more moderate Kerr comparisons. The full controls distinguish reproducible structure from exclusive privilege of the original library.","doi":"10.5281/zenodo.23888292","date":"2026-11-02","url":"/source-readout/spectral-ratios","pdfUrl":"/publications/spectral/spectral-ratios/paper.pdf","markdownUrl":"/publications/spectral/spectral-ratios/complete.md","manifestUrl":"/source-readout/spectral-ratios/manifest.json","paperSlug":"spectral-ratios","headline":"The recurrence is measurable. Its limits are measurable too.","author":"Jeremy Rodgers","programme":"source-readout","supplementUrl":"https://zenodo.org/api/records/23888292/files/Spectral_Ratio_Public_Verification.zip/content"},"kind":"complete-translated-web-edition","chapters":[{"paperId":"spectral-ratios","slug":"01-three-different-questions","title":"One signature, three different questions","description":"Strong recurrence, conditional discrimination and library specificity are separate claims. The finite results distinguish them.","order":1,"url":"/source-readout/spectral-ratios/01-three-different-questions","sourcePath":"content/paper-integrations/spectral-ratios/01-three-different-questions.mdx","sections":[{"id":"section-1","title":"A signature that travels across constructions"}],"anchors":["section-1"],"words":282},{"paperId":"spectral-ratios","slug":"02-native-operators","title":"Three native operators and their evidence","description":"The frozen Kerr rates, exact 465-state hydrogen graph and Gaussian image graphs each retain different source information.","order":2,"url":"/source-readout/spectral-ratios/02-native-operators","sourcePath":"content/paper-integrations/spectral-ratios/02-native-operators.mdx","sections":[{"id":"section-2","title":"Inputs, operators and provenance"},{"id":"section-2-1","title":"Kerr: retain the rates and the native transmission"},{"id":"section-2-2","title":"Hydrogen: build the coupling graph, not the energy spectrum"},{"id":"section-2-3","title":"Spatial graphs: keep the extraction contract visible"}],"anchors":["section-2","section-2-1","eq-1","section-2-2","eq-2","eq-3","section-2-3","eq-4","table-1"],"words":842},{"paperId":"spectral-ratios","slug":"03-exact-ratio-statistics","title":"What a ratio profile measures exactly","description":"Finite window counts become exact masses of the log-spectrum autocorrelation after self-pair subtraction and native conditioning.","order":3,"url":"/source-readout/spectral-ratios/03-exact-ratio-statistics","sourcePath":"content/paper-integrations/spectral-ratios/03-exact-ratio-statistics.mdx","sections":[{"id":"section-3","title":"Ratio statistics and mathematical foundations"},{"id":"section-3-1","title":"Count ordered pairs on their native support"},{"id":"section-3-2","title":"The exact log-autocorrelation identity"}],"anchors":["section-3","section-3-1","eq-5","eq-6","eq-7","section-3-2","eq-8","eq-9","eq-10","eq-11"],"words":466},{"paperId":"spectral-ratios","slug":"04-paired-and-conditional-controls","title":"Freeze the comparisons before reading the scores","description":"Paired libraries, three nonnested Kerr references and two hydrogen perturbations each preserve different information.","order":4,"url":"/source-readout/spectral-ratios/04-paired-and-conditional-controls","sourcePath":"content/paper-integrations/spectral-ratios/04-paired-and-conditional-controls.mdx","sections":[{"id":"section-4","title":"Frozen comparison design"},{"id":"section-4-1","title":"Paired alternative libraries"},{"id":"section-4-2","title":"Kerr references: three different preservation contracts"},{"id":"section-4-3","title":"Hydrogen shell perturbations and the short fiber pilot"}],"anchors":["section-4","section-4-1","eq-12","eq-13","section-4-2","section-4-3","eq-14"],"words":806},{"paperId":"spectral-ratios","slug":"05-recurrence-and-paired-specificity","title":"Strong recurrence, limited library specificity","description":"Five primary image graphs track the hydrogen profile, while the embryo and paired-library controls show exactly where that agreement stops.","order":5,"url":"/source-readout/spectral-ratios/05-recurrence-and-paired-specificity","sourcePath":"content/paper-integrations/spectral-ratios/05-recurrence-and-paired-specificity.mdx","sections":[{"id":"section-5","title":"Native profile recurrence"},{"id":"section-5-1","title":"The common shape and the embryo exception"},{"id":"section-5-2","title":"Similar profiles also occur under alternative libraries"}],"anchors":["section-5","section-5-1","table-2","figure-1","section-5-2","figure-2"],"words":606},{"paperId":"spectral-ratios","slug":"06-discrimination-and-robustness","title":"Where conditional discrimination survives","description":"Kerr discriminates against U and P, R is more permissive on holdout, and hydrogen shape survives detailed shell-block permutation.","order":6,"url":"/source-readout/spectral-ratios/06-discrimination-and-robustness","sourcePath":"content/paper-integrations/spectral-ratios/06-discrimination-and-robustness.mdx","sections":[{"id":"section-6","title":"Conditional discrimination and profile robustness"},{"id":"section-6-1","title":"Kerr's successes and the holdout boundary"},{"id":"section-6-2","title":"Hydrogen shape withstands shell-block permutation"},{"id":"section-6-3","title":"Hydrogen abundance changes with the readout"}],"anchors":["section-6","section-6-1","kerr-incidences","table-3","section-6-2","table-4","figure-3","section-6-3","table-5","figure-4"],"words":1010},{"paperId":"spectral-ratios","slug":"07-specificity-and-explanatory-tests","title":"What the recurrence does and does not explain","description":"The frozen portability criterion fails. Gap statistics and a density-to-profile prediction answer separate mathematical questions.","order":7,"url":"/source-readout/spectral-ratios/07-specificity-and-explanatory-tests","sourcePath":"content/paper-integrations/spectral-ratios/07-specificity-and-explanatory-tests.mdx","sections":[{"id":"section-7","title":"Library specificity fails its frozen test"},{"id":"section-8","title":"Which spectral theories could explain this profile?"},{"id":"section-8-1","title":"Consecutive gaps are a complementary observable"},{"id":"section-8-2","title":"Global density and local universality can vary independently"},{"id":"section-8-3","title":"A density explanation needs independent window predictions"}],"anchors":["section-7","figure-5","section-8","section-8-1","eq-15","section-8-2","section-8-3","eq-16","eq-17"],"words":935},{"paperId":"spectral-ratios","slug":"08-interpretation-and-reproducibility","title":"A reproducible diagnostic and the next test","description":"Finite recurrence and robustness survive the specificity failure. Independent operator predictions remain the route to a physical explanation.","order":8,"url":"/source-readout/spectral-ratios/08-interpretation-and-reproducibility","sourcePath":"content/paper-integrations/spectral-ratios/08-interpretation-and-reproducibility.mdx","sections":[{"id":"section-9","title":"What the experiment establishes"},{"id":"section-10","title":"The result in full scope"},{"id":"data-code","title":"Data and code availability"},{"id":"author-statement","title":"Author statement"}],"anchors":["section-9","section-10","data-code","author-statement"],"words":682},{"paperId":"spectral-ratios","slug":"09-verification-and-appendices","title":"Verification, invariances and the complete comparison data","description":"All five appendices, the exact invariances, density illustration, complete comparison tables, historical corrections, and references.","order":9,"url":"/source-readout/spectral-ratios/09-verification-and-appendices","sourcePath":"content/paper-integrations/spectral-ratios/09-verification-and-appendices.mdx","sections":[{"id":"appendix-a","title":"Appendix A. Numerical conventions and verification"},{"id":"appendix-b","title":"Appendix B. Invariances and nonidentifiability"},{"id":"appendix-c","title":"Appendix C. A closed-form density illustration"},{"id":"appendix-d","title":"Appendix D. All primary-core comparisons and native summaries"},{"id":"appendix-e","title":"Appendix E. Material reconstruction corrections"},{"id":"references","title":"References"}],"anchors":["appendix-a","appendix-b","eq-18","eq-19","appendix-c","eq-20","appendix-d","table-6","table-7","appendix-e","table-8","references","ref-1","ref-2","ref-3","ref-4","ref-5"],"words":2909}],"completeMarkdown":"/publications/spectral/spectral-ratios/complete.md","originalPdf":"/publications/spectral/spectral-ratios/paper.pdf"}