{"schemaVersion":1,"publication":{"id":"spectral-profiles","title":"From Source Structure to Spectral Profiles: Generation Mechanisms and Observable Readouts in the Canonical Spectral-Curvature Framework","subtitle":"Generation Mechanisms and Observable Readouts in the Canonical Spectral-Curvature Framework","description":"Hydrogen radial shells, Gaussian exchange and Kerr resonance boundary conditions generate spectral profiles by distinct mechanisms. Exact counterexamples and calibrated responses show what pooled ratios lose and what observations recover.","doi":"10.5281/zenodo.23912447","date":"2026-11-03","url":"/source-readout/spectral-profiles","pdfUrl":"/publications/spectral/spectral-profiles/paper.pdf","markdownUrl":"/publications/spectral/spectral-profiles/complete.md","manifestUrl":"/source-readout/spectral-profiles/manifest.json","paperSlug":"spectral-profiles","headline":"Follow the profile back to its source.","author":"Jeremy Rodgers","programme":"source-readout","supplementUrl":"/publications/spectral/spectral-profiles/verification.zip"},"kind":"complete-translated-web-edition","chapters":[{"paperId":"spectral-profiles","slug":"01-sources-and-readouts","title":"Three ways to generate a spectral profile","description":"The data and observation contract shared by the hydrogen, spatial and Kerr constructions.","order":1,"url":"/source-readout/spectral-profiles/01-sources-and-readouts","sourcePath":"content/paper-integrations/spectral-profiles/01-sources-and-readouts.mdx","sections":[{"id":"section-1","title":"1. The source-selection problem"},{"id":"section-2","title":"2. Realizations, readouts and retained information"},{"id":"section-2-1","title":"2.1 The mathematical interface to CSCF and Shadow Theory"},{"id":"section-2-2","title":"2.2 The original finite observable"}],"anchors":["abstract","section-1","section-2","section-2-1","equation-1","equation-2","equation-3","equation-4","section-2-2","equation-5","equation-6","equation-7","equation-8"],"words":874},{"paperId":"spectral-profiles","slug":"02-radial-shells","title":"Hydrogen from radial shells to finite counts","description":"Exact shell modes, source normalization, signed corrections and all 45 original coordinates.","order":2,"url":"/source-readout/spectral-profiles/02-radial-shells","sourcePath":"content/paper-integrations/spectral-profiles/02-radial-shells.mdx","sections":[{"id":"section-3","title":"3. Hydrogen: radial shells, normalization and finite profile control"},{"id":"section-3-1","title":"3.1 The finite source and its exact radial data"},{"id":"section-3-2","title":"3.2 An exact same-shell spectrum"},{"id":"section-3-3","title":"3.3 Adjacent shells, the minimum and signed cancellation"},{"id":"section-3-4","title":"3.4 Signed shell self-energies and a radial convergence bound"},{"id":"section-3-5","title":"3.5 Returning the bound to all original counts"},{"id":"section-3-6","title":"3.6 Cutoff concentration and the informative finite tail"}],"anchors":["section-3","section-3-1","equation-9","equation-10","section-3-2","equation-11","proposition-3-1","equation-12","section-3-3","equation-13","equation-14","equation-15","equation-16","equation-17","table-1","figure-1","section-3-4","equation-18","theorem-3-2","equation-19","equation-20","equation-21","equation-22","section-3-5","section-3-6","theorem-3-3"],"words":2291},{"paperId":"spectral-profiles","slug":"03-dipole-and-loss","title":"From a dipole bath to the measured loss","description":"The equilibrium metric, the frequency-only obstruction and an operational realization of the logarithmic readout.","order":3,"url":"/source-readout/spectral-profiles/03-dipole-and-loss","sourcePath":"content/paper-integrations/spectral-profiles/03-dipole-and-loss.mdx","sections":[{"id":"section-4","title":"4. A physical dipole carrier and an operational loss readout"},{"id":"section-4-1","title":"4.1 Angular factors and the equilibrium metric"},{"id":"section-4-2","title":"4.2 Loss mixtures realize the logarithmic readout"}],"anchors":["section-4","section-4-1","equation-23","equation-24","proposition-4-1","section-4-2","proposition-4-2","equation-25","equation-26"],"words":779},{"paperId":"spectral-profiles","slug":"04-gaussian-exchange","title":"How spatial preparation sets the spectrum","description":"Gaussian exchange, the degree-to-spectrum bound, preparation-dependent ratio laws and extraction uncertainty.","order":4,"url":"/source-readout/spectral-profiles/04-gaussian-exchange","sourcePath":"content/paper-integrations/spectral-profiles/04-gaussian-exchange.mdx","sections":[{"id":"section-5","title":"5. Spatial preparation and kernel-mass heterogeneity"},{"id":"section-5-1","title":"5.1 A conditional Gaussian-exchange realization"},{"id":"section-5-2","title":"5.2 A finite degree-to-spectrum theorem"},{"id":"section-5-3","title":"5.3 A preparation law generates a ratio distribution"},{"id":"section-5-4","title":"5.4 Extraction uncertainty and source-image scope"}],"anchors":["section-5","section-5-1","equation-27","section-5-2","theorem-5-1","equation-28","section-5-3","equation-29","equation-30","section-5-4","proposition-5-2"],"words":1013},{"paperId":"spectral-profiles","slug":"05-outgoing-poles","title":"Kerr requires the joint outgoing problem","description":"The native damping readout, angular and radial source equations, branch repair and the boundary-pole extension.","order":5,"url":"/source-readout/spectral-profiles/05-outgoing-poles","sourcePath":"content/paper-integrations/spectral-profiles/05-outgoing-poles.mdx","sections":[{"id":"section-6","title":"6. Kerr: joint angular and outgoing radial dynamics"},{"id":"section-6-1","title":"6.1 The native selection and the source boundary problem"},{"id":"section-6-2","title":"6.2 Finite angular control and barrier shape"},{"id":"section-6-3","title":"6.3 Branch identity and the complete numerical return"},{"id":"section-6-4","title":"6.4 The boundary-pole extension of the carrier picture"}],"anchors":["section-6","section-6-1","equation-31","equation-32","section-6-2","equation-33","section-6-3","section-6-4"],"words":733},{"paperId":"spectral-profiles","slug":"06-inverse-response","title":"What ratios cannot identify, calibrated response can recover","description":"Homometric carriers, exact projected dynamics and finite equal-weight recovery expose what pooling removes.","order":6,"url":"/source-readout/spectral-profiles/06-inverse-response","sourcePath":"content/paper-integrations/spectral-profiles/06-inverse-response.mdx","sections":[{"id":"section-7","title":"What ratio profiles identify, and what response adds"},{"id":"section-7-1","title":"Distinct carriers can have the same complete ratio measure"},{"id":"section-7-2","title":"A static reduction does not identify the time evolution"},{"id":"section-7-3","title":"Calibrated response completes the finite spectral target"}],"anchors":["section-7","section-7-1","proposition-7-1","section-7-2","equation-34","section-7-3","theorem-7-2"],"words":813},{"paperId":"spectral-profiles","slug":"07-tests-and-conclusion","title":"A connected source-to-readout account","description":"The three generation routes lead to concrete comparisons while preserving the boundary between construction, reproduction and physical evidence.","order":7,"url":"/source-readout/spectral-profiles/07-tests-and-conclusion","sourcePath":"content/paper-integrations/spectral-profiles/07-tests-and-conclusion.mdx","sections":[{"id":"section-8","title":"Three generation routes, one explicit observation contract"},{"id":"section-8-1","title":"Discriminating observations"},{"id":"section-8-2","title":"Keep the evidence classes separate"},{"id":"section-9","title":"The result"}],"anchors":["section-8","section-8-1","section-8-2","section-9"],"words":679},{"paperId":"spectral-profiles","slug":"08-appendices","title":"Radial formula, homogeneous preparation and verification","description":"The full exact radial sum, error bounds, circle control and all published return-count tables.","order":8,"url":"/source-readout/spectral-profiles/08-appendices","sourcePath":"content/paper-integrations/spectral-profiles/08-appendices.mdx","sections":[{"id":"appendix-a","title":"Appendix A. Exact radial evaluation and numerical conventions"},{"id":"appendix-b","title":"Appendix B. Homogeneous ring preparation"},{"id":"appendix-c","title":"Appendix C. Verification scope and numerical tables"}],"anchors":["appendix-a","equation-35","appendix-b","appendix-c","table-2","table-3"],"words":814},{"paperId":"spectral-profiles","slug":"09-references","title":"References and source connections","description":"All twelve references with links to related web editions and original bibliographic records.","order":9,"url":"/source-readout/spectral-profiles/09-references","sourcePath":"content/paper-integrations/spectral-profiles/09-references.mdx","sections":[{"id":"references","title":"References"}],"anchors":["references","ref-1","ref-2","ref-3","ref-4","ref-5","ref-6","ref-7","ref-8","ref-9","ref-10","ref-11","ref-12"],"words":304}],"completeMarkdown":"/publications/spectral/spectral-profiles/complete.md","originalPdf":"/publications/spectral/spectral-profiles/paper.pdf"}