{"schemaVersion":1,"publication":{"id":"adaptive-carriers","title":"Adaptive Spectral Carriers: Time Ordering, Reciprocal Memory, and Linked Coherent–Dissipative Response","subtitle":"Time Ordering, Reciprocal Memory, and Linked Coherent–Dissipative Response","description":"Reciprocal memory changes the carrier along the trajectory. Instantaneous alignment survives along realized histories, while time ordering and full feedback change the response.","doi":"10.5281/zenodo.23924603","date":"2026-11-03","url":"/source-readout/adaptive-carriers","pdfUrl":"/publications/spectral/adaptive-carriers/paper.pdf","markdownUrl":"/publications/spectral/adaptive-carriers/complete.md","manifestUrl":"/source-readout/adaptive-carriers/manifest.json","paperSlug":"adaptive-carriers","headline":"The carrier changes with the state it governs.","author":"Jeremy Rodgers","programme":"source-readout","supplementUrl":"/publications/spectral/adaptive-carriers/verification.zip"},"kind":"complete-translated-web-edition","chapters":[{"paperId":"adaptive-carriers","slug":"01-adapting-the-carrier","title":"One energy drives the adaptive carrier","description":"Reciprocal memory changes stiffness while a shared positive carrier controls instantaneous attenuation and phase.","order":1,"url":"/source-readout/adaptive-carriers/01-adapting-the-carrier","sourcePath":"content/paper-integrations/adaptive-carriers/01-adapting-the-carrier.mdx","sections":[{"id":"section-1","title":"1 From a fixed carrier to an adaptive source"},{"id":"section-1-1","title":"1.1 Relationship to the previous programme"},{"id":"section-1-2","title":"1.2 Source state and observable contracts"},{"id":"section-1-3","title":"1.3 Conventions"},{"id":"section-2","title":"2 A reciprocal adaptive carrier from one energy"},{"id":"section-2-1","title":"2.1 Units and physical assumptions"},{"id":"section-2-2","title":"2.2 Instantaneous CSCF realization"}],"anchors":["section-1","section-1-1","section-1-2","section-1-3","section-2","eq-1","eq-2","eq-3","eq-4","eq-5","eq-6","section-2-1","theorem-2-1","eq-7","eq-8","eq-9","eq-10","proposition-2-2","eq-11","eq-12","proposition-2-3","eq-13","section-2-2","eq-14"],"words":1016},{"paperId":"adaptive-carriers","slug":"02-ordering-and-feedback","title":"Time ordering and the complete memory response","description":"An interaction picture and a commutator bound replace fixed-carrier factorization; the full tangent retains a causal memory kernel.","order":2,"url":"/source-readout/adaptive-carriers/02-ordering-and-feedback","sourcePath":"content/paper-integrations/adaptive-carriers/02-ordering-and-feedback.mdx","sections":[{"id":"section-3","title":"3 Conditional evolution and time ordering"},{"id":"section-3-1","title":"3.1 Two pulses and asymptotic sharpness"},{"id":"section-3-2","title":"3.2 A moving but commuting control"},{"id":"section-4","title":"4 Full feedback, memory and changing coordinates"},{"id":"section-4-1","title":"4.1 Exact transient expansion despite partial positivity"},{"id":"section-4-2","title":"4.2 The connection for a changing mobility metric"},{"id":"section-4-3","title":"4.3 Why the autonomous closure certificate changes"}],"anchors":["section-3","eq-15","eq-16","eq-17","theorem-3-1","eq-18","theorem-3-2","eq-19","eq-20","eq-21","eq-22","section-3-1","eq-23","eq-24","eq-25","eq-26","section-3-2","eq-27","eq-28","section-4","eq-29","eq-30","proposition-4-1","eq-31","eq-32","eq-33","section-4-1","eq-34","eq-35","eq-36","section-4-2","eq-37","eq-38","eq-39","eq-40","section-4-3","eq-41","eq-42"],"words":1098},{"paperId":"adaptive-carriers","slug":"03-testing-the-linked-law","title":"Calibrating the linked operator response","description":"Short-time propagation recovers calibrated generators with explicit bias, noise and mobility-ratio bounds.","order":3,"url":"/source-readout/adaptive-carriers/03-testing-the-linked-law","sourcePath":"content/paper-integrations/adaptive-carriers/03-testing-the-linked-law.mdx","sections":[{"id":"section-5","title":"5 A calibrated test of linked operator response"},{"id":"section-5-1","title":"5.1 Short-time reconstruction and a controlled remainder"},{"id":"section-5-2","title":"5.2 Preparation, metric and access"}],"anchors":["section-5","eq-43","eq-44","eq-45","section-5-1","eq-46","theorem-5-1","eq-47","eq-48","eq-49","eq-50","eq-51","section-5-2"],"words":615},{"paperId":"adaptive-carriers","slug":"04-finite-checks","title":"The finite adaptive tests and what they establish","description":"Deterministic trajectories, pulses, symmetry controls and calibrated reconstruction test distinct consequences of the carrier law.","order":4,"url":"/source-readout/adaptive-carriers/04-finite-checks","sourcePath":"content/paper-integrations/adaptive-carriers/04-finite-checks.mdx","sections":[{"id":"section-6","title":"6 Executed finite calculations"},{"id":"section-6-1","title":"6.1 Feedback trajectory and independent formulation"},{"id":"section-6-2","title":"6.2 Pulse ordering and the symmetric control"},{"id":"section-6-3","title":"6.3 Response reconstruction and exact fixtures"},{"id":"section-6-4","title":"6.4 Public verification and evidence classes"},{"id":"section-7","title":"7 Consequences and focused extensions"},{"id":"section-7-1","title":"7.1 Physical implementation and driven organization"},{"id":"section-7-2","title":"7.2 Continuum domains and renormalization"},{"id":"section-8","title":"8 Conclusion"},{"id":"section-references","title":"References"}],"anchors":["section-6","section-6-1","eq-52","eq-53","table-1","figure-1","section-6-2","eq-54","eq-55","table-2","figure-2","section-6-3","eq-56","table-3","section-6-4","section-7","section-7-1","section-7-2","section-8","section-references"],"words":1587}],"completeMarkdown":"/publications/spectral/adaptive-carriers/complete.md","originalPdf":"/publications/spectral/adaptive-carriers/paper.pdf"}