{"schemaVersion":1,"publication":{"id":"sustained-carriers","title":"Sustained Adaptive Spectral States: Global Attraction, Nonlinear Gain, and Linked Coherent–Dissipative Response","subtitle":"Global Attraction, Nonlinear Gain, and Linked Coherent–Dissipative Response","description":"A declared rate port sustains nonzero states, with global attraction under a strict curvature condition. Nonlinear gain and freely responding memory distinguish the adaptive system from a matched fixed carrier.","doi":"10.5281/zenodo.23927855","date":"2026-11-03","url":"/source-readout/sustained-carriers","pdfUrl":"/publications/spectral/sustained-carriers/paper.pdf","markdownUrl":"/publications/spectral/sustained-carriers/complete.md","manifestUrl":"/source-readout/sustained-carriers/manifest.json","paperSlug":"sustained-carriers","headline":"External power sustains an adaptive response.","author":"Jeremy Rodgers","programme":"source-readout","supplementUrl":"/publications/spectral/sustained-carriers/verification.zip"},"kind":"complete-translated-web-edition","chapters":[{"paperId":"sustained-carriers","slug":"01-power-and-stationary-reduction","title":"The power that sustains an adaptive state","description":"A calibrated rate port maintains nonzero amplitude and memory, with a physical energy balance distinct from the stationary Lyapunov tilt.","order":1,"url":"/source-readout/sustained-carriers/01-power-and-stationary-reduction","sourcePath":"content/paper-integrations/sustained-carriers/01-power-and-stationary-reduction.mdx","sections":[{"id":"section-1","title":"1 From relaxing carriers to sustained adaptive states"},{"id":"section-2","title":"2 Source state, actuator and physical energy"},{"id":"section-2-1","title":"2.1 Constitutive equations and units"},{"id":"section-2-2","title":"2.2 The effort–flow input contract"},{"id":"section-3","title":"3 Global solutions and the stationary reduction"},{"id":"section-3-1","title":"3.1 A mathematical tilt distinct from stored energy"},{"id":"section-3-2","title":"3.2 Eliminating memory at stationarity"},{"id":"section-3-3","title":"3.3 Why global joint convexity is unavailable"}],"anchors":["section-1","section-2","section-2-1","eq-1","eq-2","eq-3","eq-4","section-2-2","eq-5","eq-6","eq-7","eq-8","section-3","section-3-1","eq-9","eq-10","proposition-3-1","eq-11","eq-12","eq-13","section-3-2","eq-14","eq-15","eq-16","section-3-3","eq-17"],"words":904},{"paperId":"sustained-carriers","slug":"02-global-attraction-and-gain","title":"Global attraction and nonlinear gain","description":"A sharp scalar curvature estimate yields a strict sufficient all-input stability regime and a controlled contrast gain.","order":2,"url":"/source-readout/sustained-carriers/02-global-attraction-and-gain","sourcePath":"content/paper-integrations/sustained-carriers/02-global-attraction-and-gain.mdx","sections":[{"id":"section-4","title":"4 Sharp curvature and global attraction"},{"id":"section-5","title":"5 Complete local stability and a parameter bound"},{"id":"section-6","title":"6 What the drive imposes and feedback changes"},{"id":"section-6-1","title":"6.1 Collective control and symmetric contrast gain"},{"id":"section-6-2","title":"6.2 Equal stationary power and continuing work"}],"anchors":["section-4","lemma-4-1","eq-18","eq-19","eq-20","eq-21","theorem-4-2","section-5","eq-22","eq-23","eq-24","proposition-5-1","eq-25","eq-26","eq-27","eq-28","eq-29","section-6","section-6-1","eq-30","eq-31","eq-32","eq-33","section-6-2","eq-34","corollary-6-1","eq-35"],"words":1042},{"paperId":"sustained-carriers","slug":"03-full-response","title":"The driven carrier keeps two kinds of response","description":"Conditional phase and attenuation share a carrier, while free memory changes the static and frequency transfer.","order":3,"url":"/source-readout/sustained-carriers/03-full-response","sourcePath":"content/paper-integrations/sustained-carriers/03-full-response.mdx","sections":[{"id":"section-7","title":"7 Conditional linkage and complete feedback response"},{"id":"section-7-1","title":"7.1 Affine propagation and time ordering"},{"id":"section-7-2","title":"7.2 Memory kernel and transfer operators"},{"id":"section-7-3","title":"7.3 Observable contract and required resources"}],"anchors":["section-7","section-7-1","eq-36","eq-37","eq-38","eq-39","eq-40","eq-41","section-7-2","eq-42","eq-43","eq-44","eq-45","eq-46","section-7-3"],"words":529},{"paperId":"sustained-carriers","slug":"04-driven-controls","title":"The driven tests separate power, organization and response","description":"Matched three-node controls retain the complete stability spectrum and show that equal supplied power can sustain different states.","order":4,"url":"/source-readout/sustained-carriers/04-driven-controls","sourcePath":"content/paper-integrations/sustained-carriers/04-driven-controls.mdx","sections":[{"id":"section-8","title":"8 Executed finite calculations and matched controls"},{"id":"section-8-1","title":"8.1 Fixed preparations and numerical methods"},{"id":"section-8-2","title":"8.2 Stationary organization, power and stability"},{"id":"section-8-3","title":"8.3 Conditional ordering and full response"},{"id":"section-8-4","title":"8.4 Reproducibility and evidence scope"},{"id":"section-9","title":"9 Consequences and focused extensions"},{"id":"section-references","title":"References"}],"anchors":["section-8","section-8-1","eq-47","eq-48","table-1","table-2","section-8-2","section-8-3","figure-1","section-8-4","table-3","table-4","section-9","figure-2","section-references"],"words":1502}],"completeMarkdown":"/publications/spectral/sustained-carriers/complete.md","originalPdf":"/publications/spectral/sustained-carriers/paper.pdf"}