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Generation Mechanisms and Observable Readouts in the Canonical Spectral-Curvature Framework

Jeremy Rodgers · Independent Researcher · 2026-11-03
doi:10.5281/zenodo.23912447

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From Source Structure to Spectral Profiles: Generation Mechanisms and Observable Readouts in the Canonical Spectral-Curvature Framework

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.

The operator and dynamical results use the forms, metrics, inputs and readouts stated in each chapter. Numerical checks test those realizations. Recurrence across readouts does not identify a single microscopic mechanism.

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The argument in full

Follow the chapters in order or enter at a particular question. Definitions, mathematics, proofs, constructions and substantive appendices belong to this reading edition.

  1. Three ways to generate a spectral profile

    The data and observation contract shared by the hydrogen, spatial and Kerr constructions.

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  2. Hydrogen from radial shells to finite counts

    Exact shell modes, source normalization, signed corrections and all 45 original coordinates.

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  3. From a dipole bath to the measured loss

    The equilibrium metric, the frequency-only obstruction and an operational realization of the logarithmic readout.

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  4. How spatial preparation sets the spectrum

    Gaussian exchange, the degree-to-spectrum bound, preparation-dependent ratio laws and extraction uncertainty.

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  5. Kerr requires the joint outgoing problem

    The native damping readout, angular and radial source equations, branch repair and the boundary-pole extension.

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  6. What ratios cannot identify, calibrated response can recover

    Homometric carriers, exact projected dynamics and finite equal-weight recovery expose what pooling removes.

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  7. A connected source-to-readout account

    The three generation routes lead to concrete comparisons while preserving the boundary between construction, reproduction and physical evidence.

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  8. Radial formula, homogeneous preparation and verification

    The full exact radial sum, error bounds, circle control and all published return-count tables.

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  9. References and source connections

    All twelve references with links to related web editions and original bibliographic records.

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Where the arguments meet

The Canonical Spectral-Curvature Field: A Unified Operator Origin for Coherence, Dissipation, and Spectral Budgets →
A positive selfadjoint carrier generates coherent evolution and dissipative relaxation through its functional calculus. The modular spectral measure identifies precisely what the ordered ratio readout retains.

Cross-Domain Spectral Ratio Structure: Refined Recurrence, Robustness and Diagnostic Limits →
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.

Adaptive Spectral Carriers: Time Ordering, Reciprocal Memory, and Linked Coherent–Dissipative Response →
Reciprocal memory changes the carrier along the trajectory. Instantaneous alignment survives along realized histories, while time ordering and full feedback change the response.

Sustained Adaptive Spectral States: Global Attraction, Nonlinear Gain, and Linked Coherent–Dissipative Response →
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.

Sharp Uniqueness and Bistability in Driven Adaptive Spectral Carriers →
A sharp curvature threshold gives uniqueness even at equality. Below it, the three-node realization exhibits bistability, with a complete stationary count in the stated transverse-convexity regime.

Slow Passage and Prepared Hysteresis in Adaptive Spectral Carriers →
A slow sweep delays switching past the static fold by a preparation-dependent amount. The prepared cycle has a nonzero geometric loop limit, while physical maintenance work grows as the sweep slows.

Transport and Projective Reduction in a Source–Readout Derivation of Einstein Gravity →
Reconstruct the affine connection from smooth transport, remove the projective ambiguity with a volume-restored observable, and follow the complete off-shell spin-two bootstrap to Einstein–matter dynamics within the admitted realization.

Published source: From Source Structure to Spectral Profiles: Generation Mechanisms and Observable Readouts in the Canonical Spectral-Curvature Framework. Read the original PDF alongside the web treatment.