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| Hovedforfatter: | |
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| Format: | Recurso digital |
| Sprog: | |
| Udgivet: |
Zenodo
2026
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| Online adgang: | https://doi.org/10.5281/zenodo.19212787 |
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Indholdsfortegnelse:
- <p>Projection-Shadow-Cascade argues that the deepest mistake in ordinary accounts of error, residuals, noise, and unsettled terms is the presumption that what appears as an unclosed remainder at one resolution layer can be settled at that same layer. It cannot. A shadow is not local waste, but unclosed readout. What appears as residual error is not merely a technical leftover of the present description, but the persistent readout left when projection has not yet fully closed against source-consistency. The central claim of this paper is therefore hard: unclosed readout cannot be settled at the same resolution layer. </p> <p>The real source of failure lies in an earlier false chain. Residual at one layer is repeatedly presumed to imply closure at that layer. Yet that step does not hold. Local shadow does not automatically vanish locally. A single-layer readout does not automatically possess single-layer closure-authority. No automatic entailment between adjacent resolution strata does not mean no relation; it means closure cannot be completed in one stroke and must proceed through continuous collapse, transcription, and settlement along the ladder of resolution. What is called “shadow” is precisely the readout-form of something that has not yet closed, yet continues to transmit. <br><br>Within this account, CΩ does not add one more error model, one more convergence trick, or one more vocabulary for residual noise. It cuts the source of misassignment. Local shadow belongs to CΩ as readable, transmissible, and locally retainable unclosure. Final settlement does not belong to the present layer; it belongs only to Ω. The result is sharp: a shadow is not a local accident, but the continuous settlement-readout of projectional non-closure. It does not stay where it appears. It collapses, settles, and compresses layer by layer along the resolution ladder, until closure is lawfully completed at the source-consistent level.</p> <p>Key word:error; residual; noise; uncertainty; uncertainty quantification; error propagation; convergence; multiscale; multiscale modeling; complex systems; complexity science; systems theory; systems thinking; entropy; low entropy; thermodynamics; statistical mechanics; nonequilibrium systems; dissipative systems; dynamic systems; nonlinear dynamics; chaos theory; self-organization; emergence; information theory; information dynamics; residual modeling; residual error; model error; closure model; closure problem; non-closure; incomplete closure; readout; local readout; global closure; local versus global; scale separation; resolution scale; resolution ladder; coarse graining; reduced order model; variational multiscale; model reduction; state estimation; data assimilation; adaptive systems; structural stability; attractors; metastability; stability analysis; robustness; resilience; cascading failure; cascade; shadow cascade; projection shadow; projectional readout; shadow readout; settlement; settlement chain; local settlement; final settlement; source consistency; fixpoint; ontic fixpoint; source license; admissibility; valid standing; source access; Omega closure; CΩ layer; dynamic completeness; local mismatch; local remainder; unsettled term; nonlocal transmission; layer by layer collapse; transmissibility; persistent residual; closure consistency; finite readout; local selection; local retention; interlayer coupling; cross scale dynamics; convergence analysis; asymptotic behavior; perturbation; perturbation growth; structural anomaly; residual transport; model fidelity; information barriers; readout is not closure; local error is not local closure; unclosed readout; projection shadow cascade</p>