Scale-Reset Reinsertion and Canonical-Escape Obstructions in Strict Shifted-Laguerre Zero Geometry

We isolate a structural obstruction that arises in residual strict shifted-Laguerre zero geometry after the ordinary high-revisit, fixed-decoration, compact-normal, and pure vanishing-height mechanisms have been routed or excluded. The surviving geometry has two distinct scales: quasi-isometric synchronized profile epochs are separated by singular resets $b_R = o(a_R)$ and later near-affine reinsertion. Every such strict reset carries a diverging normalized phase-energy concentration, yet the historically certified gauge-invariant selector action may vanish. Moreover, synchronized reinsertion satisfies $a_R^+ / a_R = 1 + o(1)$, so every normalized profile functional continuous under near-identity affine conjugacy has asymptotically zero endpoint decrement. On the stated population-quotiented quiet residual branch we synthesize a multiscale path word: visibility departure, reset-scale support crossing, bounded-depth subreset and $o(b_R)$ collision/service, followed by near-affine profile reinsertion. We call this the Canonical-Escape Code. The main negative result is a dependency theorem: the currently certified resource inventory does not, through the certified interfaces alone, turn this mandatory path word into a source-owned, bounded-reuse, generation-independent nonrecycling toll. In particular, the full-profile termination implication is not derivable from the certified theorem DAG. The conclusion is deliberately limited. We do not construct an infinite nonterminal strict shifted-Laguerre configuration, and we do not prove that no stronger transport or nonrecycling theorem can exist. The result is a structural obstruction theorem identifying exactly where the present positive closure mechanism stops. Residual-branch statements are conditional on the interfaces restated in the article; the accompanying P-044 Verification Supplement distinguishes direct reverification from imported historical certificates without enlarging the mathematical claims.

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Publication Details

Journal
Zenodo (CERN European Organization for Nuclear Research)
Published
2026-09-09
DOI
https://doi.org/10.5281/zenodo.22670073
Primary Topic
Theoretical and Computational Physics
Type
preprint
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preprint

Scale-Reset Reinsertion and Canonical-Escape Obstructions in Strict Shifted-Laguerre Zero Geometry

Tao Lin
Zenodo (CERN European Organization for Nuclear Research)
Theoretical and Computational Physics
preprint

Scale-Reset Reinsertion and Canonical-Escape Obstructions in Strict Shifted-Laguerre Zero Geometry

Tao Lin
preprint en

Abstract

We isolate a structural obstruction that arises in residual strict shifted-Laguerre zero geometry after the ordinary high-revisit, fixed-decoration, compact-normal, and pure vanishing-height mechanisms have been routed or excluded. The surviving geometry has two distinct scales: quasi-isometric synchronized profile epochs are separated by singular resets $b_R = o(a_R)$ and later near-affine reinsertion. Every such strict reset carries a diverging normalized phase-energy concentration, yet the historically certified gauge-invariant selector action may vanish. Moreover, synchronized reinsertion satisfies $a_R^+ / a_R = 1 + o(1)$, so every normalized profile functional continuous under near-identity affine conjugacy has asymptotically zero endpoint decrement. On the stated population-quotiented quiet residual branch we synthesize a multiscale path word: visibility departure, reset-scale support crossing, bounded-depth subreset and $o(b_R)$ collision/service, followed by near-affine profile reinsertion. We call this the Canonical-Escape Code. The main negative result is a dependency theorem: the currently certified resource inventory does not, through the certified interfaces alone, turn this mandatory path word into a source-owned, bounded-reuse, generation-independent nonrecycling toll. In particular, the full-profile termination implication is not derivable from the certified theorem DAG. The conclusion is deliberately limited. We do not construct an infinite nonterminal strict shifted-Laguerre configuration, and we do not prove that no stronger transport or nonrecycling theorem can exist. The result is a structural obstruction theorem identifying exactly where the present positive closure mechanism stops. Residual-branch statements are conditional on the interfaces restated in the article; the accompanying P-044 Verification Supplement distinguishes direct reverification from imported historical certificates without enlarging the mathematical claims.

Zenodo (CERN European Organization for Nuclear Research)
Theoretical and Computational Physics
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