Critical Scale Transfer, Birth-Action Bounds, and Same-Trajectory Caloric Headroom in Periodic 3D Navier–Stokes
Year: 2026
Type: preprint
Abstract: Restricted research draft — unpublished working record. This manuscript consolidates the PRF-NS Chat 8 research sequence RUN-01 through RUN-08 for the three-dimensional incompressible periodic Navier–Stokes equations. The work develops a governed chain of exact identities, directed analytic bounds, adversarial controls, and explicit failure classifications around critical-scale transfer and recurrence. The principal bounded results include exact heat-scale and shell-transfer identities; a finite-mass / divergent-first-moment recurrence reduction; an exact finite three-channel switching classification with geometric all-history summability in the declared model; an overlapping-Fourier correction to packetwise dissipation arguments; a scale-independent lower bound on the nonlinear-source action required for bounded-clock critical annular child birth; an environment-strain / residual-source action dichotomy; and a bounded same-trajectory result showing coexistence of a nonzero second critical child with strict First-Caloric headroom. In particular, the critical annular birth analysis establishes that bounded-parabolic-clock order-one child formation cannot become arbitrarily inexpensive merely by moving to higher frequency. The resulting action lower bound is formulated in the critical Lt2H˙−1/2L_t^2\dot H^{-1/2} nonlinear-source scale. The same-trajectory R3C-FC branch additionally closes the previously open local First-Caloric-headroom coexistence gate for a suitable nonzero amplitude, while preserving the frozen observation geometry. These results do not establish multi-generation recurrence. Mature next-generator quality, third-child formation, infinite recurrence, NS-generated C-Rigidity, and Type-II / far-field R-Rigidity remain open. Claim boundary: global regularity remains OPEN; no finite-time singularity is constructed; no solution of the Navier–Stokes Millennium Prize Problem is claimed; worldwide novelty is not claimed; and no external peer-review result is represented by this draft. Status: RESTRICTED / INTERNAL / RESEARCH DRAFT v0.1. Preparation or deposit of this record does not constitute authorization for public release. All Rights Reserved — Restricted Research Draft Copyright © 2026 Alexanja Senke. All rights reserved. Scholarly reading and citation are permitted under applicable law. No license is granted to reproduce, redistribute, republish, adapt, translate, create derivative works from, commercially exploit, or otherwise disseminate this draft or its accompanying research artifacts without the prior written permission of the copyright holder. No patent, software, implementation, certification, conformity-assessment, trade-secret, or other proprietary right is granted or implied.
Author: Senke, Alexanja
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7212080002
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