© 2026 Aqora Quantum S.A.S.

Terms Privacy Legal Notice

Projected Channel Renormalization for Cutoff-Regularized Coulomb BBGKY Residuals: Conditional Dynamic Estimates and Contrast Budgets

Panasenko

Published Jun 16, 2026• 0 citations

Abstract

We formulate a conditional projected-channel renormalization theorem forcutoff-regularized Coulomb BBGKY residuals. The starting point is the spectralobstruction that a similarity transform Z−1W Z cannot attenuate a non-zeroHermitian matrix witness in full operator norm. The replacement mechanismstudied here is a non-similarity observation channel: in the minimal model, aPauli-diagonal completely positive trace-preserving channel acts on an M2(C)internal layer and damps declared contrast observables while preserving thetrace sector. The main result is a conditional dynamic gate theorem: if theresidual source, comparison defect, derivative budget, interaction-transportcommutator, and dual-orbit attenuation assumptions are supplied by a concretecutoff model or by an upstream higher-correlation gate, then the projectedwitness component is controlled with an explicit error budget. The theoremis deliberately conditional; it is not a cutoff-free Coulomb closure, not apropagation-of-chaos theorem in trace norm, and not a derivation of thesource budget from the full BBGKY hierarchy. Its contribution is to isolate theexact price of an E6-type operator-valued renormalization: contrast damping,observable-comparison loss, derivative compatibility, and source-budget controlmust all be paid separately.

DOI: 10.5281/zenodo.20722434

Related papers

Noncommutative and Operator-Renormalized Coulomb BBGKY Gates: Similarity Obstruction, Projected Witness Absorption, Uniform Norms, Derivative Budgets, Dual-Defect Completion, Projector Unification, Notation Audit, and Gate-Outcome Mapping

Panasenko

This preprint is written in Ukrainian. It develops a toy-model theorem note for the E4/E6 escape gates in a post-obstruction BBGKY/Coulomb closure program. The manuscript proves a spectral obstruction to full witness attenuation by invertible similarity renormalization and formulates projected, quotient, and non-similarity channel alternatives with explicit comparison budgets. The work is a toy-gate impossibility and certification note; it does not claim cutoff-free Coulomb BBGKY closure. Препринт написано українською мовою. У роботі розроблено toy-model theorem note для шлюзів E4/E6 у пост-обструкційній програмі BBGKY/Coulomb closure. Основний результат — спектральна перешкода для повного поглинання witness через інвертовану similarity-ренормалізацію, а також projected/quotient/non-similarity channel альтернативи з явними comparison budgets. Робота не стверджує cutoff-free Coulomb BBGKY closure.

•Jun 16, 2026•0 citations

Microscopic Pair-Correlation Criteria for Cutoff-Regularized Singular BBGKY Defect Channels

Panasenko

This preprint develops a microscopic pair-correlation framework for cutoff-regularized Coulomb-type BBGKY defect channels. A smooth radial cutoff separates the transition shell, an active mesoscopic annulus, and the macroscopic projected-response region. On the active annulus the paper uses an amplitude formulation F_epsilon = u_epsilon^2, where the radial amplitude belongs to a uniform shell-admissible class allowing correlation-hole behavior without imposing a cutoff-independent positive lower bound. The second-hierarchy defect current is decomposed, in a tested distributional sense, into macroscopic projected, shell-pair, pair-residual, three-body, and stress components. The scalar-pair-generated defect class is closed in the calibrated dual norm, while three-body residues outside this class are detected by annihilating test functionals. A model angular example illustrates how non-radial shell components can have positive distance from scalar radial pair corrections. The manuscript formulates basis-dependent leakage conditions preventing shell-scale residuals from contaminating the macroscopic Gram/Riesz certificate and provides sufficient conditions for convergence of the selected defect identity in a fixed tested distributional channel. No cutoff-free Coulomb closure, trace-norm propagation of chaos, full many-body derivation, or complete Bogoliubov fluctuation theorem is claimed.

•Jun 7, 2026•0 citations

Projected Commutator Cancellation for Pauli-Type Channels: A Conditional Parity Gate for BBGKY Bridge Diagnostics

Panasenko

This preprint develops a conditional projected parity-cancellation gate for commutator terms in Pauli-type projected channels within a BBGKY bridge diagnostic framework. It replaces a naive empty-window commutator obstruction by a verifiable conditional criterion involving resolution loss, parity leakage, and tail control. The result is a conditional gate theorem, not a proof of unconditional cutoff-free Coulomb BBGKY closure.

•Jun 19, 2026•0 citations

Rate Compatibility and Commutator Obstructions for Projected-Channel BBGKY Bridge Estimates

Panasenko

This preprint gives a rate-compatibility and obstruction certificate for a projected-channel finite-depth BBGKY bridge. The main result identifies the channel-exponent compatibility window qγ − θ < ν < a required for simultaneous trace-sector harmlessness and commutator decay. For the canonical cutoff scaling in the finite-depth s = 2,3,4 regimes, this window is empty, showing that the bridge cannot be upgraded to an unconditional closure theorem under the current rates. The manuscript records the source-budget ledger, the commutator obstruction, parameter-sensitivity tables, and the precise assumptions that future E1/E2/E3 escape routes would need to improve.

•Jun 17, 2026•0 citations

Anisotropic Pauli-Channel Optimization for Minimum Comparison Loss in Projected BBGKY Bridges under CPTP Constraints

Panasenko

This preprint develops an anisotropic Pauli-channel optimization layer for projected BBGKY bridge estimates under CPTP constraints. It refines the isotropic depolarizing-channel bridge by replacing a scalar attenuation parameter with a sectorwise Pauli-diagonal channel, formulating the admissible channel set through the Pauli CPTP tetrahedron, and deriving a weighted convex projection problem with KKT and active-set certification. The paper preserves the conditional nature of the underlying bridge estimates: it does not claim cutoff-free Coulomb BBGKY closure or automatic sectorwise commutator decay.

•Jun 19, 2026•0 citations

Projected Fock-Space Channels for Finite-Rank Tensor Correctors: Symmetric Gram Realization and Bogoliubov Leakage Bounds

Panasenko

This preprint develops a projected Fock-space channel framework for finite-rank tensor correctors. The selected two-particle fluctuation channel is realized inside the condensate-orthogonal bosonic Fock space through a symmetric Gram metric with exchange terms. The manuscript proves a correspondence isometry, formulates the projected Bogoliubov comparison as a Duhamel leakage identity, and separates the projected-channel error into resolved leakage, three-body leakage, and finite-dimensional model discrepancy. The paper also provides sufficient spectral-tail conditions for resolved leakage, a regular smoothed Fourier benchmark on the three-dimensional torus, a bounded three-body leakage functional linked to microscopic obstruction diagnostics, and a metric-conditioning transfer estimate for the symmetric two-particle Gram matrix. The results are finite-dimensional and conditional: no full many-body derivation, trace-norm propagation of chaos, automatic N^{-1/2} rate, or cutoff-free Coulomb closure is claimed. This version v0.8 incorporates audit-correction and submission-readiness changes, including metric-consistent symmetric lifting, complex test-density convention, form-domain Duhamel clarification, explicit Fourier lattice-tail constants, and expanded conditioning estimates.

•Jun 7, 2026•0 citations

We formulate a conditional projected-channel renormalization theorem forcutoff-regularized Coulomb BBGKY residuals. The starting point is the spectralobstruction that a similarity transform Z−1W Z cannot attenuate a non-zeroHermitian matrix witness in full operator norm. The replacement mechanismstudied here is a non-similarity observation channel: in the minimal model, aPauli-diagonal completely positive trace-preserving channel acts on an M2(C)internal layer and damps declared contrast observables while preserving thetrace sector. The main result is a conditional dynamic gate theorem: if theresidual source, comparison defect, derivative budget, interaction-transportcommutator, and dual-orbit attenuation assumptions are supplied by a concretecutoff model or by an upstream higher-correlation gate, then the projectedwitness component is controlled with an explicit error budget. The theoremis deliberately conditional; it is not a cutoff-free Coulomb closure, not apropagation-of-chaos theorem in trace norm, and not a derivation of thesource budget from the full BBGKY hierarchy. Its contribution is to isolate theexact price of an E6-type operator-valued renormalization: contrast damping,observable-comparison loss, derivative compatibility, and source-budget controlmust all be paid separately.

This preprint is written in Ukrainian. It develops a toy-model theorem note for the E4/E6 escape gates in a post-obstruction BBGKY/Coulomb closure program. The manuscript proves a spectral obstruction to full witness attenuation by invertible similarity renormalization and formulates projected, quotient, and non-similarity channel alternatives with explicit comparison budgets. The work is a toy-gate impossibility and certification note; it does not claim cutoff-free Coulomb BBGKY closure. Препринт написано українською мовою. У роботі розроблено toy-model theorem note для шлюзів E4/E6 у пост-обструкційній програмі BBGKY/Coulomb closure. Основний результат — спектральна перешкода для повного поглинання witness через інвертовану similarity-ренормалізацію, а також projected/quotient/non-similarity channel альтернативи з явними comparison budgets. Робота не стверджує cutoff-free Coulomb BBGKY closure.

This preprint develops a microscopic pair-correlation framework for cutoff-regularized Coulomb-type BBGKY defect channels. A smooth radial cutoff separates the transition shell, an active mesoscopic annulus, and the macroscopic projected-response region. On the active annulus the paper uses an amplitude formulation F_epsilon = u_epsilon^2, where the radial amplitude belongs to a uniform shell-admissible class allowing correlation-hole behavior without imposing a cutoff-independent positive lower bound. The second-hierarchy defect current is decomposed, in a tested distributional sense, into macroscopic projected, shell-pair, pair-residual, three-body, and stress components. The scalar-pair-generated defect class is closed in the calibrated dual norm, while three-body residues outside this class are detected by annihilating test functionals. A model angular example illustrates how non-radial shell components can have positive distance from scalar radial pair corrections. The manuscript formulates basis-dependent leakage conditions preventing shell-scale residuals from contaminating the macroscopic Gram/Riesz certificate and provides sufficient conditions for convergence of the selected defect identity in a fixed tested distributional channel. No cutoff-free Coulomb closure, trace-norm propagation of chaos, full many-body derivation, or complete Bogoliubov fluctuation theorem is claimed.

This preprint gives a rate-compatibility and obstruction certificate for a projected-channel finite-depth BBGKY bridge. The main result identifies the channel-exponent compatibility window qγ − θ < ν < a required for simultaneous trace-sector harmlessness and commutator decay. For the canonical cutoff scaling in the finite-depth s = 2,3,4 regimes, this window is empty, showing that the bridge cannot be upgraded to an unconditional closure theorem under the current rates. The manuscript records the source-budget ledger, the commutator obstruction, parameter-sensitivity tables, and the precise assumptions that future E1/E2/E3 escape routes would need to improve.

This preprint develops an anisotropic Pauli-channel optimization layer for projected BBGKY bridge estimates under CPTP constraints. It refines the isotropic depolarizing-channel bridge by replacing a scalar attenuation parameter with a sectorwise Pauli-diagonal channel, formulating the admissible channel set through the Pauli CPTP tetrahedron, and deriving a weighted convex projection problem with KKT and active-set certification. The paper preserves the conditional nature of the underlying bridge estimates: it does not claim cutoff-free Coulomb BBGKY closure or automatic sectorwise commutator decay.

This preprint develops a projected Fock-space channel framework for finite-rank tensor correctors. The selected two-particle fluctuation channel is realized inside the condensate-orthogonal bosonic Fock space through a symmetric Gram metric with exchange terms. The manuscript proves a correspondence isometry, formulates the projected Bogoliubov comparison as a Duhamel leakage identity, and separates the projected-channel error into resolved leakage, three-body leakage, and finite-dimensional model discrepancy. The paper also provides sufficient spectral-tail conditions for resolved leakage, a regular smoothed Fourier benchmark on the three-dimensional torus, a bounded three-body leakage functional linked to microscopic obstruction diagnostics, and a metric-conditioning transfer estimate for the symmetric two-particle Gram matrix. The results are finite-dimensional and conditional: no full many-body derivation, trace-norm propagation of chaos, automatic N^{-1/2} rate, or cutoff-free Coulomb closure is claimed. This version v0.8 incorporates audit-correction and submission-readiness changes, including metric-consistent symmetric lifting, complex test-density convention, form-domain Duhamel clarification, explicit Fourier lattice-tail constants, and expanded conditioning estimates.