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.
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 manuscript develops a certified finite-resolution statistical inverse-readout framework for singular density-selected phase kicks. The framework constructs a weak weighted topology directly from noisy pixelized data, certifies stability through a computable spectral gap, and returns either a strictly certified reconstruction or a certified obstruction under declared assumptions. The draft includes an initial proof-of-concept numerical trace for a two-dimensional logarithmic Coulomb benchmark and a reproducibility package. No external experimental datasets were used. Numerical material is synthetic and generated from the equations and parameters described in the manuscript and reproducibility package.
This preprint presents a finite-dimensional quantum-simulation framework for selected TEBAC 9D/9D+ topological phases, with emphasis on synthetic-dimensional encoding, spectral-gap diagnostics, portal-channel observables, and Qiskit-ready Hamiltonian construction. The manuscript formulates a finite-lattice simulation target for the internal TEBAC sector and encodes the model through Pauli-sum Hamiltonians suitable for NumPy exact diagonalization, Qiskit Aer simulation, and future IBM Runtime execution. The central simulation Hamiltonian is organized schematically as
Hsim=HDirac(N)+Hgauge(N)+Htop(N)+Hchannel(N). The paper develops a concrete two-qubit benchmark v0.1 and a four-qubit finite-lattice sector v0.2. For the four-qubit sector, the manuscript gives an explicit Pauli decomposition, exact spectrum, spectral-gap diagnostic, topological proxy, link-sector markers, fidelity diagnostic, and determinant diagnostic. A key contribution of this version is the transition from a hardware-ready protocol to an executed local emulator report. The v0.2 four-qubit sector is evaluated through NumPy exact computation and local Qiskit Aer execution, including ideal sampling, readout-noisy sampling, and readout-mitigation recovery. For the topological proxy
Q4=⟨ZZZZ⟩,the reported values are:
Q4exact=0.986000,Q4Aer,ideal=0.986572±0.001805,Q4Aer,noisy=0.775391±0.006977,and
Q4mitigated=0.993137±0.008936. The manuscript also includes a Qiskit Aer / IBM Runtime execution skeleton, an error-mitigation roadmap, and a validation ledger. The included code package provides the Python scripts used for the NumPy and local Qiskit Aer runs. This preprint should be read as a companion algorithmic module to the TEBAC portal-channel preprint. The portal-channel preprint formulates the geometric and quantum-informational target model; the present manuscript formulates and partially executes a finite-dimensional quantum-simulation protocol for selected spectral, topological, and channel-level diagnostics. The RH and BSD modules of the broader TEBAC 9D/9D+ programme are discussed only methodologically. They are not used as physical inputs for quantum simulation. Their role is to motivate the common operator--spectrum--trace/determinant--comparison architecture used across the TEBAC programme. This version does not claim a laboratory realization of a physical TEBAC portal, a physical 9D/13D geometry on quantum hardware, or a remote IBM/Google hardware backend result. It reports a local NumPy and Qiskit Aer execution and provides a hardware-ready path toward future cloud-backend experiments.
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.