This paper develops a reduced transport-obstruction testbed designed to stress the obstruction decomposition introduced in the companion admissibility manuscript. The goal is not to simulate quantum measurement in full, but to determine whether the same decomposition remains diagnostically useful when failure modes are deliberately separated. A phase-adaptive dual-vortex braid evolves against a deformable background under six conditions, including a no-crisis control: amplitude attenuation, smoothed phase null, phase-jitter projector failure, memory wipe, and phase-jitter plus memory wipe. Across a 20-seed ensemble and an α sweep {0.10,0.20,0.35,0.50,0.65,0.80,0.90}, the full field (A+B)+αΞi+(1−α)Ξf reconstructs the numerically computed transport defect to machine precision, with worst residuals of order 10−15. Uniform amplitude attenuation remains essentially invisible to the normalized diagnostic, while phase-jitter failure produces the largest immediate control-subtracted defect shock and memory wipe produces the strongest sustained post-crisis deviation. A second normalization by sector control norms reveals selective excitation: phase corruption is A-dominated, memory wipe is Ξi-dominated, and the combined crisis inherits both. Control-subtracted sector maps show that these distinctions are not merely scalar; they have spatial morphology. Finally, a boundary-swap control shows that the memory signature exchanges Ξi ↔Ξf under boundary-label exchange, while the phase-jitter signature remains A-dominated. Thereducedtestbedthereforesupportsaboundedbutsubstantiveclaim: theobstruction decompositionisnotmerelyexact; itisdiagnosticallygeometry-sensitive, sector-resolved, and role-aware.
This paper develops a reduced transport-obstruction testbed designed to stress the obstruction decomposition introduced in the companion admissibility manuscript. The goal is not to simulate quantum measurement in full, but to determine whether the same decomposition remains diagnostically useful when failure modes are deliberately separated. A phase-adaptive dual-vortex braid evolves against a deformable background under six conditions, including a no-crisis control: amplitude attenuation, smoothed phase null, phase-jitter projector failure, memory wipe, and phase-jitter plus memory wipe. Across a 20-seed ensemble and an α sweep {0.10,0.20,0.35,0.50,0.65,0.80,0.90}, the full field (A+B)+αΞi+(1−α)Ξf reconstructs the numerically computed transport defect to machine precision, with worst residuals of order 10−15. Uniform amplitude attenuation remains essentially invisible to the normalized diagnostic, while phase-jitter failure produces the largest immediate control-subtracted defect shock and memory wipe produces the strongest sustained post-crisis deviation. A second normalization by sector control norms reveals selective excitation: phase corruption is A-dominated, memory wipe is Ξi-dominated, and the combined crisis inherits both. Control-subtracted sector maps show that these distinctions are not merely scalar; they have spatial morphology. Finally, a boundary-swap control shows that the memory signature exchanges Ξi ↔Ξf under boundary-label exchange, while the phase-jitter signature remains A-dominated. Thereducedtestbedthereforesupportsaboundedbutsubstantiveclaim: theobstruction decompositionisnotmerelyexact; itisdiagnosticallygeometry-sensitive, sector-resolved, and role-aware.
This paper develops a geometry-first account of quantum transport in which admis- sible local flow is constrained by the nodal and phase structure of a two-boundary wave field. The central quantitative device is the power-family density˜ ρα ∝ρα i ρ1−α f together with an obstruction decomposition of the numerically computed log-transport defect into an irreducible geometric term A, a density-reweighting term B, and weighted one- boundary correction fields. Two benchmark models were examined: a driven anisotropic harmonic packet mismatch (Model A) and a double-slit barrier with a postselected detector packet (Model B). In Model A the representative density scan has a sharp optimum at α= 0.2, reducing max Enat from 3.377 ×10−1 at α= 1/2 to 1.740 ×10−1 . In Model B the optimum is shallow near α= 0.5 and the minimum remains high, with max Enat = 6.516 ×10−1. Across both models, the full field (A+ B) + αΞi+ (1−α)Ξf reconstructs the computed defect to machine precision, with peak relative residuals of order 10−16, while the obstruction-only comparison remains O(1). The numerical evidence therefore distinguishes negotiable smooth mismatch from hard obstruction within the tested transport representation and supports a sharpened admissibility frame- work. A reservoir-like interpretation is presented only as a conjectural extension: the established result is the exact obstruction decomposition and its contrasting behaviour across smooth and interference-dominated geometries.
This paper develops a mathematical framework for two-boundary quantum admissibility. Given an initial wave field ψi = √ρiexp(iSi/ℏ) and a final, post-selected, or backward-evolving effect wave field ϕf= √ρf exp(iSf/ℏ), the central question is not merely where both amplitudes are non-zero. The question is whether an intermediate support structure can simultaneously satisfy the transport requirements imposed by both boundaries. The framework introduces a log-transport defect Dα associated with the power-family density ρα = ρα i ρ1−α f transported by the symmetric boundary velocity v= (ui+uf)/2. The defect admits an exact decomposition into an irreducible geometric obstruction, a density-reweighting channel, and one-boundary continuity residuals. This decomposition generates a hierarchy of repair classes ranging from global density reweighting through local density repair and finally to topological obstruction characterized by nodal winding mismatch. The framework lifts naturally from ordinary space to full configuration space, where the primary object is not a trajectory but a connected component of low-obstruction support. These components, termed admissible support tubes, provide a geometric description of conditional event connectivity under two-boundary constraints. The framework does not modify the Born rule, does not introduce hidden signalling, and does not identify weak values with literal particle trajectories. It proposes a diagnostic geometry for conditional quantum support based on exact transport compatibilit
This document develops a mathematical framework for two-boundary quantum admissibility. Given initial and final wave fields ψi = √ρieiSi/ℏ and ϕf= √ρfeiSf /ℏ , one asks when an intermediate local support structure is compatible with both boundary data. The central diagnostic is the log-transport defect of a power-family density ρα = ρα i ρ1−α f transported by the symmetrized velocity v = (ui + uf)/2. 1This defect decomposes exactly into an irreducible geometric obstruction, a density- reweighting channel, and one-boundary continuity residuals. The scalar parameter α is thereby recognized not as the whole theory, but as the first repair test. Scalar reweighting removes only a one-dimensional projection of the geometric-mean defect. Promoting α to a local field α(x,t) converts the repair problem into a first-order transport equation, and failure of that equation gives a stronger form of obstruction. Finally, nodal winding mismatch TC = m 2πℏ C(ui−uf)·dℓ= ni(C)−nf(C) is invariant under scalar and local density reweightings, yielding a non-reweightable topological obstruction. The framework lifts naturally to configuration space, where physical event succession is described by admissible support connectivity rather than by ordinary- space path continuity. Classical trajectories arise as narrow projected support tubes, while quantum nonclassicality appears when admissible connectivity persists in configuration space although its ordinary-space projection is broad, thresholded, or coarse-grained. Coherence dynamics and holonomy sectors are discussed as extensions of the admissibility hierarchy rather than as part of its theorem-level core.
Thismanuscriptproposesastrongerunifiedtheorysynthesizingtwopreviouslyseparatedideas: two-boundary admissibility geometry and weak-osmotic source-active closure in Sutherland-type action-reaction dynamics. The first ingredient supplies a diagnostic geometry of compatibility for pre-/post-selected or initial/final quantum boundary data through a log-transport defect, density repair hierarchy, nodal winding obstruction, and configuration-space support tubes. The second ingredient supplies an effective closed reaction law in which a guidance-mismatch field is no longer arbitrary but is tied to a regularized imaginary weak momentum, producing a compensated local source that redistributes wave intensity while preserving total trace. The present synthesis argues that these structures should not remain independent. If two-boundary transport mismatch is physically meaningful, then the natural next step is not merely to diagnose where support is admissible, but to formulate a candidate compensated dynamics on admissible support and to state explicitly where density-only reaction must fail due to phase-topological obstruction. The resulting proposal is a two-boundary trace-preserving closure on an interpolating density family ρα = ρα i ρ1−α f and symmetric transport field v= (ui + uf)/2. A regularized weak-osmotic mismatch ∆pα is built from ∇ln ρα,δ, but its action is gated by an admissibility weight derived from the defect hierarchy. The effective source is written in exact replicator-compensation form σα = ρα(gα−⟨gα⟩ρα ), guaranteeing exact global norm preservation on the chosen regular domain. This makes it possible to distinguish kinematically repairable mismatch, dynamically amplifiable low-obstruction support, and topologically forbidden sectors that no density reweighting can resolve. Branch drift, barrier correction, tube reinforcement, and relative support selection are then reformulated as compensated source-per-mass imbalances on connected components of low-defect configuration-space support. The manuscript is explicit about status boundaries. The geometric defect decomposition, support-tube language, and topological obstruction analysis are exact at the stated regularity level. The trace-preserving source closure is a proposed effective extension, not accepted quantum mechanics. The no-signalling boundary is isolated as an explicit marginal-source condition and verified in the stated symmetry and barrier-gated sectors; a fully relativistic completion remains a separate extension. What is claimed is narrower but more useful: the combined framework yields a mathematically sharper theory of admissible source-active quantum support in which compatibility geometry and reaction dynamics constrain one another rather than remaining disconnected.
We formulate a conditional geometric framework for a phase bypass of a zero sector. The calibrated order parameter is a smooth section of a Hermitian complex line bundle, not a complete normalized quantum state. At a transverse zero, its normalized section has no canonical continuous extension to a full neighbourhood in the original space, whereas its pullback extends uniquely and smoothly to the exceptional boundary of the real oriented blow-up. The boundary value is determined by the vertical derivative and records the incoming normal direction; it does not select an outgoing path. On a controlled scattering component, a Hamiltonian flow supplies the missing dynamical datum under explicit transversality, two-sided non-trapping, completeness, and uniqueness assumptions. The resulting first-exit map is a symplectomorphism and is C1 persistent under small C2 perturbations of shifted Hamiltonians with uniform C3 control and quantitative regularity, flight-time, boundary-separation, and intersection-isolation margins. A Koopman–cocycle operator transports an internal fibre over this map but remains a classical construction unless a separate quantum realization is supplied. For a symmetry-constrained cubic exceptional-point slice, analytic continuation gives exact C3 monodromy, and a companion generator admits a formal GKSL-compatible no-jump embedding after a uniform loss shift. An engineered retain/erase benchmark provides programmed positive control and independently calibrated erase and lifted-EP3 nulls. The register-free bridge forbids deliberate injection of the orientation label, defines a natural carrier as minimal process memory across a certified causal break, and separates Hilbert-space spectral subspaces from Liouville-space operator modes. Exact memory identification is stated as a reversible full-algebra sufficiency criterion. A separate approximate theorem converts finite recovery and predictive-factorization errors into quantitative information and output-distribution bounds. A unified analytic benchmark derives the section, first-exit dynamics, resolved-to-control map, spectral family, and Kato transport from one calibrated joint model. These results define a falsifiable certification programme; they do not claim a completed hardware realization or a universal law of phase bypass.
Finite quantum environments can relax local probes without acting as canonical baths. We study this distinction for a probe qubit coupled to a programmable bath of (N) qubits under excitation-number-conserving dynamics. The conserved charge partitions the Hilbert space into sectors. We characterize probe-level bath emergence using the sector-resolved late-time population (pe(q)), the sector-memory variance (MN), and a global Gibbs-fit error (ΔGglobal). Exact simulations with Haar-random pure states in each complete fixed-charge sector yield sector-dependent populations close to the maximally mixed-sector benchmark (pe(q)=q/(N+1)), producing a nonzero Gibbs obstruction. We then construct charge-preserving Floquet circuits using (Rz) phases and (XX+YY) exchange gates, validate them with ideal and noisy Qiskit simulations, and implement finite-depth experiments on IBM Fez. For (N=4) and (ε=0), the hardware data give (MN≃0.044), (ΔGglobal≃0.558), and charge preservation near 0.90 after readout mitigation. A paired symmetry-breaking scan using bath (Rx(ε)) rotations reduces both diagnostics while increasing charge leakage, but does not erase sector ordering over the accessible depths. These results show that equilibration within constrained sectors is insufficient to produce a single sector-independent Gibbs state for the probe.