This companion appendix provides a standalone numerical supplement to the current reciprocal quantum hydrodynamics manuscript. The goal is narrow and explicit: to convert the paper’s one-dimensional periodic Weaver verification protocol into an executable, auditable simulation model. The supplement records the dimen- sionless verification system, the numerical scheme, the diagnostic contract, a baseline full-system run, a modal verdict sweep across the mobility exponents n= 0.5,1.0,1.5, and a nodal ϵ-descent stress test. The main numerical findings are that mass is preserved to machine precision in the reported runs, the high-mode modal response exhibits the predicted threshold ordering across the n= 1 transition, and decreasing ϵ strongly amplifies the anomaly magnitude near nodal structure while remaining controlled in the present regularized reduced solver. These results strengthen the manuscript’s verification and falsifiability claims, while leaving the singular ϵ→0 limit, higher-dimensional non-normality diagnostics, and experimental calibration as open targets.
This companion appendix provides a standalone numerical supplement to the current reciprocal quantum hydrodynamics manuscript. The goal is narrow and explicit: to convert the paper’s one-dimensional periodic Weaver verification protocol into an executable, auditable simulation model. The supplement records the dimen- sionless verification system, the numerical scheme, the diagnostic contract, a baseline full-system run, a modal verdict sweep across the mobility exponents n= 0.5,1.0,1.5, and a nodal ϵ-descent stress test. The main numerical findings are that mass is preserved to machine precision in the reported runs, the high-mode modal response exhibits the predicted threshold ordering across the n= 1 transition, and decreasing ϵ strongly amplifies the anomaly magnitude near nodal structure while remaining controlled in the present regularized reduced solver. These results strengthen the manuscript’s verification and falsifiability claims, while leaving the singular ϵ→0 limit, higher-dimensional non-normality diagnostics, and experimental calibration as open targets.
We formulate a regularized reciprocal extension of quantum hydrodynamics motivated by action-reaction symmetry in pilot-wave theory and by Sutherland-type post-quantum back-reaction schemes. The reciprocal anomaly is sourced by the imaginary part of the local momentum weak value. In the formal unregularized limit this gives the minimal closure ∆p proportional to Im(pw ). Since that reduced closure is singular at nodes and generically behaves as an effectively open dynamics, we construct a bounded completion on the torus by introducing: (i) a nodal regularization Aε =−(ℏ/2m)∇ln(ρ+ ε), (ii) a smooth information-limited mobility controlled by a nonnegative global admissibility functional built from relative entropy and regularized Fisher information, and (iii) a transported Eulerian memory field encoding cumulative reciprocal activity. The resulting model is a globally coupled nonlinear PDE for (ρ,S,M) with Hamiltonian advection, bounded reciprocal transport, capillarity-regularized quantum pressure, and local memory loading. We prove exact identities for weak-value decomposition, mass conservation, reciprocal-current entropy- gradient form, and memory-energy balance. We then state an energy-controlled local classical well-posedness theorem for fixed ε>0, based on a high-regularity Sobolev–capillarity energy. A modal asymptotic result shows that if the mobility exponent satisfies n>1, ultraviolet amplification is suppressed in a Fisher-dominated fixed-amplitude scaling regime, with an extended condition for amplitude-decaying spectra. In reciprocal equilibrium the model reduces to a regularized Madelung-type quantum hydrodynamics, recovering the standard unregularized system formally as ε →0 away from nodal singularities. The framework remains a candidate closure rather than an established physical theory, but its mathematical content is explicit enough to be analyzed, simulated, and falsified.
A supplied bounded reciprocal plane supports compatible elliptic, metric and symplectic geometry, but it does not itself select a physical quantum system or an absolute action scale. This paper organizes an assumption-controlled finite architecture of cell size, convex polarity, composition, paired transport and operational access. It distinguishes amplitude and phase-space interpretations, vector complementation and polarity of regions, local cell projections and global body composition, and geometric holonomy and measured response. The mathematical analysis includes a conditional polarity selector, a forward projection/section identity for supplied symplectic ellipsoids, an explicit counterexample to a fixed-splitting converse for general ellipsoids, inverse-transpose paired transport, a common-connection criterion and reference-dependent response comparisons. No primitive derivation of a quantum state cone, tensor product, minimum action, physical instrument or probability law is claimed. The accompanying source-and-evidence supplement contains the manuscript source, three preserved Python exact-check programs, and a partial Lean 4.19.0 formalization. Audited records of a local run support acceptance of 99 theorem/lemma declarations and 33 definitions/abbreviations. The actual set-level geometry of the concrete ellipsoid counterexample is included; the full convex-lattice, capacity, projective, all-rank geometric and smooth-connection results are not all formalized. This is not full-paper formal verification, external human peer review or a new compiler run. All selected command streams and type/axiom output remain verbatim. One local-run receipt is provided as a clearly labelled path-normalized derivative, with its original hash retained. The full private lineage is preserved separately. The current reading edition is version 1.0; the unchanged version 0.3 materials are retained only as verification baselines.
A theoretical and computational framework separating accepted protocol support, record-quality diagnostics, replicated entropy moments and implementation-level bookkeeping. A bounded positive effect induces a completed quotient Hilbert space; integer density-matrix moments are calculated through permutations on identical product copies; signed entropy increments telescope along a fixed reduction. Version 3.2 clarifies support versus distinguishability, finite-dimensional assumptions, higher-order observables, finite-copy uncertainty, numerical rank, logarithm units, additive ledgers and the limits of return diagnostics. A failed chosen inverse does not alone establish irreversible dynamics, and zero entropy residual does not establish state or apparatus return. The companion provides new reproducible central-spin and 500-state SWAP checks, an explicitly defined dephasing control, the recovered historical ledger script and its rerun, editable equations and manuscript sources. Missing historical central-spin and entropy-fit generators are disclosed. The associated Finite Record Protocol Calculator v0.3.0 supplies instrument/record diagnostics, Python and JavaScript parity checks, strict validation and a reduced-state entropy-path interface. This is the first deposit of this manuscript series, superseding working drafts v1.0 through v3.1. All examples are analytic or simulated; no laboratory measurements, empirical anchor, independent Born-rule derivation, emergent geometry or thermodynamic cost inferred from the accepted effect alone are claimed. The manuscript uses CC BY 4.0. Executable software and source code in the companion retain separate rights; see LICENSE_SCOPE.txt and software_dependency/RIGHTS.txt.
This record contains a manuscript and supporting reproducibility materials for “Ledger-Valid Recovery Diagnostics for Quantum Computing: A Prespecified Sequential Audit for Claim-Limited Recovery Validation.” The paper proposes a methodological validation framework for quantum-computing recovery claims. Its central claim is that endpoint recovery success is necessary but not sufficient for a strong recovery claim when calibration failure, false-carrier acceptance, postselection artifacts, leakage, sentinel blindness, or hidden discard can carry failure modes out of view. The manuscript introduces a prespecified S0–S4 ledger audit that converts familiar diagnostic ingredients—label calibration, candidate recovery, false-carrier challenge tests, postselection/leakage accounting, and sentinel observability—into an ordered, claim-limiting taxonomy. A supportive recovery claim is permitted only when all required gates pass; otherwise, the first failed stage determines a lower claim ceiling and an interpretable failure class. The evaluation is based on synthetic endpoint-level validation suites rather than circuit-level simulation or hardware data. These suites test the behavior of the decision architecture under clean support, degraded observability, false-carrier artifacts, postselection/leakage artifacts, sentinel-blind cases, correlated artifacts, and adversarial overlap. The results show a strong specificity/sensitivity tradeoff: the full ledger protocol sharply reduces synthetic non-support supportive-call rates relative to endpoint-only reporting, but with substantial loss of mechanism-positive support sensitivity. The paper explicitly treats this as a conservative claim-validity architecture, not as a new quantum error-correcting code, new physical observable, hardware speedup, or proof of improved device performance. The supporting materials document the final synthetic validation protocol, endpoint definitions, decision-bound implementation, direction-aware threshold sensitivity analysis, latent-threshold eligibility analysis, mechanism-negative/latent-eligible boundary cases, and figure/table traceability. The archive is intended to support review of the manuscript’s aggregate numerical claims and methodological provenance. Hardware implementation, independent simulator validation, and full raw-event-ledger reproduction are identified as future extensions. Suggested keywords: quantum computing; quantum error correction; validation methodology; recovery diagnostics; leakage; postselection; benchmarking; synthetic validation; decision architecture; reproducibility.
### Overview This repository and associated documentation introduce a transformative framework that shifts the traditional perspective on physical fields, relativistic quantum systems, and nuclear models. By unifying complex computational checks and precise data analysis, this work bridges theoretical innovations with practical, automated verification tools. ### Key Contributions & Scope * **Relativistic Quantum Systems:** Implements rigorous automated checks for hydrogen-like systems incorporating Dirac corrections and advanced wave equation solvers. * **Nuclear Models & Data Tables:** Features robust analytical tools for processing mass tables, binding energies, and nuclear structure parameters. * **Automated Verification Framework (`exchange_field_check_package_V3`):** Provides a comprehensive suite of modular scripts (`run_checks.sh`, modular model checkers) designed to ensure high reproducibility and precision in physical calculations. ### Contents of the Archive * `exchange_field_check_package_V3/`: Core package containing validation modules, test scripts, and historical/iterative round records. * Analytical scripts for atomic structures, nuclear properties, and comparative data verification. ### Usage & Quick Start To execute the automated verification suite, run: ```bash bash exchange_field_check_package_V3 /run_checks.sh # Summary This work presents a methodological and interpretational framework for Quantum Mechanics (QM) based on a **medium-first wave approach**. It does not introduce new physical laws or speculative forces; rather, it demonstrates how standard quantum phenomena—such as discrete spectra, wave-function collapse, and non-locality—can be naturally interpreted as **discrete exchange events** between continuous field modes and localized resonators within a wave medium. ### Key Highlights & Results - **Standard Physics Alignment**: The framework fully recovers established results of standard quantum mechanics and Quantum Electrodynamics (QED) without introducing non-standard free parameters. - **Hydrogen Atom & Dirac Spectrum**: Exact analytical and numerical match for the relativistic Hydrogen spectrum via the 2-component Dirac wave equation in a Coulomb field (reproducing the fine structure, 2P3/2 splitting, and 2S1/2−2P1/2 orbital structure). - **Helium Atom Ground State**: Verification of the two-electron configuration space representation (Hylleraas expansion) yielding E0=−2.903724 Hartree. - **Lamb Shift & Radiative Corrections**: Explains leading-order QED radiative shifts via mode-exchange dynamics with the zero-point wave field. - **Bell's Inequalities & Non-Locality**: Analyzes classical acoustic and hydrodynamic analogies (e.g., KdV solitons, walker drops), showing why 3D classical models fail Bell tests and demonstrating how non-locality is properly accommodated in ConfigurationSpace rather than standard 3D physical space. - **Thermodynamic & Biological Scales**: Connects medium viscosity, field density, and discrete thermal exchange equations (kBT) across scales ranging from chemical bonding to biological systems. ### Scope & Intent This work serves as an **educational, interpretational, and computational bridge** to demystify standard quantum mechanics. It provides Python/SciPy verification scripts to allow independent reproduction of all wave-equation solutions, spectral distributions, and mode-coupling c alculations. A single two-term law, dθ/dt = A − ρθ, with a toll m ≥ 1 at every door, tested against measured data in 511 rounds with the pass mark written before each number. 33 claims audited: 12 derived, 3 computed, 3 agree with measurement, 1 prediction (carrier 11 869.5 Hz, never measured), 4 parameters, 6 open, 4 killed. All failures published. 28 checks re-run from the package.
Quantum Mechanics from Constraint and Closure: A Structural Explanation and Derivational Roadmap assembles a sequence of ENSO quantum-foundations results into a single explanatory architecture. The paper asks why central structures of quantum mechanics—complex phase, conjugation, quadratic norm, Schrödinger dynamics, spinorial return, Born weighting, and measurement—belong together rather than appearing as an unrelated collection of formal ingredients. The proposed route begins with constraint-bearing distinction and minimal maintained recursion. Within an explicit primitive two-state class, recursive minimality selects the Fibonacci structure and its Perron root ϕ. Exchange completion (symmersion) derives a reciprocal pair, continuity and composability lift that pair to reciprocal flow, and bounded return selects a rotational generator satisfying J2=−I. Constraint-bearing eigenmodes then become phase-readable in Schrödinger form once ℏ supplies the action scale. Reciprocal product and exchange map exactly to quadratic norm and complex conjugation; Euclidean orthogonal composition fixes squared weight; repeatability leads to orthogonal projection; and intrinsic closure supplies the framework for event readability. A new canonical result provides an independent convergence. For a real symplectic system containing a genuinely non-real, non-unit scale-phase eigenmode, reality and symplectic reciprocity force the spectral orbit λ, λ̄, λ⁻¹, λ̄⁻¹ Such a mode is impossible in real symplectic dimension two; four dimensions are minimal. The resulting reciprocal-conjugate quartet contains exactly the reciprocal pairings used in the earlier closure geometry. The accompanying reproducibility archive contains the manuscript source, direct construction validator, adversarial null-test suite, captured outputs, machine-readable results, near-symplectic perturbation diagnostics, exact symbolic audit, validation-run provenance note, and package checksums. All twelve declared null tests pass in both recorded executions. The paper distinguishes completed mathematics, structural derivation, exact representation, and the remaining roadmap toward a fully native reconstruction of quantum theory. For further information about the ENSO Framework, please contact Eric Needham:ensotheory1@gmail.com