Consolidated Technical Addendum on Continuous Bidirectional Transport - Quantum BIC Dynamics and Classical Cooperative Transport with Calibrated Reset Controls
Overview This consolidated technical addendum accompanies Metastable Quantum Cavitation as a Continuous Bidirectional Transport Framework (DOI: 10.5281/zenodo.22944164). It integrates, revises, and extends the computational and methodological material presented in two previously published supplements: Beyond Mean Subsystem Distinguishability: A Distributional Heterogeneity of Local-Perturbation Accessibility (DOI: 10.5281/zenodo.23196395). Metastable Quantum Cavitation Technical Supplement No. 1 (DOI: 10.5281/zenodo.23305447). Scope and methodology The addendum examines phase-dependent transport and information-accessibility properties through complementary computational frameworks, including a three-qubit open quantum system governed by Lindblad dynamics, a separate classical continuous-time Markov model, and distributional distinguishability analyses using local perturbations. The quantum and classical models are treated as distinct constructions; no microscopic derivation of one from the other is claimed. The accompanying computational archive contains supporting data, numerical results, implementation materials, and reproducibility documentation. Main findings and limitations The analyses identify parameter-dependent transport responses and distributional distinctions that are not fully characterized by mean subsystem distinguishability alone. However, favorable changes in selected transport observables do not establish a general net energetic advantage. The reported accessibility tests likewise do not demonstrate universal superiority of the proposed measurement approach. The results are model-specific computational findings. They do not constitute experimental confirmation of metastable quantum cavitation, a demonstrated microscopic mechanism for the proposed physical framework, or evidence of gravitational effects. Relationship to previous publications This consolidated edition supersedes the two earlier supplements as the preferred technical and computational reference. Both preceding publications remain independently accessible and retain their historical provenance, original attribution, and bibliographic identity. The original framework paper remains the primary conceptual publication. This addendum provides its updated technical and computational supporting material. Reproducibility The deposited computational archive is provided to facilitate independent inspection and reproduction of the reported analyses. An accompanying SHA-256 checksum enables verification of archive integrity.
Overview This consolidated technical addendum accompanies Metastable Quantum Cavitation as a Continuous Bidirectional Transport Framework (DOI: 10.5281/zenodo.22944164). It integrates, revises, and extends the computational and methodological material presented in two previously published supplements: Beyond Mean Subsystem Distinguishability: A Distributional Heterogeneity of Local-Perturbation Accessibility (DOI: 10.5281/zenodo.23196395). Metastable Quantum Cavitation Technical Supplement No. 1 (DOI: 10.5281/zenodo.23305447). Scope and methodology The addendum examines phase-dependent transport and information-accessibility properties through complementary computational frameworks, including a three-qubit open quantum system governed by Lindblad dynamics, a separate classical continuous-time Markov model, and distributional distinguishability analyses using local perturbations. The quantum and classical models are treated as distinct constructions; no microscopic derivation of one from the other is claimed. The accompanying computational archive contains supporting data, numerical results, implementation materials, and reproducibility documentation. Main findings and limitations The analyses identify parameter-dependent transport responses and distributional distinctions that are not fully characterized by mean subsystem distinguishability alone. However, favorable changes in selected transport observables do not establish a general net energetic advantage. The reported accessibility tests likewise do not demonstrate universal superiority of the proposed measurement approach. The results are model-specific computational findings. They do not constitute experimental confirmation of metastable quantum cavitation, a demonstrated microscopic mechanism for the proposed physical framework, or evidence of gravitational effects. Relationship to previous publications This consolidated edition supersedes the two earlier supplements as the preferred technical and computational reference. Both preceding publications remain independently accessible and retain their historical provenance, original attribution, and bibliographic identity. The original framework paper remains the primary conceptual publication. This addendum provides its updated technical and computational supporting material. Reproducibility The deposited computational archive is provided to facilitate independent inspection and reproduction of the reported analyses. An accompanying SHA-256 checksum enables verification of archive integrity.
Metastable Quantum Cavitation — Technical Supplement No. 1 This technical supplement accompanies the original publication Metastable Quantum Cavitation as a Continuous Bidirectional Transport Framework (L. Benedettini, A.M. Sabatini, 2026; DOI: https://doi.org/10.5281/zenodo.22944164). It extends the original theoretical framework through explicitly specified and reproducible numerical investigations of continuous bidirectional quantum transport in a three-part B–I–C architecture. The study introduces a fully defined Hamiltonian, phase-dependent modulation, matched META/NO-META controls, open-system Lindblad dynamics, and dissipative load models with explicit energy accounting. The computational investigation includes 76 open-system simulations, 38 matched comparisons, and six closed-system trajectories, supported by numerical convergence tests, analytical benchmarks, and sensitivity analyses. Results demonstrate phase-dependent transport behavior, bidirectional current activity, and genuine load back-action. The energetic response depends on the chosen parameters and load model; no universal enhancement or independent energy source is established. The numerical implementations presented here differ from the exploratory calculations in the original publication. Consequently, they neither confirm nor refute the previously reported approximately +0.8% load enhancement under its original protocol. A separate semiclassical discussion retains the illustrative weak-field gravitational scaling as a theoretical hypothesis, without claiming an experimentally demonstrated spacetime effect. Reproducibility: The accompanying BIC_reproducibility_package.zip provides Python source code, simulation parameters, numerical datasets, validation tests, and integrity hashes, enabling independent inspection and reproduction of the reported computational results. This publication is intended as an independent technical and computational supplement to the original framework, not as a replacement or revised version of the primary paper. Licensing: The scientific manuscript (PDF), figures, and accompanying documentation are licensed under Creative Commons Attribution 4.0 International (CC BY 4.0). The original Python source code included in the reproducibility archive is licensed under the MIT License. Third-party dependencies retain their respective licenses.
This work develops a conceptual framework for metastable quantum transport based on continuous, phase-controlled tunneling between coupled subsystems. In contrast to an earlier capture–deadband–release formulation, the revised architecture maintains finite coupling throughout the transport cycle and treats reverse flow not necessarily as a loss, but as part of the total bidirectional dynamical activity of the system. The framework combines metastable interfacial modulation, quantum tunneling, local entropy/information redistribution, open-system transport, and explicit energy transduction. A series of dimensionless proof-of-principle toy models is used to test thermodynamic consistency and to distinguish four quantities that can otherwise be easily conflated: local entropy redistribution, net current, bidirectional current activity, and extractable work. Closed-system simulations preserve global von Neumann entropy while allowing local entropies and correlations to evolve. Open-system models explicitly account for reservoir energy, external drive work, dissipation, and load extraction. The numerical tests show that metastable phase modulation can modify internal bidirectional current activity and energy exchange with the drive. In a selected parameter regime, a passive bidirectional transduction model also exhibits a small, phase-dependent increase in load output relative to a non-metastable control. The results do not imply entropy-to-energy conversion, over-unity operation, or a new fundamental entropy current. Rather, they identify a thermodynamically consistent transport architecture whose potential novelty lies in combining continuous metastable modulation with the operational use of bidirectional current activity as a possible transduction resource. The work concludes by defining a falsifiable research program toward a microscopic, platform-specific realization and experimental comparison with an equivalent non-metastable control. The revised manuscript also develops a separate exploratory semiclassical extension, examining the chain from metastable transport to stress-energy redistribution, linearized metric response, and recursive backreaction. The analysis indicates that a nonzero stress-energy perturbation can formally source a metric perturbation, while gravitational coupling at ordinary laboratory scales makes the resulting response extremely small and the recursive feedback strongly subcritical. The extension therefore defines a quantitative failure boundary for practical causal engineering rather than providing evidence of a macroscopic modification of spacetime causality.
This is the Technical Supplement — the proof-dense companion and the canonical formal record for the paper's claims. The main paper argues; the supplement proves. Every load-bearing claim traces to a named check function in the APF verification engine, and the supplement is the document a referee should audit first. The supplement is self-contained for Paper 14: every definition, proof, and grade the paper rests on appears in this one document — the substrate primitives and the marginal admissibility floor, proved; the locality and cost-uniqueness lemmas; the Δ calculus with both fences' witnesses written out; the Boolean-defender bridge with its five certified physical hypotheses and the 3-4-5 worked witness computed on the page; the gate pipeline with a gate-by-axiom comparison to the operational-reconstruction literature (Hardy; Chiribella–D'Ariano–Perinotti; Masanes–Müller; Barnum–Wilce; Spekkens; Abramsky–Brandenburger); the native correlation family constructed explicitly, rung by rung; the resolution triad set against standard thermodynamics (Landauer, erasure, environment-assisted recovery); a consolidated readings register listing every claim below [P] with its falsifier and status; a glossary mapping the framework's vocabulary onto standard quantum-information terms; and a worked end-to-end instance — device to interrogation normal form to exact feasibility certificate to priced ledger, with every tolerance explicit. A reproducibility appendix pins every claim to the APF theorem bank at a named GitHub commit and the archived Engine release (DOI 10.5281/zenodo.18529115); the certificates reproduce deterministically in exact rational arithmetic. About the series. Admissibility Physics is a structural realist reconstruction program built on a single commitment: any bounded region of the world can hold only finitely many distinctions. A principle of least enforcement cost then selects, among all the ways those distinctions might be arranged, the configurations a finite world can sustain. From this the content of physics is reconstructed rather than postulated: the Standard Model's gauge group and matter content, the Hilbert-space and Born-rule architecture of quantum mechanics, the geometry and field equations of general relativity, the four laws of thermodynamics, and the large-scale budget of cosmology emerge as different readings of one finite-capacity ledger. The unification is quantitative as well as conceptual: the framework's dimensionless constants appear not as free parameters but as counts read off that ledger — among them the dark-energy fraction ΩΛ = 42/61 and the weak mixing angle sin2θW = 3/13 — fixed, in the strongest cases, to within current measurement. The core derivation runs Papers 0–11; the extension papers carry the individual sectors. Each paper's main text and Technical Supplement is deposited separately; every quantitative claim traces to a named, executable check in the public theorem bank (over 3,800 bank-registered theorems, 48 quantitative predictions); and each result is carried at an explicit, graded level of confidence — from analytically forced to structurally grounded — with the measurements that would refute it named. Admissibility Physics is offered as a candidate, not a finished theory. If the program holds, the laws of physics could not have been otherwise: they are what a finite world permits. Website: admissibilityphysics.com. Engine and theorem bank: https://github.com/Ethan-Brooke/APF-Engine. Full series and latest deposits: Zenodo community admissibility_physics. The Engine — Admissibility Physics: An Executable Constraint Framework and Constants Map — DOI 10.5281/zenodo.18529115. Paper 0 — What Physics Permits: A Constraint-First Framework for Physics — DOI 10.5281/zenodo.18439523 Paper 1 — The Enforceability of Distinction — DOI 10.5281/zenodo.18439200 Paper 2 — Finite Admissibility and the Failure of Global Description — DOI 10.5281/zenodo.18439274 Paper 3 — Entropy, Time, and Accumulated Cost — DOI 10.5281/zenodo.18439363 Paper 4 — Admissibility Constraints and Structural Saturation — DOI 10.5281/zenodo.18439397 Paper 5 — Quantum Structure from Finite Enforceability — DOI 10.5281/zenodo.18439433 Paper 6 — Dynamics and Geometry as Optimal Admissible Reallocation — DOI 10.5281/zenodo.18439445 Paper 7 — A Minimal Quantum of Action from Finite Admissibility — DOI 10.5281/zenodo.18439513 Paper 8 — The Admissibility-Capacity Ledger — DOI 10.5281/zenodo.19721384 Paper 9 — The Geometric Substrate as Cost Structure of Comparison Continuations — DOI 10.5281/zenodo.20041675 Paper 10 — The Calculus of Finite Continuability — DOI 10.5281/zenodo.20041680 Paper 11 — Forced Universality from Capacity-Bounded Admissibility — DOI 10.5281/zenodo.20684198 Paper 12 — The Gauge Sector of Admissibility Physics — DOI 10.5281/zenodo.21212521 Paper 13 — The Minimal Admissibility Core — DOI 10.5281/zenodo.18361446 Paper 14 — The Quantum Story — DOI 10.5281/zenodo.21212188 Paper 16 — Markov Breakdown and the Hard Problems — DOI 10.5281/zenodo.20684207 Paper 18 — The Electroweak Sector as a Capacity Equilibrium — DOI 10.5281/zenodo.20684209 Paper 19 — Large-Angle CMB Suppression as a Finite-Continuability Constraint — DOI 10.5281/zenodo.21199218 Paper 20 — The Enforcement Crystal — DOI 10.5281/zenodo.18531732 Paper 23 — Magnetically Dark Winding-Class Quantum Processors — DOI 10.5281/zenodo.21199220 Paper 24 — The Recruitment-Radius Extension — Foundations — DOI 10.5281/zenodo.20684211 Paper 25 — The Recruitment-Radius Extension: Applications — DOI 10.5281/zenodo.21199222 Paper 28 — Absolute Mass Scales from Electroweak Capacity Saturation — DOI 10.5281/zenodo.20684215 Paper 29 — Plaquette Representation Dominance and Confinement — DOI 10.5281/zenodo.20684218 Paper 30 — A Tube Mechanism for the Lattice Mass Gap — DOI 10.5281/zenodo.20684220 Paper 31 — Osterwalder–Schrader Structure of Lattice Yang–Mills — DOI 10.5281/zenodo.20684222 Paper 32 — Quark Anchors as APF Trace Masses — DOI 10.5281/zenodo.21199226 Paper 33 — Trace-to-Scheme Export Architecture — DOI 10.5281/zenodo.20684224 Paper 35 — The Dark Sector as a Two-Role Capacity Decomposition — DOI 10.5281/zenodo.20684228 Paper 36 — The Missing Floor — DOI 10.5281/zenodo.21199228 Paper 37 — Collapse as Realignment — DOI 10.5281/zenodo.21199231 Paper 38 — Unification as Ledger — DOI 10.5281/zenodo.21199233 Paper 39 — Coherent Phase Regimes in the APF Interface Engine — DOI 10.5281/zenodo.21199235 Paper 40 — The Thermodynamics of Finite Distinction (Between Symmetry and the Void) — DOI 10.5281/zenodo.20684235 Paper 41 — The Horizon as a Continuation Ledger — DOI 10.5281/zenodo.20684241 Paper 42 — The Weak Mixing Angle Is Not Free — DOI 10.5281/zenodo.20684245 Paper 43 — The Neutrino Sector — DOI 10.5281/zenodo.21194191 Paper 44 — What a Finite Theory Owes the Continuum — DOI 10.5281/zenodo.21195874 Paper 45 — What the Vacuum Can Keep — DOI 10.5281/zenodo.21194195 Paper 46 — The Strong CP Angle Is Not Free — DOI 10.5281/zenodo.21194197 Paper 47 — The Confinement Antecedent Is Not Forced — DOI 10.5281/zenodo.21194199 Paper 48 — The Light-Bending Weight Is Not Free — DOI 10.5281/zenodo.21199627 Technical Supplements cross-link to their main paper via isSupplementTo and to the engine via isDocumentedBy. Concept DOIs above resolve to the latest version.
Duplicate record. The canonical deposit for this paper is APF Paper 5 — Quantum Structure from Finite Enforceability (Technical Supplement) (DOI 10.5281/zenodo.19908706). This record is retained because published Zenodo DOIs cannot be removed; please cite the canonical record. Technical Supplement to Paper 5 of the Admissibility Physics Framework (APF), Quantum Structure as Least-Cost Admissible Bookkeeping. Paper 5 derives the complete quantum formalism — linearity, complex Hilbert space, tensor products, Born's rule, unitary and CPTP dynamics, measurement as class change, spectral-action internalisation, and UV-completion closure — from PLEC (A1, MD, A2, BW) plus the capacity quantization Ctot = 61, deff = 102 imported from Papers 1–4. The supplement provides self-contained proofs of the theorems compressed to sketch form in the main paper. Linearity from coherent-distinction closure. Tlinearity: if sector states |ψ1⟩, |ψ2⟩ are admissible and coherent-distinction-closed, then their normalised linear combination α|ψ1⟩ + β|ψ2⟩ with |α|2 + |β|2 = 1 is admissible. Complex Hilbert space. THilbert: the state space is a complex Hilbert space ℋ with inner product induced by the cost functional, and the field selection 𝔽 = ℂ is inherited from Paper 1's field-selection tier. Tensor product. Ttensor: composite systems factorise as ℋAB = ℋA ⊗ ℋB under admissibility of joint distinction. Born's rule. TBorn: measurement outcome probabilities are Pr(k | ρ) = Tr(Pk ρ) with {Pk} the projective decomposition operators corresponding to admissible partition classes — derived, not postulated. Unitary and CPTP dynamics. THermitian and TCPTP: admissible state evolution is Hermitian-generated for closed systems and CPTP for open systems, both from minimum-cost bookkeeping. Measurement as class change. Tdecoherence: measurement is the transition from an admissible coherent superposition to an admissible classical register, formalised as a class change on the equivalence structure of admissible states. Spectral-action internalisation. Lspectral_action_internal: the Connes spectral action coincides with the APF partition function under the Boltzmann cutoff. Full proof in Paper 7 Technical Supplement §S.4. UV-completion closure. LQG_P1_closure: the admissibility framework remains consistent under Paper 1's structural extension to UV scales. Explicit countermodels exclude the main published quantum-reconstruction alternatives (Hardy 2001, Masanes–Müller 2011, d'Ariano–Chiribella–Perinotti 2010, Rovelli relational). Red-team section analyses three paper-specific hypotheses (H1 coherent-distinction closure, H2 tensor-product admissibility, H3 spectral-action compatibility). Theorem index, dependency diagram, and changelog close the document. Readable without prior exposure to the APF series. Code and reproducibility. GitHub repository Colab walkthrough notebook (one-click) Interactive dependency DAG About the series. Admissibility Physics derives the Standard Model gauge group, fermion content, quantum formalism, Lorentzian spacetime, the Einstein field equations, the cosmological constant, and the neutrino, strong-CP, and dark sectors from a single assumption — that enforcement is finite at every causally connected region — with zero free parameters. The core derivation runs Papers 0–11; the extension papers carry the individual sectors. Each paper's main text and Technical Supplement is deposited separately, and every quantitative claim traces to a named, executable check in the public theorem bank (over 3,800 bank-registered theorems across roughly 450 modules, 48 quantitative predictions). Website: admissibilityphysics.com. Engine and theorem bank: https://github.com/Ethan-Brooke/APF-Engine. Full series and latest deposits: Zenodo community admissibility_physics. The Engine — Admissibility Physics: An Executable Constraint Framework and Constants Map — DOI 10.5281/zenodo.18529115. Paper 0 — What Physics Permits: A Constraint-First Framework for Physics — DOI 10.5281/zenodo.18439523 Paper 1 — The Enforceability of Distinction — DOI 10.5281/zenodo.18439200 Paper 2 — Finite Admissibility and the Failure of Global Description — DOI 10.5281/zenodo.18439274 Paper 3 — Entropy, Time, and Accumulated Cost — DOI 10.5281/zenodo.18439363 Paper 4 — Admissibility Constraints and Structural Saturation — DOI 10.5281/zenodo.18439397 Paper 5 — Quantum Structure from Finite Enforceability — DOI 10.5281/zenodo.18439433 Paper 6 — Dynamics and Geometry as Optimal Admissible Reallocation — DOI 10.5281/zenodo.18439445 Paper 7 — A Minimal Quantum of Action from Finite Admissibility — DOI 10.5281/zenodo.18439513 Paper 8 — The Admissibility-Capacity Ledger — DOI 10.5281/zenodo.19721384 Paper 9 — The Geometric Substrate as Cost Structure of Comparison Continuations — DOI 10.5281/zenodo.20041675 Paper 10 — The Calculus of Finite Continuability — DOI 10.5281/zenodo.20041680 Paper 11 — Forced Universality from Capacity-Bounded Admissibility — DOI 10.5281/zenodo.20684198 Paper 13 — The Minimal Admissibility Core — DOI 10.5281/zenodo.18361446 Paper 16 — Markov Breakdown and the Hard Problems — DOI 10.5281/zenodo.20684207 Paper 18 — The Electroweak Sector as a Capacity Equilibrium — DOI 10.5281/zenodo.20684209 Paper 20 — The Enforcement Crystal — DOI 10.5281/zenodo.18531732 Paper 24 — The Recruitment-Radius Extension — Foundations — DOI 10.5281/zenodo.20684211 Paper 28 — Absolute Mass Scales from Electroweak Capacity Saturation — DOI 10.5281/zenodo.20684215 Paper 29 — Plaquette Representation Dominance and Confinement — DOI 10.5281/zenodo.20684218 Paper 30 — A Tube Mechanism for the Lattice Mass Gap — DOI 10.5281/zenodo.20684220 Paper 31 — Osterwalder–Schrader Structure of Lattice Yang–Mills — DOI 10.5281/zenodo.20684222 Paper 33 — Trace-to-Scheme Export Architecture — DOI 10.5281/zenodo.20684224 Paper 35 — The Dark Sector as a Two-Role Capacity Decomposition — DOI 10.5281/zenodo.20684228 Paper 40 — The Thermodynamics of Finite Distinction (Between Symmetry and the Void) — DOI 10.5281/zenodo.20684235 Paper 41 — The Horizon as a Continuation Ledger — DOI 10.5281/zenodo.20684241 Paper 42 — The Weak Mixing Angle Is Not Free — DOI 10.5281/zenodo.20684245 Paper 43 — The Neutrino Sector — DOI 10.5281/zenodo.21194191 Paper 44 — What a Finite Theory Owes the Continuum — DOI 10.5281/zenodo.21195874 Paper 45 — What the Vacuum Can Keep — DOI 10.5281/zenodo.21194195 Paper 46 — The Strong CP Angle Is Not Free — DOI 10.5281/zenodo.21194197 Paper 47 — The Confinement Antecedent Is Not Forced — DOI 10.5281/zenodo.21194199 Technical Supplements cross-link to their main paper via isSupplementTo and to the engine via isDocumentedBy. Concept DOIs above resolve to the latest version. Author. Ethan Brooke, Independent Researcher, San Anselmo, California, USA. ORCID: 0009-0001-2261-4682 LinkedIn: linkedin.com/in/ethanbrooke GitHub: github.com/Ethan-Brooke Contact: brooke.ethan@gmail.com
This record contains version 2 of the preprint “Identifiability Limits in Experimental Tests of Quantum Collapse.” It supersedes the conceptually broader first version deposited under DOI 10.5281/zenodo.19617199 and substantially revises the framing, formal results and experimental analysis. The paper formulates experimental tests of objective-collapse dynamics as an operational identifiability problem. It shows that finite accessible CPTP process statistics cannot uniformly distinguish fundamental nonunitarity from an unrestricted unitary-environment dilation. It then separates visibility loss, record formation and global measurement access, and derives a nuisance-profiled Fisher-information criterion for determining when complementary measurement channels jointly identify a shared collapse-parameter vector. A four-arm matched-control architecture is proposed that combines baseline stability, coherent reversibility, calibrated decoherence, durable-record formation and at least one independent side-effect channel. The result is a falsifiable experimental decision framework and a boundary on what accessible data can establish; it is not presented as an ontological solution of the quantum measurement problem. A major technical revision is available as version 3 under DOI 10.5281/zenodo.22072199. This record contains version 2 of the preprint “Identifiability Limits in Experimental Tests of Quantum Collapse.” It supersedes the conceptually broader first version deposited under DOI 10.5281/zenodo.19617199 and substantially revises the framing, formal results and experimental analysis. The paper formulates experimental tests of objective-collapse dynamics as an operational identifiability problem. It shows that finite accessible CPTP process statistics cannot uniformly distinguish fundamental nonunitarity from an unrestricted unitary-environment dilation. It then separates visibility loss, record formation and global measurement access, and derives a nuisance-profiled Fisher-information criterion for determining when complementary measurement channels jointly identify a shared collapse-parameter vector. A four-arm matched-control architecture is proposed that combines baseline stability, coherent reversibility, calibrated decoherence, durable-record formation and at least one independent side-effect channel. The result is a falsifiable experimental decision framework and a boundary on what accessible data can establish; it is not presented as an ontological solution of the quantum measurement problem. Files in this record:1. Main preprint PDF.2. Reproducibility package containing the journal-neutral source, editable manuscript, original figures, deterministic calculation and figure-generation code, machine-readable results, citation metadata and SHA-256 checksums. The included calculations are deterministic mathematical and synthetic checks; they are not experimental validation.
Overview This Zenodo repository contains the research artifacts associated with the manuscript: “Christoffel-Symbol-Encoded Geodesics on Quantum Hardware: Toward an Experimental Platform for Curvature-Quantum Interplay” The repository accompanies the APS journal submission and contains the submission manuscript, computational notebook, experimental run notes, quantum circuit files, an interactive HTML module, and handwritten theoretical and conceptual notes developed during the research. These materials are provided to support transparency, reproducibility, verification, and further exploration of the proposed framework for encoding Christoffel-symbol information into quantum circuits and studying geodesic dynamics on quantum hardware. Note: This archive contains the APS submission draft and research-development artifacts. Some files are working notes, intermediate materials, or experimental documentation and should not be interpreted as part of the final published version of the manuscript. Repository Contents 1. APS Submission Draft The Submission Draft_Final folder contains the manuscript and supporting notes associated with the APS journal submission. The primary manuscript is: ChristoffelSymbolEncoding_Final_submission_draft.pdf This PDF contains the manuscript prepared for submission to the APS journal. The folder also contains supporting documentation associated with the reported experimental results. 2. Computational Notebook The repository contains: Geodesic.ipynb This Jupyter Notebook contains computational material associated with the proposed framework and the analysis of the experimental results. The notebook includes calculations and analysis used during the development and evaluation of the Christoffel-symbol-encoded geodesic circuits. The notebook represents a research and submission working artifact and is included to document the computational workflow and analysis. The notebook can be opened using: Jupyter Notebook JupyterLab Google Colab Other compatible Jupyter environments 3. Interactive HTML Module The HTML_file folder contains an interactive HTML implementation of the setup described in the manuscript. The HTML module is designed so that users can download it and interact with or modify the setup locally without requiring an account or login. Using the HTML module Download the HTML_file folder from this repository. Open the included index.html file in a modern web browser. Explore the interactive setup. Modify the available parameters/settings directly in the interactive module. Use the modified configuration to explore how changes affect the corresponding setup. No login or external account is required to use or modify the locally downloaded HTML module. The HTML artifact is provided as an accessible, interactive research tool intended to make the experimental setup easier to inspect and explore. Note: The HTML module is a local interactive artifact. Its behavior may depend on the browser and the capabilities implemented in the provided HTML/JavaScript files. 4. QASM Quantum Circuits The repository contains the following OpenQASM circuit files: geodesic_.qasm geodesic_schwarzschild.qasm geodesic-flat.qasm These files contain the quantum circuits used to implement and investigate the proposed geodesic encoding. The QASM files can be imported into compatible IBM Quantum/Qiskit environments, including the IBM Quantum Composer where supported, for inspection and execution. Researchers can use these files to: Inspect the circuit construction. Examine the gate-level implementation. Reproduce the circuit setup. Modify the circuits for additional experiments. Execute the circuits on compatible quantum simulators. Execute the circuits on available IBM quantum hardware. Hardware execution considerations The circuits were designed for execution on real quantum hardware. Results from subsequent executions may not be numerically identical to the results reported in the manuscript. This is expected for experiments performed on noisy quantum hardware because measured results can depend on: Hardware calibration Qubit coherence and connectivity Gate and readout errors Device noise Compilation/transpilation Backend configuration Execution date and time Number of measurement shots Therefore, the QASM files are intended to provide the reproducible circuit and experimental procedure, while acknowledging the time-dependent nature of physical quantum hardware. 5. Handwritten Theoretical and Conceptual Notes The Handwritten Theory Notes folder contains handwritten material documenting the conceptual and theoretical development of the research. The materials include: Initial theoretical ideas Derivations and calculations Circuit-design sketches Christoffel-symbol encoding concepts Spacetime and geodesic illustrations Experimental setup notes Run-specific observations Additional conceptual development related to the curvature–quantum interplay They are included to document the development of the underlying research idea and provide additional context for the methodology presented in the manuscript. These materials should be considered research-development notes rather than polished manuscript material. Experimental Run Documentation The repository includes documentation of the experimental runs used in developing and evaluating the proposed framework. The experimental artifacts include: Quantum circuit files in QASM format Computational analysis in the Jupyter notebook Run-specific written observations Handwritten experimental notes Interactive visualization and exploration of the proposed setup The run notes are included to provide additional context concerning the observed behavior of the circuits on quantum hardware. Because the experiments involve real quantum hardware, variations between executions are expected. The purpose of providing the circuit files and associated documentation is therefore to enable researchers to reproduce the experimental setup, circuit construction, and methodology, rather than to imply that every hardware execution will produce exactly identical measurement statistics. Reproducibility The artifacts in this repository are intended to facilitate independent examination and reproduction of the work. The principal reproducibility components are: Artifact Purpose Geodesic.ipynb Computational calculations and analysis .qasm files Gate-level quantum circuit implementations index.html Interactive and locally modifiable representation of the setup Submission PDF Scientific description of the proposed methodology and experiments Results notes Documentation of experimental observations Handwritten notes Conceptual and theoretical development of the approach For quantum-hardware experiments, reproducibility should be understood in the context of noisy and time-varying physical hardware. Re-execution of the same circuit can result in different measurement statistics even when the circuit parameters and experimental protocol are unchanged. Accordingly, the repository provides the information necessary to reproduce the circuit construction and experimental methodology, while hardware-dependent numerical variations should be expected. File Organization Christoffel_Symbol_Encoding_Submission/ │ ├── Geodesic.ipynb │ ├── geodesic_.qasm ├── geodesic_schwarzschild.qasm ├── geodesic-flat.qasm │ ├── HTML_file/ │ └── index.html │ ├── Handwritten Theory Notes/ │ ├── Run1.HEIC │ ├── Run2.HEIC │ ├── Page1.HEIC │ ├── Page2.HEIC │ ├── Page3.HEIC │ ├── Fig1a) Chris_Symbol_encoding.drawio.png │ └── fig2_spacetime_geodesic.png │ └── Submission Draft_Final/ ├── ChristoffelSymbolEncoding_Final_submission_draft.pdf └── Copy of Notes-on-results.docx Authors Dr. Hemanth Gudaparthi, Dr. Yacine Merdjemak The handwritten theoretical notes, conceptual sketches, and research-development materials included in this archive were prepared by Dr. Hemanth Gudaparthi during the development of the work. He also implemented the quantum circuit, applied the error-mitigation protocol, analyzed the measurement results, and wrote the manuscript Dr. Yacine Merdjemak has provided input on the reasoning, the approach, and the quantum circuit implementation, reviewed the manuscript, and commented on the theoretical framework and result interpretation. Associated Manuscript Christoffel-Symbol-Encoded Geodesics on Quantum Hardware: Toward an Experimental Platform for Curvature-Quantum Interplay The manuscript included in this repository represents the APS journal submission draft associated with these research artifacts. Please refer to the final published version of the manuscript for the authoritative bibliographic record once publication is complete. Citation If you use the computational notebooks, QASM circuits, interactive HTML module, experimental notes, handwritten notes, or other materials from this repository, please cite the associated manuscript: Hemanth Gudaparthi, Yacine Merdjemak, Christoffel-Symbol-Encoded Geodesics on Quantum Hardware: Toward an Experimental Platform for Curvature-Quantum Interplay, 2026, https://doi.org/10.5281/zenodo.22162434 The citation should be updated to the final journal bibliographic information when the manuscript is published. Use of the Materials These materials are provided for research, educational, verification, and scholarly exploration. Users are encouraged to: Examine and modify the locally available HTML module. Inspect and modify the QASM circuits. Re-run the computational notebook. Reproduce the experimental circuit construction. Extend the framework to additional parameters, circuit depths, geometries, or quantum hardware platforms. Please cite the associated manuscript