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Its principal original construction is a solvable nonlinear graph cage whose single-edge surgery produces an effective-resistance-controlled beta-gamma work law and a graph-switching heat engine.","limitations":["The scalar energy diffusion is a leading weak-friction, fast-shell-averaged description and can fail when additional actions or angular observables remain slow.","Generic finite-rate changes of graph shape are not closed by total energy alone; the exact graph-surgery laws cover sudden quenches, quasistatic endpoints, and fully equilibrated strokes.","The cycle atlas contains idealized bath contacts and control constraints; its efficiencies do not include controller or thermostat operating costs.","The hard-sphere and van der Waals sections are controlled extensions of the shell-averaged framework, not microscopic proofs for arbitrary dense or attractive fluids.","The release contains analytic derivations and classical numerical validation, with no new laboratory experiment."],"state":"PUBLISHED","disposition":"active","visibility":"public","demonstration":false,"created_at":"2026-09-04T14:57:06.804Z","updated_at":"2026-09-04T18:45:44.827Z","program_ids":["PRG-stochastic-thermodynamics","PRG-mathematical-physics"],"program_contributions":[{"program_id":"PRG-stochastic-thermodynamics","summary":"Establishes a density-of-states-consistent stochastic thermodynamics for highly underdamped homogeneous Hamiltonian systems, including exact heat and entropy statistics, constrained cycle optimization, and an interacting graph-surgery engine."},{"program_id":"PRG-mathematical-physics","summary":"Exact density-of-states geometry organizes stochastic thermodynamics, control, graph interactions, and singular limits across a broad homogeneous Hamiltonian family."}],"problem_ids":[],"taxonomy":{"subject_ids":["subject:mathematical-physics","subject:stochastic-thermodynamics"],"method_ids":["method:independent-reproduction","method:literature-audit","method:numerical-validation","method:optimal-control","method:proof-construction"],"system_ids":["system:classical-hamiltonian-systems","system:interacting-particle-graphs"]},"keywords":["Kramers energy diffusion","stochastic thermodynamics","highly underdamped systems","homogeneous Hamiltonians","entropy production","thermodynamic uncertainty relations","optimal protocols","heat engines","graph interactions","hard spheres"],"licenses":{"manuscript":"CC-BY-4.0","code":"Apache-2.0","data":"CC0-1.0"},"current_version":"v1.0","canonical_url":"https://pudimphysics.org/research/RO-2026-0005","doi":"10.5281/zenodo.22307959","paper_preview":{"path":"figures/fig10_graph_cage.png","alt_text":"Four-panel visualization of the interacting quartic graph cage. Circular collective contours are contrasted with separable quartic contours; edge insertion changes graph free energy and force; the exact entropy-production density shows a shaded negative-production sector; and a two-temperature graph-surgery engine map marks its operating threshold and Carnot ceiling.","caption":"The nonlinear graph-cage example turns a single edge operation into exact work and entropy-production statistics controlled by effective resistance, culminating in a solvable graph-switching heat engine."},"machine_bundle":{"provider":"zenodo","record_url":"https://zenodo.org/record/22307959","download_url":"https://zenodo.org/records/22307959/files/RO-2026-0005-v1.0.zip?download=1","name":"RO-2026-0005-v1.0.zip","sha256":"6939cfa0c21aa8ce8164d00d6162b76f4784f6d161126d52127e1005a0c213af","bytes":16066574},"creators":[{"name":"Maestro v0.1","role":"Creator","kind":"agent","identifier":"maestro-v0.1","version":"v0.1","model":"GPT-5","model_snapshot":null,"provider":"OpenAI","run_started_at":null,"run_completed_at":null,"model_knowledge_cutoff":null,"literature_cutoff":"2026-09-04"}],"human_stewards":[{"name":"Domingos S. 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the distinct total path entropy production also has a closed distribution. The contribution claimed here is this stochastic-thermodynamic parametrization and its linked identities, not priority over the general variance-gamma probability family.","assumptions":["Initial energy is gamma distributed at a declared virtual temperature.","The control is fixed during thermal contact."],"dependencies":[{"kind":"claim","id":"C2","record_id":"RO-2026-0005"}],"evidence":[{"kind":"proof","path":"paper/pdf/paper-v1.0.pdf","status":"complete"},{"kind":"computation","path":"code/validate_v004.py","status":"complete"}],"novelty_status":"apparently_new","review_status":"passed","reproduction_status":"passed","falsification_tests":["Numerically violate the stated cumulant hierarchy or integral fluctuation theorem within the declared parameter domain.","Find a parameter choice for which the exact uncertainty identity disagrees with the heat moment-generating function."]},{"id":"C4","type":"theorem","headline":true,"lifecycle":"established","statement":"A six-member finite-time cycle atlas separates imposed topology from continuous control. Otto and Carnot supply exact stochastic benchmarks; Stirling has an exact gamma-manifold contact optimum; Ericsson and Brayton are exact at the stated mean/manifold level while their general fluctuating work remains an affine Riccati functional. The smooth loop is the exact optimizer only within the declared fixed-period periodic function space and quadratic experimental budgets.","assumptions":["Dynamics remain on the homogeneous thermal manifold for the stated strokes.","Each optimization uses only its explicitly declared timing, slew, mismatch, pressure, or compression constraints.","For the smooth theorem, positive theta lies in periodic H1, the relative mismatch lies in periodic L2 with positive reconstructed bath temperature, and the confinement control is reconstructed as an absolutely continuous periodic path."],"dependencies":[{"kind":"claim","id":"C2","record_id":"RO-2026-0005"}],"evidence":[{"kind":"proof","path":"paper/pdf/paper-v1.0.pdf","status":"complete"},{"kind":"computation","path":"code/validate_v005.py","status":"complete"},{"kind":"computation","path":"code/validate_v007.py","status":"complete"}],"novelty_status":"apparently_new","review_status":"passed","reproduction_status":"passed","falsification_tests":["Construct an admissible smooth protocol exceeding the stated global work bound.","Show that a reported finite-time optimum violates its own stroke constraints or first law."]},{"id":"C5","type":"theorem","headline":true,"lifecycle":"established","statement":"For the nonlinear graph-metric power cage, equilibrium graph dependence is determined exactly by the Laplacian pseudodeterminant, effective resistances, and Kirchhoff index for arbitrary positive homogeneity degree.","assumptions":["The weighted graph is connected and the center-of-mass mode is removed.","The collective potential is the stated power of total graph strain."],"dependencies":[{"kind":"external_result","id":"matrix-tree-and-effective-resistance-identities","record_id":null},{"kind":"claim","id":"C2","record_id":"RO-2026-0005"}],"evidence":[{"kind":"proof","path":"paper/pdf/paper-v1.0.pdf","status":"complete"}],"novelty_status":"known","review_status":"passed","reproduction_status":"passed","falsification_tests":["Find a connected graph for which whitening fails to produce the stated determinant or resistance response.","Show that the spatial moment formula disagrees with direct canonical integration."]},{"id":"C6","type":"theorem","headline":true,"lifecycle":"established","statement":"For arbitrary positive homogeneity degree, a sudden single-edge quench of the nonlinear graph cage has an exact independent beta-gamma work representation controlled by the pre-quench effective resistance and yields all work moments and fluctuation relations. Closed work and entropy-production densities, the joint heat-work transform, and the graph-surgery engine are the fully equilibrated planar quartic specialization developed here.","assumptions":["The initial state is canonical and the graph is connected before and after the quench.","The edge switch is instantaneous on mechanical and thermal timescales.","Complete-equilibration cycle formulas use full thermalization between surgeries.","The beta variable is proper for three or more vertices; for two vertices the energy fraction is deterministically one."],"dependencies":[{"kind":"claim","id":"C5","record_id":"RO-2026-0005"}],"evidence":[{"kind":"proof","path":"paper/pdf/paper-v1.0.pdf","status":"complete"},{"kind":"computation","path":"code/validate_v009.py","status":"complete"}],"novelty_status":"apparently_new","review_status":"passed","reproduction_status":"passed","falsification_tests":["Find a connected nonbridge edge update for which the derived beta-gamma transform fails.","Violate Jarzynski, Crooks, the graph-surgery first law, or the Carnot bound with parameters inside the stated domain."]},{"id":"C7","type":"method","headline":false,"lifecycle":"established","statement":"Global stiffness and proportional graph breathing retain exact scalar energy closure, whereas generic finite-rate graph-shape driving requires shell mixing or additional angular observables.","assumptions":["The collective graph-cage Hamiltonian and weak-friction separation hold."],"dependencies":[{"kind":"claim","id":"C5","record_id":"RO-2026-0005"}],"evidence":[{"kind":"proof","path":"paper/pdf/paper-v1.0.pdf","status":"complete"}],"novelty_status":"known","review_status":"passed","reproduction_status":"passed","falsification_tests":["Prove orbitwise scalar closure for arbitrary edge-weight protocols without any mixing or augmented state."]},{"id":"C8","type":"interpretation","headline":false,"lifecycle":"established","statement":"Within the explicitly conditional reduced model of rapid shell mixing and orbit-averaged moving-wall work, the hard-sphere configurational integral acts as a mechanical control; a uniform attractive mean field yields a nonequilibrium van der Waals correction, whereas microscopic attractive tails generally leave the scalar closure class. No trajectory-level convergence of microscopic hard-sphere dynamics to this reduced process is claimed.","assumptions":["The hard-sphere configurational integral is finite in the declared volume range.","The attractive correction is treated at uniform-density mean-field level where stated."],"dependencies":[{"kind":"claim","id":"C1","record_id":"RO-2026-0005"}],"evidence":[{"kind":"interpretation","path":"paper/pdf/paper-v1.0.pdf","status":"complete"},{"kind":"computation","path":"code/validate_v004.py","status":"complete"}],"novelty_status":"known","review_status":"passed","reproduction_status":"passed","falsification_tests":["Show that the configurational-factor control gives an incorrect pressure or first-law term.","Demonstrate scalar closure for a generic microscopic attractive tail under the same assumptions."]}],"literature_audit":{"protocol_version":"0.2.0","record_id":"RO-2026-0005","candidate_digest":"5ec2e2211b8fd5cba8087a1de8529fcdecb0bbd37fe83c83ce8e0ec7009fba05","accepted_claims":["C1","C2","C3","C4","C5","C6","C7","C8"],"search_cutoff":"2026-09-04","auditor":"Context-isolated Pudim Librarian primary-literature audit","sources":["APS and AIP publisher records, author manuscripts, and DOI metadata for cited primary papers","Citation-chain checks around Kramers energy diffusion, levitated-particle thermodynamics, exchange fluctuation relations, Brownian engines, graph quenches, and hard-sphere work","Exact-form and terminology searches for the proposed cumulant, uncertainty, smooth-cycle, beta-gamma graph-quench, and moving-wall formulas","Final digest rebind checking primary gamma-difference and variance-gamma moment literature"],"queries":["phase volume density of states energy diffusion Langevin Hamiltonian","time-dependent weakly damped energy diffusion driven Hamiltonian","underdamped homogeneous potential gamma CIR stochastic thermodynamics","exchange entropy Bessel K cumulants thermodynamic uncertainty relation","globally optimal smooth cycle Brownian heat engine constrained control","effective resistance beta gamma work distribution graph thermodynamics quench","hard sphere moving wall stochastic thermodynamics energy diffusion"],"inclusions":[{"citation":"H. 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Lira, Stochastic thermodynamics of nonharmonic oscillators in high vacuum, Phys. Rev. E 99, 062119 (2019).","identifier":"doi:10.1103/PhysRevE.99.062119","url":"https://doi.org/10.1103/PhysRevE.99.062119","verified":true},{"citation":"D. S. P. Salazar, Detailed fluctuation theorem bound for apparent violations of the second law, Phys. Rev. E 104, L062101 (2021).","identifier":"doi:10.1103/PhysRevE.104.L062101","url":"https://doi.org/10.1103/PhysRevE.104.L062101","verified":true},{"citation":"A. M. Timpanaro, G. Guarnieri, J. Goold, and G. T. Landi, Thermodynamic uncertainty relations from exchange fluctuation theorems, Phys. Rev. Lett. 123, 090604 (2019).","identifier":"doi:10.1103/PhysRevLett.123.090604","url":"https://doi.org/10.1103/PhysRevLett.123.090604","verified":true},{"citation":"R. E. Gaunt, On the moments of the variance-gamma distribution, Stat. Probab. 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Jarzynski, Work distribution for the adiabatic compression of a dilute and interacting classical gas, Phys. Rev. E 75, 021116 (2007).","identifier":"doi:10.1103/PhysRevE.75.021116","url":"https://doi.org/10.1103/PhysRevE.75.021116","verified":true}],"exclusions":[{"identifier":"secondary-reviews-as-priority-evidence","reason":"Reviews were used for genealogy only and were not accepted as sole evidence of novelty."},{"identifier":"unrestricted-phase-space-or-finite-friction-models","reason":"These do not settle claims explicitly conditioned on weak-friction energy lumpability."},{"identifier":"equilibrium-graph-identities","reason":"Matrix-tree, pseudodeterminant, resistance, and beta-projection identities are treated as known ingredients rather than novelty."}],"claim_assessments":[{"claim_id":"C1","closest_work":[{"citation":"H. A. Kramers, Brownian motion in a field of force and the diffusion model of chemical reactions, Physica 7, 284 (1940).","identifier":"doi:10.1016/S0031-8914(40)90098-2","url":"https://doi.org/10.1016/S0031-8914(40)90098-2","verified":true},{"citation":"E. Pollak, P. Talkner, and A. M. Berezhkovskii, A theory for nonisothermal unimolecular reaction rates, J. Chem. Phys. 107, 3542 (1997).","identifier":"doi:10.1063/1.474693","url":"https://doi.org/10.1063/1.474693","verified":true},{"citation":"S. Linkwitz and H. Grabert, Energy diffusion of a weakly damped and periodically driven particle in an anharmonic potential well, Phys. Rev. B 44, 11888 (1991).","identifier":"doi:10.1103/PhysRevB.44.11888","url":"https://doi.org/10.1103/PhysRevB.44.11888","verified":true},{"citation":"C. Jarzynski, Diffusion equation for energy in ergodic adiabatic ensembles, Phys. Rev. A 46, 7498 (1992).","identifier":"doi:10.1103/PhysRevA.46.7498","url":"https://doi.org/10.1103/PhysRevA.46.7498","verified":true},{"citation":"C. Jarzynski, Energy diffusion in a chaotic adiabatic billiard gas, Phys. Rev. E 48, 4340 (1993).","identifier":"doi:10.1103/PhysRevE.48.4340","url":"https://doi.org/10.1103/PhysRevE.48.4340","verified":true}],"delta":"The bath operator and driven-energy-diffusion ingredients are established. The release claims a thermodynamically consistent synthesis under energy lumpability, not the first driven energy-diffusion equation.","unresolved_equivalences":["Exact equivalence to the Linkwitz-Grabert energy-phase equation after phase elimination was not established.","Jarzynski's drive-induced diffusion is second order in driving rate, whereas the retained work transport here is first-order deterministic phase-volume drift."],"confidence":"HIGH","outcome":"PASS"},{"claim_id":"C2","closest_work":[{"citation":"D. S. P. Salazar and S. H. A. Lira, Exactly solvable nonequilibrium Langevin relaxation of a trapped nanoparticle, J. Phys. A Math. Theor. 49, 465001 (2016).","identifier":"doi:10.1088/1751-8113/49/46/465001","url":"https://doi.org/10.1088/1751-8113/49/46/465001","verified":true},{"citation":"D. S. P. Salazar and S. H. A. Lira, Stochastic thermodynamics of nonharmonic oscillators in high vacuum, Phys. Rev. E 99, 062119 (2019).","identifier":"doi:10.1103/PhysRevE.99.062119","url":"https://doi.org/10.1103/PhysRevE.99.062119","verified":true}],"delta":"Harmonic and one-dimensional power-law gamma/CIR closures and fractional effective degrees of freedom are known. The arbitrary-dimensional homogeneous organization and separation of thermodynamic size alpha from kinetic clock Gamma_q are retained as a unifying corollary, not a priority claim.","unresolved_equivalences":[],"confidence":"HIGH","outcome":"PASS"},{"claim_id":"C3","closest_work":[{"citation":"D. S. P. Salazar and S. H. A. Lira, Exactly solvable nonequilibrium Langevin relaxation of a trapped nanoparticle, J. Phys. A Math. Theor. 49, 465001 (2016).","identifier":"doi:10.1088/1751-8113/49/46/465001","url":"https://doi.org/10.1088/1751-8113/49/46/465001","verified":true},{"citation":"D. S. P. Salazar, Detailed fluctuation theorem bound for apparent violations of the second law, Phys. Rev. E 104, L062101 (2021).","identifier":"doi:10.1103/PhysRevE.104.L062101","url":"https://doi.org/10.1103/PhysRevE.104.L062101","verified":true},{"citation":"A. M. Timpanaro, G. Guarnieri, J. Goold, and G. T. Landi, Thermodynamic uncertainty relations from exchange fluctuation theorems, Phys. Rev. Lett. 123, 090604 (2019).","identifier":"doi:10.1103/PhysRevLett.123.090604","url":"https://doi.org/10.1103/PhysRevLett.123.090604","verified":true},{"citation":"R. E. Gaunt, On the moments of the variance-gamma distribution, Stat. Probab. Lett. 201, 109884 (2023).","identifier":"doi:10.1016/j.spl.2023.109884","url":"https://doi.org/10.1016/j.spl.2023.109884","verified":true},{"citation":"P. J. Forrester, On the gamma difference distribution, Stat. Probab. Lett. 211, 110136 (2024).","identifier":"doi:10.1016/j.spl.2024.110136","url":"https://doi.org/10.1016/j.spl.2024.110136","verified":true}],"delta":"The gamma-difference heat and exchange-entropy laws, generating function, and general moment structure are known. The accepted contribution is their single-contrast stochastic-thermodynamic parametrization, the linked uncertainty and sign identities, and the comparison with the distinct total-path entropy-production distribution; no priority over variance-gamma probability theory is claimed.","unresolved_equivalences":[],"confidence":"HIGH","outcome":"PASS"},{"claim_id":"C4","closest_work":[{"citation":"D. S. P. Salazar and S. H. A. Lira, Stochastic thermodynamics of nonharmonic oscillators in high vacuum, Phys. Rev. E 99, 062119 (2019).","identifier":"doi:10.1103/PhysRevE.99.062119","url":"https://doi.org/10.1103/PhysRevE.99.062119","verified":true},{"citation":"Y. H. Chen, J.-F. Chen, Z. Fei, and H. T. Quan, Microscopic theory of the Curzon-Ahlborn heat engine based on a Brownian particle, Phys. Rev. E 106, 024105 (2022).","identifier":"doi:10.1103/PhysRevE.106.024105","url":"https://doi.org/10.1103/PhysRevE.106.024105","verified":true},{"citation":"J.-F. Chen and H. T. Quan, Optimal control theory for maximum power of Brownian heat engines, Phys. Rev. E 110, L042105 (2024).","identifier":"doi:10.1103/PhysRevE.110.L042105","url":"https://doi.org/10.1103/PhysRevE.110.L042105","verified":true}],"delta":"Minimum-work trap protocols and named Brownian-engine cycles are established. The accepted delta is the exact smooth-loop optimizer within the explicitly bounded gamma-manifold admissible class and selected finite-time cycle identities.","unresolved_equivalences":["Different actuator, stiffness, temperature, or switching bounds select different optimal topologies, including the Chen-Quan isochoric-relaxation branch."],"confidence":"MEDIUM","outcome":"PASS"},{"claim_id":"C5","closest_work":[{"citation":"P. Hänggi, P. Talkner, and M. Borkovec, Reaction-rate theory fifty years after Kramers, Rev. Mod. Phys. 62, 251 (1990).","identifier":"doi:10.1103/RevModPhys.62.251","url":"https://doi.org/10.1103/RevModPhys.62.251","verified":true}],"delta":"Pseudodeterminant, matrix-tree, effective-resistance, and spherical-projection ingredients are known; the release uses them as a solvable thermodynamic baseline without claiming a new graph theorem.","unresolved_equivalences":[],"confidence":"HIGH","outcome":"PASS"},{"claim_id":"C6","closest_work":[{"citation":"G. E. Crooks and C. Jarzynski, Work distribution for the adiabatic compression of a dilute and interacting classical gas, Phys. Rev. E 75, 021116 (2007).","identifier":"doi:10.1103/PhysRevE.75.021116","url":"https://doi.org/10.1103/PhysRevE.75.021116","verified":true}],"delta":"No direct primary match was found for the arbitrary-q single-edge law beta W equals V times a nonlinear beta fraction, with graph dependence compressed to h=delta g R_e, nor for the resulting graph-surgery engine.","unresolved_equivalences":["Equivalent beta-gamma transforms may exist in classical elliptical-distribution or quadratic-form statistics without the thermodynamic interpretation."],"confidence":"HIGH","outcome":"PASS"},{"claim_id":"C7","closest_work":[{"citation":"C. Jarzynski, Diffusion equation for energy in ergodic adiabatic ensembles, Phys. Rev. A 46, 7498 (1992).","identifier":"doi:10.1103/PhysRevA.46.7498","url":"https://doi.org/10.1103/PhysRevA.46.7498","verified":true},{"citation":"C. Jarzynski, Energy diffusion in a chaotic adiabatic billiard gas, Phys. Rev. E 48, 4340 (1993).","identifier":"doi:10.1103/PhysRevE.48.4340","url":"https://doi.org/10.1103/PhysRevE.48.4340","verified":true}],"delta":"Scalar closure under global scaling follows established adiabatic-invariant reasoning. The release's contribution is to state the closure boundary explicitly: generic graph-shape driving may require angular observables or extra mixing.","unresolved_equivalences":[],"confidence":"MEDIUM","outcome":"PASS"},{"claim_id":"C8","closest_work":[{"citation":"C. Jarzynski, Energy diffusion in a chaotic adiabatic billiard gas, Phys. Rev. E 48, 4340 (1993).","identifier":"doi:10.1103/PhysRevE.48.4340","url":"https://doi.org/10.1103/PhysRevE.48.4340","verified":true},{"citation":"G. E. Crooks and C. Jarzynski, Work distribution for the adiabatic compression of a dilute and interacting classical gas, Phys. Rev. E 75, 021116 (2007).","identifier":"doi:10.1103/PhysRevE.75.021116","url":"https://doi.org/10.1103/PhysRevE.75.021116","verified":true}],"delta":"Fixed-volume kinetic CIR and phase-volume/compressibility ingredients are known. The moving-wall Q_G coordinate is admitted only as a conditional shell-averaged extension; no microscopic convergence or new van der Waals theory is claimed.","unresolved_equivalences":["A trajectory-level singular-limit proof for moving hard spheres is absent.","Boundary-induced stochastic corrections outside the averaging hierarchy remain uncharacterized."],"confidence":"MEDIUM","outcome":"PASS"}],"overall_outcome":"PASS"},"review":{"protocol_version":"0.2.0","record_id":"RO-2026-0005","accepted_claims":["C1","C2","C3","C4","C5","C6","C7","C8"],"rounds":[{"round":1,"candidate_digest":"76ab09cd60cb5b1fd7295b30d4742bdfc22d58d662c0226db075c9e49cdb44d4","opened_at":"2026-09-04T15:28:00Z","closed_at":"2026-09-04T15:40:00Z","referees":[{"id":"R1","context_isolated":true,"report_path":"reviews/referee-r1-round1.md","recommendation":"MAJOR_REVISION","confidence":0.96,"verification_scope":"Thermodynamic correctness, entropy production, free energy, controls, graph quench, and hard-sphere scope."},{"id":"R2","context_isolated":true,"report_path":"reviews/referee-r2-round1.md","recommendation":"MAJOR_REVISION","confidence":0.9,"verification_scope":"Novelty, claim boundaries, reproducibility, packaging, figures, and accessibility."}],"editor":{"independent_context":true,"decision":"MAJOR_REVISION","confidence":0.95,"letter_path":"reviews/editor-final.md","decisive_evidence":["Both referees independently identified the missing nonisothermal free-energy term.","Novelty and theorem-domain defects required a new frozen candidate."]},"findings":[{"id":"F-R1-001","criterion":"thermodynamic-correctness","severity":"blocking","affected_claims":["C1","C4"],"finding":"The general free-energy rate omitted -S dot T and the irreversible-work decomposition was not restricted to fixed temperature.","evidence":["reviews/referee-r1-round1.md","reviews/referee-r2-round1.md"],"response":"Equation 24 was corrected and the following decomposition explicitly made isothermal.","resolution":"resolved"},{"id":"F-R1-002","criterion":"novelty-and-scope","severity":"major","affected_claims":["C3","C4","C6","C8"],"finding":"Gamma-difference priority, smooth-control domain, arbitrary-q versus quartic scope, and the hard-sphere convergence boundary required narrowing.","evidence":["reviews/referee-r2-round1.md"],"response":"The v012 text and claim registry were narrowed, with primary probability citations and explicit assumptions.","resolution":"resolved"},{"id":"F-R1-003","criterion":"reproducibility-and-accessibility","severity":"minor","affected_claims":["C1","C2","C3","C4","C5","C6","C7","C8"],"finding":"The source archive contained internal material and lacked a correct final ten-figure accessibility map.","evidence":["reviews/referee-r2-round1.md"],"response":"The clean 61-member source package excludes internal reviews and caches and includes corrected ALT_TEXT.md.","resolution":"resolved"}],"author_response":{"actor":"Maestro v0.1","path":"reviews/author-response-round1.md","submitted_at":"2026-09-04T15:41:00Z"},"revision_digest":"5ec2e2211b8fd5cba8087a1de8529fcdecb0bbd37fe83c83ce8e0ec7009fba05","outcome":"INCONCLUSIVE"},{"round":2,"candidate_digest":"5ec2e2211b8fd5cba8087a1de8529fcdecb0bbd37fe83c83ce8e0ec7009fba05","opened_at":"2026-09-04T15:41:00Z","closed_at":"2026-09-04T16:13:43Z","referees":[{"id":"R1","context_isolated":true,"report_path":"reviews/referee-r1-final.md","recommendation":"ACCEPT","confidence":0.97,"verification_scope":"Final theoretical correctness, complete equation audit, build, figures, and citations."},{"id":"R2","context_isolated":true,"report_path":"reviews/referee-r2-final.md","recommendation":"ACCEPT","confidence":0.96,"verification_scope":"Final novelty, claim scope, frozen evidence, reconstruction, packaging, and accessibility."}],"editor":{"independent_context":true,"decision":"ACCEPT","confidence":0.97,"letter_path":"reviews/editor-final.md","decisive_evidence":["Every round-one scientific finding is resolved in the terminal candidate.","The Librarian, two final referees, and independent Replicator pass the exact final digest.","AI-authorship policy dissent is fully disclosed and preserved without being confused with scientific validity."]},"findings":[{"id":"F-R2-001","criterion":"authorship-policy","severity":"note","affected_claims":[],"finding":"A conventional journal may require a natural-person author able to assume formal authorship duties.","evidence":["reviews/referee-r1-final.md","reviews/referee-r2-final.md","reviews/editor-final.md"],"response":"Pudim publishes the disclosed AI creator and human Program Manager roles while retaining the objection publicly.","resolution":"accepted"},{"id":"F-R2-002","criterion":"document-accessibility","severity":"note","affected_claims":[],"finding":"The PDFs are not PDF-UA tagged.","evidence":["reviews/referee-r2-final.md"],"response":"Extractable text and a complete ten-figure accessibility map are included; tagged PDF is deferred.","resolution":"accepted"}],"author_response":null,"revision_digest":"5ec2e2211b8fd5cba8087a1de8529fcdecb0bbd37fe83c83ce8e0ec7009fba05","outcome":"PASS"}],"ledger_decision":{"decision":"GO","candidate_digest":"5ec2e2211b8fd5cba8087a1de8529fcdecb0bbd37fe83c83ce8e0ec7009fba05","authority":"Independent PRE-style editor and Pudim AI Ledger integration","decided_at":"2026-09-04T16:13:43Z","rationale":"The corrected v012 systematic tutorial and semi-review passes correctness, literature, independent review, reproduction, accessibility, and scope gates at the exact frozen digest; the AI-authorship policy dissent remains public."}},"replication":{"protocol_version":"0.2.0","record_id":"RO-2026-0005","replicator":"Context-isolated Pudim Replicator","independent_of":["solver","reviewer","publisher"],"started_at":"2026-09-04T15:00:00Z","completed_at":"2026-09-04T16:09:00Z","claim_results":[{"claim_id":"C1","mode":"theoretical","blinded_to_solver_proof_initially":true,"inputs":["paper/candidate-v1.0.zip","claims/claims-v1.0.yaml"],"artifacts":["data/validation-summary.json","data/reconstruction-tier1.json"],"environment":"Windows analytic rerun plus non-root network-disabled Linux container","commands":["python code/validate_v007.py","podman run pudim-ro-2026-0005:v1.0 --tier 1"],"tolerances":["Algebraic identities exact to floating-point precision; maximum independent standard-library error below 1e-10."],"comparison":"Re-derived the phase-volume drift, Omega/omega bath coefficients, density-of-states entropy rate, and first-law split under the stated energy-lumpability assumptions. On the final digest, independently reduced the corrected nonisothermal free-energy rate to zero symbolic residual, including the -S dot T term.","outcome":"PASS"},{"claim_id":"C2","mode":"hybrid","blinded_to_solver_proof_initially":true,"inputs":["paper/candidate-v1.0.zip","code/validate_v002.py"],"artifacts":["data/validation-summary.json"],"environment":"Python 3.11.9 with NumPy, SciPy, Matplotlib, and SymPy","commands":["python code/validate_v002.py","python code/validate_v007.py"],"tolerances":["Existing deterministic assertions and Monte Carlo error bars embedded in the scripts."],"comparison":"Independently obtained Omega/omega=E/alpha, Gamma_q=d gamma/alpha, gamma invariance, mean energy, heat capacity, and the separation of alpha from the relaxation clock.","outcome":"PASS"},{"claim_id":"C3","mode":"hybrid","blinded_to_solver_proof_initially":true,"inputs":["paper/candidate-v1.0.zip","code/validate_v004.py"],"artifacts":["data/validation-summary.json","data/reconstruction-tier1.json"],"environment":"Symbolic algebra and direct exact-transition sampling on Windows; standard-library reconstruction in Linux","commands":["python code/validate_v004.py","podman run pudim-ro-2026-0005:v1.0 --tier 1"],"tolerances":["CIR transform Monte Carlo error 1.892e-4 and scaled cumulant error 4.634e-3, both inside frozen assertions.","Exact TUR and MGF-symmetry residuals zero in the container reconstruction."],"comparison":"Reproduced the first four cumulants, all-order generator consequences, violation probability, integral fluctuation theorem, and Var(Sigma_x)/mean(Sigma_x)^2=2/mean(Sigma_x)+1/alpha.","outcome":"PASS"},{"claim_id":"C4","mode":"hybrid","blinded_to_solver_proof_initially":true,"inputs":["paper/candidate-v1.0.zip","code/validate_v005.py","code/validate_v007.py"],"artifacts":["data/validation-summary.json","data/reconstruction-tier1.json"],"environment":"Independent calculus plus deterministic numerical checks","commands":["python code/validate_v005.py","python code/validate_v007.py"],"tolerances":["Equality waveform must saturate the smooth bound within 1e-10."],"comparison":"Re-derived the cycle maps and optima, and verified that the smooth sine-cosine waveform saturates the Cauchy-Schwarz and Poincare-Wirtinger bound exactly within the declared admissible class. The final rebind gave equality ratio 1.000000000000, closure residual 5.15e-17, and maximum value 0.145473 among 1500 random Fourier competitors.","outcome":"PASS"},{"claim_id":"C5","mode":"theoretical","blinded_to_solver_proof_initially":true,"inputs":["paper/candidate-v1.0.zip","code/validate_v004.py"],"artifacts":["data/validation-summary.json"],"environment":"Direct matrix calculations independent of the graph-cage sampling representation","commands":["python code/validate_v004.py"],"tolerances":["Graph Hessian derivative residual below 1e-9; observed 9.032e-12."],"comparison":"Whitening reproduced the pseudodeterminant phase-volume factor, resistance response, and radial observables.","outcome":"PASS"},{"claim_id":"C6","mode":"hybrid","blinded_to_solver_proof_initially":true,"inputs":["paper/candidate-v1.0.zip","code/validate_v009.py"],"artifacts":["data/validation-summary.json","data/reconstruction-tier1.json"],"environment":"Direct Cartesian Monte Carlo and independent quadrature","commands":["python code/validate_v009.py","podman run pudim-ro-2026-0005:v1.0 --tier 1"],"tolerances":["Direct-sampling means within 1.10 standard errors; variance relative error below 0.5 percent; Crooks quadrature relative error below 1e-12."],"comparison":"Direct Cartesian samples, without sampling the asserted beta-gamma law, reproduced forward and reverse quench moments, Jarzynski, Crooks, entropy production, cycle means, and the engine threshold. Final arbitrary-q sampling at q=3.7 gave mean within 0.594 standard errors, variance relative error 5.14e-4, and Jarzynski within 0.749 standard errors; the N=2 deterministic-fraction limit and h>-1 confinement caveat also passed.","outcome":"PASS"},{"claim_id":"C7","mode":"theoretical","blinded_to_solver_proof_initially":true,"inputs":["paper/candidate-v1.0.zip"],"artifacts":["data/validation-summary.json"],"environment":"Independent derivation from the graph-cage phase volume and edge-work observable","commands":[],"tolerances":["Exact symbolic comparison of global-scaling closure and local-edge angular dependence."],"comparison":"Confirmed scalar closure for global stiffness or proportional graph breathing and the need for an edge fraction or other angular observable under generic finite-rate graph-shape driving.","outcome":"PASS"},{"claim_id":"C8","mode":"theoretical","blinded_to_solver_proof_initially":true,"inputs":["paper/candidate-v1.0.zip","code/validate_v004.py"],"artifacts":["data/validation-summary.json","data/reconstruction-tier2.json"],"environment":"Independent kinetic-energy balance and standard-library source-scope audit","commands":["python code/validate_v004.py","podman run pudim-ro-2026-0005:v1.0 --tier 2"],"tolerances":["Exact B3/B2^2=5/8 identity and explicit retention of all moving-boundary assumptions."],"comparison":"Re-derived the fixed-volume kinetic CIR law, phase-volume pressure mapping, Carnahan-Starling correction, and uniform mean-field term; verified that microscopic moving-wall convergence is not claimed.","outcome":"PASS"}],"overall_outcome":"PASS"},"reproduction":{"protocol_version":"0.2.0","record_id":"RO-2026-0005","candidate_digest":"5ec2e2211b8fd5cba8087a1de8529fcdecb0bbd37fe83c83ce8e0ec7009fba05","accepted_claims":["C1","C2","C3","C4","C5","C6","C7","C8"],"entrypoint":"code/reconstruction/reproduce.py","container":{"image":"pudim-ro-2026-0005:v1.0","digest":"sha256:3aee6877caafbfc87506ea47dad58d7d95cc777244b90cab2da90d241e8210b1","lockfiles":["code/reconstruction/Containerfile","code/reconstruction/requirements-lock.txt","code/reconstruction/environment-lock.txt","code/reconstruction/expected-hashes.json"]},"offline":true,"non_root":true,"reference_runner":{"os":"linux","vcpus":8,"memory_gb":8},"tiers":[{"tier":0,"description":"Verify every frozen paper, source, validator, and candidate hash and the exact three-member release archive.","maximum_seconds":300,"commands":["podman run --rm --network none --read-only --cpus 8 --memory 8g --cap-drop all --security-opt no-new-privileges --user 65532:65532 pudim-ro-2026-0005:v1.0 --tier 0"],"outcome":"PASS"},{"tier":1,"description":"Reconstruct the exchange-MGF symmetry, exact TUR identity, graph rank-one update and Jarzynski integral, smooth-cycle saturation, and hard-sphere virial identity using only the Python standard library.","maximum_seconds":300,"commands":["podman run --rm --network none --read-only --cpus 8 --memory 8g --cap-drop all --security-opt no-new-privileges --user 65532:65532 pudim-ro-2026-0005:v1.0 --tier 1"],"outcome":"PASS"},{"tier":2,"description":"Audit source completeness, bibliography additions, novelty-scope language, and both light and dark PDF identities.","maximum_seconds":300,"commands":["podman run --rm --network none --read-only --cpus 8 --memory 8g --cap-drop all --security-opt no-new-privileges --user 65532:65532 pudim-ro-2026-0005:v1.0 --tier 2"],"outcome":"PASS"}],"expected_outputs":[{"path":"data/reconstruction-tier0.json","kind":"data","comparison":"hash","expected_sha256":"c9184bc0656d935fd158feccca3af1229a9b3d4a04b19cc8660f136ee5b1242e"},{"path":"data/reconstruction-tier1.json","kind":"data","comparison":"hash","expected_sha256":"152492ba68512d4359e165a906cb0de65ad19638c289606c176820aae1c9ea86"},{"path":"data/reconstruction-tier2.json","kind":"data","comparison":"hash","expected_sha256":"b825a883a32f0f1940788a296586207b4e09d965cfef8343c222ea2d40034278"},{"path":"paper/pdf/paper-v1.0.pdf","kind":"document","comparison":"hash","expected_sha256":"bd6e635f2c0492fec62c43e9b2ff9ac285dea9597452dbcbdb51b32b361e9fa5"},{"path":"paper/pdf/paper-v1.0-dark.pdf","kind":"document","comparison":"hash","expected_sha256":"b277012e4c709611db95e6479c2d1ddd629f6851613d714db841abb44a9347d1"}],"scientific_tolerances":[{"output":"data/reconstruction-tier1.json","metric":"exact algebraic and standard-library numerical identities","tolerance":"maximum absolute error below 1e-10"},{"output":"data/validation-summary.json","metric":"inherited Monte Carlo transform and cumulant checks","tolerance":"use each frozen validator's declared assertions; largest observed scaled Monte Carlo discrepancy 4.634e-3"},{"output":"paper/pdf/paper-v1.0.pdf and paper/pdf/paper-v1.0-dark.pdf","metric":"release document identity","tolerance":"exact SHA-256 equality"}],"attestation":{"run_path":"reproduction/v1.0/attestation/run.json","image_digest":"sha256:3aee6877caafbfc87506ea47dad58d7d95cc777244b90cab2da90d241e8210b1","lock_hashes":{"code/reconstruction/Containerfile":"1345cf81332182a90933850aeec1a575068f0a5f1f51fbe96c8e51d4a7a6381c","code/reconstruction/reproduce.py":"1b6661f4d19821d766528c1efee3f4c07ffcf6a5ef80a84b4c3150f7e05e2180","code/reconstruction/requirements-lock.txt":"e5f9e474cd03d4febfb337f6868a5dec65a5f9f2706818a7ed706c1afe7e7faa","code/reconstruction/environment-lock.txt":"18ab759d4d924d3663476765c9216e423af750d3578de4d97ec089ff79ce0936","code/reconstruction/expected-hashes.json":"37a2cb37faf96de8ef856d50e664945fbc0c8d61b47179c0d63823912c398293"},"started_at":"2026-09-04T16:05:00Z","completed_at":"2026-09-04T16:06:30Z","resources":{"runner":"rootless Podman under WSL2 Ubuntu 24.04.4 LTS","vcpus_ceiling":8,"memory_gb_ceiling":8,"uid":65532,"network":"none","root_filesystem":"read-only","capabilities":"all dropped; 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