{ "vercy": "1.0-draft", "publication": { "status": "research-draft", "adjudicationStatus": "unreviewed", "publishableCanonical": false, "generatedAt": "2026-09-12T10:07:19Z", "providers": [ "Codex" ], "breadth": "recalled by Codex without web access - no source was read", "missingProviders": [], "pass": 2, "cost": { "grok": { "seconds": 21.2, "error": "Reading additional input from stdin...\nOpenAI Codex v0.153.4\n--------\nworkdir: R:\\02_PROJECTS\\02_Meta_Models_Platforms\\Ver.cy\\current\\thing-registry-backlog\nmodel: gpt-6-astra\nprovider: openai\napproval: never\nsandbox: read-only\nreasoning effort: none\nreasoning summaries: none\nsession id: 01a09514-ad3d-7421-adda-ad5b6eb86f9f\n--------\nuser\nDescribe what is already known about one registered thing. Answer as JSON only, no prose around it.\n\nThing: Gross-Pitaevskii equation\nSense to describe: (none recorded)\nDomain code: INF.MED\nAlso known as: (none)\n\n\nContext for this batch of 1001 things:\n# Batch", "usd": 0.0, "recall": true }, "codex": { "seconds": 84.9, "error": "Reading additional input from stdin...\nOpenAI Codex v0.153.4\n--------\nworkdir: R:\\02_PROJECTS\\02_Meta_Models_Platforms\\Ver.cy\\current\\thing-registry-backlog\nmodel: gpt-6-astra\nprovider: openai\napproval: never\nsandbox: read-only\nreasoning effort: none\nreasoning summaries: none\nsession id: 01a09514-ad4e-70e1-9b9a-3f212027d15c\n--------\nuser\nYou are drafting a Vercy meta-model for one registered thing. Answer as JSON only, no prose around it.\n\nThing: Gross-Pitaevskii equation\nRegistry id: vr.tr.gross-pitaevskii-equation\nPlane / domain: INF / INF.MED\nRegistry definition: (none recorded)\nNames folde" } }, "enrichment": { "pass": 3, "engine": "claude", "producedAt": "2026-10-06T12:00:00Z", "ingestedAt": "2026-10-06T08:46:39+00:00", "fields": [ "agent_conduct", "ethics", "failure_modes_and_hazards", "owners", "visual_identification" ] }, "gate": { "passed": true, "version": "1.0", "at": "2026-10-07T10:10:33+00:00", "evidence": [ "completeness 1.00", "sense: Wikidata description", "2 live sources", "review by codex: pass" ] } }, "metaModel": { "id": "THING-Q910667", "registryId": "vr.tr.gross-pitaevskii-equation", "name": "Gross–Pitaevskii equation", "version": "0.1.0-research.1", "entryKind": "thing", "family": "Thing Registry", "domain": [ "INF.MED" ], "status": "research-draft" }, "canonicalUrl": "https://ver.cy/models/thing/q910667/", "model": { "registry_id": "vr.tr.gross-pitaevskii-equation", "name": "Gross–Pitaevskii equation", "purpose": "Enable an agent to recognize a Gross-Pitaevskii formulation, assess its physical applicability, and select defensible calculations and interpretations of condensate behavior.", "definition": "The Gross-Pitaevskii equation is a nonlinear Schrödinger equation describing the mean-field evolution of the condensate order parameter in a dilute, weakly interacting Bose gas, usually with interactions represented by a local cubic term.", "scope_statement": "This model owns the mathematical identity, conventions, applicability conditions, problem specification, and validation requirements of the Gross-Pitaevskii equation registered as vr.tr.gross-pitaevskii-equation, including explicit relationships to reduced and extended formulations.", "in_scope": [ "Time-dependent and stationary scalar Gross-Pitaevskii formulations", "Condensate order parameter, normalization, interaction coefficient, and units", "Mean-field assumptions and limits of applicability", "External potentials, geometry, initial conditions, and boundary conditions", "Stationary states, dynamics, stability, and numerical verification", "Boundaries between the baseline equation, dimensional reductions, and named extensions" ], "out_of_scope": [ "Bose-Einstein condensation as a physical phenomenon in general", "Complete many-body quantum states and microscopic interaction models", "The nonlinear Schrödinger equation family beyond its condensate interpretation", "Experimental apparatus design and atomic species catalogues", "Software implementation details belonging to individual solvers", "Full finite-temperature, strongly correlated, and quantum fluctuation theories" ], "distinguishing_features": [ "The dependent field represents a condensate order parameter; its normalization determines whether its squared magnitude is a number density or a probability density.", "The baseline scalar equation contains a local cubic term g|ψ|²ψ representing contact interactions, alongside kinetic and external-potential terms.", "Its condensate interpretation and physically specified coupling distinguish it from a generic cubic nonlinear Schrödinger equation with arbitrary coefficients.", "The stationary equation is a nonlinear eigenvalue problem with chemical potential constrained by normalization; chemical potential must not automatically be identified with total energy per particle.", "Bogoliubov-de Gennes equations describe perturbations around a condensate solution, whereas the Gross-Pitaevskii equation governs the underlying mean field." ], "characteristics": [ { "name": "Equation formulation", "kind": "category", "unit_or_values": "time-dependent; stationary; explicitly identified extension", "why_it_matters": "Determines whether the agent should evolve an initial state, solve a constrained stationary problem, or inspect additional physics." }, { "name": "Order-parameter normalization", "kind": "category", "unit_or_values": "integral |ψ|² dV = N₀; integral |φ|² dV = 1; other explicitly defined convention", "why_it_matters": "Controls density interpretation and whether a particle-number factor appears in the nonlinear coefficient." }, { "name": "Spatial dimensionality", "kind": "category", "unit_or_values": "3D; effective 2D; effective 1D", "why_it_matters": "Changes field units, coupling units, and the assumptions required to eliminate confined directions." }, { "name": "Particle mass", "kind": "measurement", "unit_or_values": "kg or a declared nondimensional mass scale", "why_it_matters": "Sets the kinetic coefficient and physical length and time scales." }, { "name": "Interaction specification", "kind": "measurement", "unit_or_values": "s-wave scattering length aₛ in m; baseline 3D coupling g = 4πℏ²aₛ/m in J·m³", "why_it_matters": "Sets the strength and sign of the contact nonlinearity; reduced-dimensional couplings require separate derivation." }, { "name": "Diluteness parameter", "kind": "measurement", "unit_or_values": "n|aₛ|³, dimensionless for a 3D gas", "why_it_matters": "Helps assess the dilute-gas assumption but does not by itself establish mean-field validity." }, { "name": "Confinement and driving", "kind": "relation", "unit_or_values": "external potential V(r,t), domain geometry, and any declared rotating reference frame", "why_it_matters": "Defines the physical problem and determines which conservation checks are appropriate." }, { "name": "Solution assessment", "kind": "state", "unit_or_values": "unverified; converged; stationary; dynamically stable; unstable; applicability unresolved", "why_it_matters": "Separates successful computation from physical validity and stability." } ], "affordances": [ "Recognize equivalent formulations by reconciling units, normalization, and reference frames.", "Assess whether a specified condensate regime supports a scalar mean-field treatment.", "Construct a stationary or initial-boundary-value problem from physical inputs.", "Compute candidate condensate profiles and dynamics with recorded approximation limits.", "Extract density, phase, current, energy, and defect observables under explicit conventions.", "Reject unsupported interpretations or route the problem to an appropriate extended theory." ], "agent_conduct": { "may": [ "Explain the Gross-Pitaevskii equation and its uses in physics.", "Solve or simulate it in models the agent is authorized to work on." ], "must_not": [ "Present mean-field results outside their validity range as reliable.", "Fabricate numerical or experimental results.", "Misattribute derivations." ], "requires_human": [ "Publishing new results." ] }, "ethics": { "considerations": [ "Accurate science communication matters for trust.", "Credit for scientific work matters." ], "affected_parties": [ "Researchers", "Students" ] }, "owners": { "steward": "Nobody owns the equation; researchers answer for their use of it.", "master_systems": [] }, "visual_identification": [ "Appears in physics texts as a nonlinear Schrodinger equation with a cubic interaction term." ], "failure_modes_and_hazards": [ "Misapplication outside the dilute, weakly interacting regime.", "Numerical instability in simulations." ], "what_it_is_for": [ "The Gross-Pitaevskii equation is used in theoretical and computational studies of dilute, weakly interacting Bose-Einstein condensates.", "It describes condensate density and phase and supports investigations of trapped states, collective motion and vortices within a mean-field approximation." ], "facets_not_applicable": { "interfaces": "No regulatory requirement or technical standard is intrinsic to this theoretical physics equation." } }, "sources": [ { "id": "wikidata", "title": "Wikidata item Q910667: Gross–Pitaevskii equation", "url": "https://www.wikidata.org/wiki/Q910667", "url_status": "live", "what_it_supports": "identity and sense of the item", "checked_by": "wikidata-api" }, { "id": "wikipedia-en", "title": "Wikipedia: Gross–Pitaevskii equation", "url": "https://en.wikipedia.org/wiki/Gross%E2%80%93Pitaevskii_equation", "url_status": "live", "what_it_supports": "general description of the item", "checked_by": "wikidata-api sitelink" } ], "structure": { "bundles": [ { "id": "equation-identity-and-conventions", "name": "Equation identity and conventions", "description": "Establish which Gross-Pitaevskii equation is being represented and how its symbols map to physical quantities.", "rationale": "Apparently identical equations can predict different densities and interaction strengths when normalization or scaling differs.", "layers": [ { "id": "canonical-formulation", "name": "Canonical formulation", "description": "Identify the baseline differential equation and its stationary specialization.", "findings": [ { "id": "scalar-contact-form", "name": "Scalar contact form", "description": "For a particle-number-normalized field, the baseline form is iℏ∂tψ = [−ℏ²∇²/(2m) + V + g|ψ|²]ψ. Record departures term by term. See [Pitaevskii and Stringari, Nonuniform Bose Gases at Zero Temperature](https://academic.oup.com/book/26678/chapter-abstract/195458863).", "questions": [ { "text": "What is the exact operator equation, including every sign, coefficient, and additional term?", "kind": "definition", "id": "scalar-contact-form-q01" }, { "text": "Which reference supports this formulation and its interpretation of the field?", "kind": "provenance", "id": "scalar-contact-form-q02" } ] } ] }, { "id": "normalization-and-scaling", "name": "Normalization and scaling", "description": "Make physical and dimensionless representations interchangeable without changing the problem.", "findings": [ { "id": "field-and-coefficient-conventions", "name": "Field and coefficient conventions", "description": "Require an explicit normalization integral and length, time, energy, and field scales before comparing coefficients or observables.", "questions": [ { "text": "Does the field integrate to unity, condensate number, or another declared quantity, and where is the particle-number factor placed?", "kind": "definition", "id": "field-and-coefficient-conventions-q01" }, { "text": "What transformation recovers physical density, time, and energy from the dimensionless variables?", "kind": "measurement", "id": "field-and-coefficient-conventions-q02" } ] } ] } ] }, { "id": "mean-field-applicability", "name": "Mean-field applicability", "description": "Record why the equation is an adequate approximation for the proposed system.", "rationale": "A mathematically valid solution can describe the wrong physics when depletion, correlations, or thermal effects are substantial.", "layers": [ { "id": "dilute-condensate-regime", "name": "Dilute condensate regime", "description": "Assess interaction, condensation, and temperature assumptions separately.", "findings": [ { "id": "regime-evidence", "name": "Regime evidence", "description": "The standard treatment concerns weakly interacting, dilute condensates near the zero-temperature limit; applicability needs evidence for the actual system. See [Pethick and Smith, Theory of the condensed state](https://www.cambridge.org/core/books/abs/boseeinstein-condensation-in-dilute-gases/theory-of-the-condensed-state/19D43707671194C5704F4B1FE10055DA).", "questions": [ { "text": "What density and scattering-length estimates determine the relevant diluteness parameter across the cloud?", "kind": "measurement", "id": "regime-evidence-q01" }, { "text": "What evidence bounds thermal population, quantum depletion, and correlations sufficiently for the intended observable?", "kind": "boundary", "id": "regime-evidence-q02" } ] } ] }, { "id": "dimensional-and-physical-extensions", "name": "Dimensional and physical extensions", "description": "Distinguish justified reductions from additions that change the governing model.", "findings": [ { "id": "reduction-and-extension-contract", "name": "Reduction and extension contract", "description": "Require a derivation or cited justification for effective dimensionality and identify nonlocal interactions, multiple components, dissipation, noise, or fluctuation corrections explicitly.", "questions": [ { "text": "Which confinement and energy-scale conditions justify eliminating spatial directions, and how was the effective coupling obtained?", "kind": "boundary", "id": "reduction-and-extension-contract-q01" }, { "text": "Which omitted physical effect would invalidate the baseline equation for this task, and which linked formulation addresses it?", "kind": "action", "id": "reduction-and-extension-contract-q02" } ] } ] } ] }, { "id": "physical-problem-specification", "name": "Physical problem specification", "description": "Supply the information needed to turn an equation into a determinate condensate problem.", "rationale": "The equation alone does not select a condensate state, a trajectory, or a physically meaningful computational domain.", "layers": [ { "id": "interactions-and-confinement", "name": "Interactions and confinement", "description": "Record physical coefficients and the environment acting on the condensate.", "findings": [ { "id": "parameter-and-potential-definition", "name": "Parameter and potential definition", "description": "Specify mass, interaction coefficient, particle number, potential, and reference frame with their provenance and uncertainty.", "questions": [ { "text": "What values and uncertainties define mass, scattering length, condensate number, and any effective coupling?", "kind": "measurement", "id": "parameter-and-potential-definition-q01" }, { "text": "What function defines confinement or driving, and is any rotational term expressed in a declared rotating frame?", "kind": "definition", "id": "parameter-and-potential-definition-q02" } ] } ] }, { "id": "domain-and-state-data", "name": "Domain and state data", "description": "Specify boundary behavior and either initial data or stationary-state selection constraints.", "findings": [ { "id": "problem-closure", "name": "Problem closure", "description": "Treat phase information, topology, normalization, and boundary conditions as substantive inputs rather than solver defaults.", "questions": [ { "text": "What initial complex field or stationary-state constraints select the intended physical state?", "kind": "definition", "id": "problem-closure-q01" }, { "text": "Which boundary conditions represent the physical system, and which boundaries merely truncate the computational domain?", "kind": "boundary", "id": "problem-closure-q02" } ] } ] } ] }, { "id": "states-observables-and-stability", "name": "States, observables, and stability", "description": "Connect solutions to condensate quantities and distinguish existence from stability.", "rationale": "An agent must distinguish a stationary candidate, an energy minimum, a metastable state, and an unstable excitation.", "layers": [ { "id": "stationary-state-selection", "name": "Stationary state selection", "description": "Interpret the nonlinear stationary equation and its normalization constraint.", "findings": [ { "id": "chemical-potential-and-energy", "name": "Chemical potential and energy", "description": "Record the stationary ansatz ψ(r,t) = φ(r)exp(−iμt/ℏ), the associated energy functional, and the constraints used to select a solution.", "questions": [ { "text": "Is the target a ground state, a constrained minimum, or an excited stationary branch?", "kind": "definition", "id": "chemical-potential-and-energy-q01" }, { "text": "How are chemical potential and total energy computed separately under the chosen normalization?", "kind": "measurement", "id": "chemical-potential-and-energy-q02" } ] } ] }, { "id": "observable-and-perturbation-interpretation", "name": "Observable and perturbation interpretation", "description": "Define measurable outputs and evidence for stability or instability.", "findings": [ { "id": "condensate-observables", "name": "Condensate observables", "description": "Attach explicit extraction rules to density, phase, current, collective motion, and vortices. These are established mean-field applications discussed in [Dalfovo et al., Theory of Bose-Einstein condensation in trapped gases](https://arxiv.org/abs/cond-mat/9806038).", "questions": [ { "text": "How are density, current, and phase-derived quantities calculated, including behavior near field zeros?", "kind": "measurement", "id": "condensate-observables-q01" }, { "text": "What phase-winding and density evidence distinguishes a vortex from a numerical artifact?", "kind": "measurement", "id": "condensate-observables-q02" } ] }, { "id": "stability-evidence", "name": "Stability evidence", "description": "Keep energetic stability, linear dynamical stability, and finite-time persistence as separate assessments.", "questions": [ { "text": "What constrained energy comparison or linearized perturbation analysis supports the stated stability classification?", "kind": "measurement", "id": "stability-evidence-q01" }, { "text": "Which perturbations and observation times have been tested before using this solution to predict persistent behavior?", "kind": "action", "id": "stability-evidence-q02" } ] } ] } ] }, { "id": "calculation-validation-and-use", "name": "Calculation validation and use", "description": "Determine whether a computed result is reproducible and accurate enough for its proposed use.", "rationale": "Nonlinear evolution, localized defects, and unstable branches require checks beyond solver completion.", "layers": [ { "id": "numerical-adequacy", "name": "Numerical adequacy", "description": "Match solution methods and resolution to the requested state or trajectory.", "findings": [ { "id": "method-and-resolution-evidence", "name": "Method and resolution evidence", "description": "Require convergence evidence for relevant spatial and temporal scales; imaginary-time relaxation must be identified as a state-finding method.", "questions": [ { "text": "Does the selected method find the requested branch or evolution, and what initialization or constraints could bias its result?", "kind": "action", "id": "method-and-resolution-evidence-q01" }, { "text": "How do the target observables change under mesh, time-step, solver-tolerance, and domain-size refinement?", "kind": "measurement", "id": "method-and-resolution-evidence-q02" } ] } ] }, { "id": "physical-and-mathematical-checks", "name": "Physical and mathematical checks", "description": "Assess residuals, conservation or balance laws, and agreement with appropriate reference cases.", "findings": [ { "id": "acceptance-and-escalation", "name": "Acceptance and escalation", "description": "Define task-specific acceptance criteria using equation residuals, applicable invariants, benchmark limits, and independent physical evidence.", "questions": [ { "text": "Which norm and energy conservation or balance laws apply to this potential, boundary treatment, and equation variant?", "kind": "boundary", "id": "acceptance-and-escalation-q01" }, { "text": "What residual, benchmark agreement, and observable uncertainty must be achieved before accepting the result or escalating to another theory?", "kind": "action", "id": "acceptance-and-escalation-q02" } ] } ] } ] }, { "id": "evidence-and-external-alignment", "name": "Evidence and external alignment", "description": "What the world already says about this thing, gathered so the model can be checked against it.", "rationale": "A model that cannot be lined up against existing standards, identifiers and practice cannot be adopted by anyone who already uses them.", "layers": [ { "id": "reported-evidence", "name": "Reported evidence", "description": "Findings from the breadth pass, kept separate from the structural claims.", "findings": [ { "id": "evidence-confidence-notes", "name": "Check these first", "description": "Recalled without web access and unsourced; every item is a lead to verify.", "evidence": [ "The supplied domain code INF.MED should be checked against the registry taxonomy; this entity is a mathematical equation used in quantum many-body physics.", "Normalization conventions differ: the squared order-parameter magnitude may represent particle density or a probability density, changing where particle number appears in the interaction coefficient.", "No universal measurement ranges or equation-specific regulatory standards are supplied; validity and parameter scales depend on the physical system and equation variant." ], "questions": [ { "id": "evidence-confidence-notes-q01", "text": "Which of these check these first hold for the sense of Gross-Pitaevskii equation this model covers, and on what evidence?", "kind": "provenance" } ] }, { "id": "evidence-kinds", "name": "Kinds and varieties", "description": "Recalled without web access and unsourced; every item is a lead to verify.", "evidence": [ "Time-dependent Gross-Pitaevskii equation", "Time-independent or stationary Gross-Pitaevskii equation", "Coupled Gross-Pitaevskii equations for multicomponent condensates", "Dissipative Gross-Pitaevskii equation", "Nonlocal Gross-Pitaevskii equation for interactions such as dipolar interactions", "Effective one-dimensional and two-dimensional Gross-Pitaevskii equations" ], "questions": [ { "id": "evidence-kinds-q01", "text": "Which of these kinds and varieties hold for the sense of Gross-Pitaevskii equation this model covers, and on what evidence?", "kind": "provenance" } ] }, { "id": "evidence-real-world-use", "name": "Real-world use", "description": "Recalled without web access and unsourced; every item is a lead to verify.", "evidence": [ "Calculating condensate density profiles and ground states in trapping potentials", "Simulating condensate expansion, interference and collective oscillations", "Studying quantized vortices and superfluid flow", "Modelling matter-wave solitons", "Investigating condensates in optical lattices and coupled traps" ], "questions": [ { "id": "evidence-real-world-use-q01", "text": "Which of these real-world use hold for the sense of Gross-Pitaevskii equation this model covers, and on what evidence?", "kind": "provenance" } ] }, { "id": "evidence-failure-modes-and-hazards", "name": "Failure modes and hazards", "description": "Recalled without web access and unsourced; every item is a lead to verify.", "evidence": [ "The basic mean-field approximation becomes unreliable when strong correlations or substantial condensate depletion are important.", "The usual zero-temperature equation omits thermal-cloud dynamics and finite-temperature damping.", "A local contact-interaction term alone cannot represent important long-range interactions.", "Reduced-dimensional models require appropriate confinement assumptions and effective coupling constants.", "Attractive interactions can produce collapse in the model; physical descriptions near collapse may require particle losses and corrections beyond mean-field theory." ], "questions": [ { "id": "evidence-failure-modes-and-hazards-q01", "text": "Which of these failure modes and hazards hold for the sense of Gross-Pitaevskii equation this model covers, and on what evidence?", "kind": "provenance" } ] }, { "id": "evidence-neighbours", "name": "Neighbouring kinds and how to tell them apart", "description": "Recalled without web access and unsourced; every item is a lead to verify.", "evidence": [ { "name": "Nonlinear Schrödinger equation", "difference": "This is the broader mathematical family; the Gross-Pitaevskii equation has a condensate order parameter and interaction parameters interpreted through a Bose-gas mean-field model." }, { "name": "Linear Schrödinger equation", "difference": "The usual linear equation has no density-dependent self-interaction term, whereas the Gross-Pitaevskii equation generally includes one." }, { "name": "Bogoliubov-de Gennes equations", "difference": "For Bose condensates, these describe small excitations obtained by linearizing about a condensate solution, rather than its full nonlinear evolution." }, { "name": "Bose-Hubbard model", "difference": "This is a quantum lattice many-body model that can describe correlations and insulating phases absent from a basic condensate mean-field equation." }, { "name": "Ginzburg-Landau theory", "difference": "It describes order parameters through a phenomenological free-energy framework; similar equation forms do not imply the same microscopic derivation or physical regime." } ], "questions": [ { "id": "evidence-neighbours-q01", "text": "Which of these neighbouring kinds and how to tell them apart hold for the sense of Gross-Pitaevskii equation this model covers, and on what evidence?", "kind": "provenance" } ] } ] } ] } ] }, "openQuestions": [ "Does an existing Vercy world-model publication already cover this equation, requiring the registry entry to link to that publication?", "Which named extensions should be represented within this entry, and which should be linked as distinct registered concepts?", "Does the assigned INF.MED domain intentionally include mathematical equations, or does this entry require a classification correction?", "Which primary derivations should anchor the publication's historical attribution, normalization conventions, and reduced-dimensional formulations?", "Which application regimes and target observables will determine acceptable depletion, thermal contribution, numerical error, and validation thresholds?" ], "statistics": { "bundles": 6, "layers": 11, "findings": 16, "questions": 27 } }