{"uid":"cap_0mZ-1Qjvaamb9ohuqKuHR","slug":"gray-scott-reaction-diffusion-complete-mass-transfer-ledger-064448af","name":"Gray-Scott Reaction-Diffusion Complete Mass Transfer Ledger","description":"Recover a spatially coupled reaction-diffusion artifact and its full feed/conversion/removal accounting.","url":"https://detect.halowerk.com/v1/F-TD2000-GEO-INDUSTRY-B011/periodic-gray-scott-reaction-diffusion-complete-mass-transfer-ledger?utm_source=zero.xyz","method":"POST","headers":{},"bodySchema":{"type":"object","properties":{"artifact":{"type":"object","required":["grayScott"],"properties":{"grayScott":{"type":"object","required":["data","claim"],"properties":{"data":{"type":"object","required":["initial_u","initial_v","diffusivity_u","diffusivity_v","feed_rate","conversion_rate","spacing","timestep","sample_steps"],"properties":{"spacing":{"type":"number","maximum":10,"minimum":0.1},"timestep":{"type":"number","maximum":0.1,"minimum":0.0001},"feed_rate":{"type":"number","maximum":1,"minimum":0},"initial_u":{"type":"array","items":{"type":"array","items":{"type":"number","maximum":1.5,"minimum":0},"maxItems":8,"minItems":4},"maxItems":8,"minItems":4},"initial_v":{"type":"array","items":{"type":"array","items":{"type":"number","maximum":1.5,"minimum":0},"maxItems":8,"minItems":4},"maxItems":8,"minItems":4},"sample_steps":{"type":"array","items":{"type":"integer","maximum":128,"minimum":0},"maxItems":8,"minItems":1},"diffusivity_u":{"type":"number","maximum":1,"minimum":0},"diffusivity_v":{"type":"number","maximum":1,"minimum":0},"conversion_rate":{"type":"number","maximum":1,"minimum":0}},"additionalProperties":false},"claim":{}},"additionalProperties":false}},"additionalProperties":false}}},"responseSchema":null,"example":null,"exampleRequest":null,"tags":["x402"],"displayCostAmount":"0.003","displayCostAsset":"USDC","priceDynamic":false,"priceHint":null,"priceStatus":"priced","priceSource":"probe","requiresHandshake":false,"reviewCount":0,"rating":{"score":"0.00","successRate":"0.00","reviews":0,"stars":null,"state":"unrated"},"availabilityStatus":"unknown","priceObserved":null,"sessionDeposit":null,"pricing":{"kind":"static","summary":"$0.003/call","primary":{"kind":"static","protocol":"x402","network":"base","amountUsd":"0.003","per":"call","confidence":"exact"},"accepted":[{"kind":"static","protocol":"x402","network":"base","amountUsd":"0.003","per":"call","confidence":"exact"}]},"paymentMethods":[{"uid":"pm_B2232Xut4jweOGcrfda6p","protocol":"x402","methodType":"crypto","chain":"base","mode":"charge","costAmount":"0.003","costPer":"request","priority":0,"asset":"0x833589fCD6eDb6E08f4c7C32D4f71b54bdA02913","unit":"request","depositMicros":null,"planRef":null}],"brandName":null,"brandSlug":null,"brandBaseUrl":null,"brandDocsUrl":null,"whatItDoes":"Simulates spatially coupled Gray-Scott reaction-diffusion dynamics on a 2D grid and returns a full mass-transfer ledger including feed, conversion, and removal accounting at specified time steps.","exampleAgentPrompt":"Run a Gray-Scott reaction-diffusion simulation on a 4x4 grid, with initial U values all 1.0 and initial V values all 0.0 except the center seeded at 0.5, diffusivity_u of 0.2, diffusivity_v of 0.1, feed rate 0.04, conversion rate 0.06, grid spacing 1.0, timestep 0.01, and sample snapshots at steps 0, 32, and 64 — then give me the complete mass-transfer ledger showing feed, conversion, and removal accounting.","exampleUseCases":[{"title":"Turing pattern stability analysis","prompt":"I want to study whether a specific Gray-Scott parameter set produces stable Turing patterns — set U diffusivity to 0.16, V diffusivity to 0.08, feed rate 0.035, conversion rate 0.065, a 6x6 initial grid with U near 1 and V seeded at 0.25 in the interior, spacing 1.0, timestep 0.005, and sample at steps 0, 64, and 128. Give me the full mass-transfer ledger so I can check the feed and removal balance over time."},{"title":"Chemical wave propagation accounting","prompt":"Simulate a Gray-Scott chemical wave on an 8x8 grid with initial U all set to 1.0 and V set to 0.5 in a central 2x2 patch, diffusivity_u 0.2, diffusivity_v 0.1, feed rate 0.06, conversion rate 0.062, spacing 0.5, timestep 0.02, sampling at steps 10, 50, and 100 — I need the complete conversion and removal accounting to validate my mass conservation model."},{"title":"Parameter sweep baseline snapshot","prompt":"I need a baseline Gray-Scott run to anchor my parameter sweep: 4x4 grids with U initialized to 0.5 everywhere and V to 0.25, diffusivity_u 0.1, diffusivity_v 0.05, feed 0.04, conversion 0.06, spacing 1.0, timestep 0.01, sampled at steps 0 and 128. Return the full feed, conversion, and removal ledger so I can compare it against perturbed runs."}],"resultDescription":"The endpoint returns the simulated Gray-Scott reaction-diffusion artifact containing concentration fields (U and V) at each requested sample step, along with a complete mass-transfer ledger that details the cumulative feed (inflow of U), conversion (U→V reaction), and removal (outflow of V) at each sampled timestep, enabling full mass-balance verification.","failureModes":["Invalid grid dimensions (must be 4–8 rows and 4–8 columns per axis) return a validation error","Diffusivity, feed, or conversion values outside [0,1] are rejected","Timestep outside [0.0001, 0.1] or spacing outside [0.1, 10] cause schema validation failure","Sample steps exceeding 128 or empty sample_steps array return an error","Missing required fields (initial_u, initial_v, diffusivity_u, diffusivity_v, feed_rate, conversion_rate, spacing, timestep, sample_steps) result in a 400-level error","Payment failure (insufficient USDC balance for x402) prevents execution"],"whenToPreferThis":"Choose this endpoint when you need a numerically rigorous Gray-Scott reaction-diffusion simulation with explicit, structured mass-transfer accounting (feed, conversion, removal) for small 2D grids (up to 8x8), particularly when you need to verify mass balance or extract spatiotemporal concentration snapshots at precise timesteps. Prefer this over generic PDE solvers when the Gray-Scott model (two-species autocatalytic reaction with periodic boundary conditions) is your specific target and you require the full ledger output rather than just final-state concentration fields.","instructions":null,"reviewSummary":null,"reviewSummaryHighlights":null,"reviewSummaryConcerns":null,"reviewSummaryGeneratedAt":null,"activationCount":0,"lastUsedAt":null,"lastSuccessfullyRanAt":null,"lastHealthCheckAt":"2026-11-04T06:41:07.938Z","isFirstParty":false,"canonicalSlug":"gray-scott-reaction-diffusion-complete-mass-transfer-ledger-064448af"}