{"uid":"cap_nv8_fZ5OdiLxnVR12XoIX","slug":"abelian-sandpile-sink-stabilization-odometer-4eac2a26","name":"Abelian Sandpile Sink Stabilization & Odometer","description":"An offline chip-firing model test agent needs the unique stabilized configuration, per-vertex toppling counts and chips absorbed by a sink. Not checking arbitrary Petri boundedness or a supplied transition trace.","url":"https://detect.halowerk.com/v1/F-NIGHT-ECMA/abelian-sandpile-sink-stabilization-odometer?utm_source=zero.xyz","method":"POST","headers":{},"bodySchema":{"type":"object","properties":{"artifact":{"type":"object","required":["sandpile"],"properties":{"sandpile":{"type":"object","required":["adjacency","sink","chips","claim"],"properties":{"sink":{"type":"integer","maximum":15,"minimum":0},"chips":{"type":"array","items":{"type":"integer","maximum":256,"minimum":0},"maxItems":16,"minItems":2},"claim":{"type":"array","items":{"type":"integer","maximum":2048,"minimum":0},"maxItems":16,"minItems":2},"adjacency":{"type":"array","items":{"type":"array","items":{"type":"integer","maximum":8,"minimum":0},"maxItems":16,"minItems":2},"maxItems":16,"minItems":2}},"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_NYBhdk_Vfqumityu0MCGV","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":"Stabilizes an abelian sandpile model on a finite graph with a designated sink, returning the unique stable chip configuration, per-vertex toppling counts (odometer), and chips absorbed by the sink.","exampleAgentPrompt":"Stabilize this abelian sandpile: 4 vertices, sink at vertex 0, adjacency matrix [[0,2,1,0],[2,0,1,0],[1,1,0,2],[0,0,2,0]], starting chips [0,3,5,2], and my claimed odometer is [0,1,2,1]. Give me the unique stable configuration, per-vertex toppling counts, and how many chips the sink absorbed.","exampleUseCases":[{"title":"Offline chip-firing model verification","prompt":"I have a chip-firing graph with 5 vertices, sink at vertex 2, adjacency [[0,1,0,0,0],[1,0,2,0,0],[0,2,0,1,1],[0,0,1,0,2],[0,0,1,2,0]], starting chips [0,4,0,6,3], and I think the odometer is [0,2,0,3,1]. Can you stabilize it and tell me if my odometer is correct, what the stable chip configuration is, and how many chips fell into the sink?"},{"title":"Educational sandpile simulation","prompt":"For my discrete math homework, I need to stabilize a sandpile on a 3-vertex graph with sink at vertex 0, adjacency [[0,2,1],[2,0,1],[1,1,0]], and initial chips [0,5,4] with claimed odometer [0,2,2]. What is the stable configuration and how many times does each non-sink vertex topple?"},{"title":"Algorithm correctness testing","prompt":"I'm testing my chip-firing implementation and want to cross-check: graph has 6 vertices, sink at vertex 5, adjacency is a 6x6 matrix [[0,1,1,0,0,0],[1,0,0,1,0,0],[1,0,0,1,0,0],[0,1,1,0,2,0],[0,0,0,2,0,3],[0,0,0,0,3,0]], starting chips [0,3,3,4,2,0], claimed odometer all zeros. What's the actual stable configuration and correct odometer?"}],"resultDescription":"Returns the unique stable chip configuration (array of non-negative integers per vertex), the odometer (array of toppling counts per vertex), and the total number of chips absorbed by the designated sink vertex during stabilization.","failureModes":["Adjacency matrix dimensions inconsistent with chips/claim arrays — returns validation error","Sink index out of range (>15 or negative) — rejected by schema","Chip values exceeding 256 or odometer values exceeding 2048 — schema rejection","Graph not connected or no path to sink — may result in non-termination or error","Adjacency matrix not symmetric (directed graph) — may produce unexpected results","Claim array length mismatch with adjacency matrix size — returns error"],"whenToPreferThis":"Use this endpoint when you need an authoritative, offline-capable computation of abelian sandpile stabilization on small finite graphs (up to 16 vertices) including the odometer function and sink absorption count. Prefer it over manual simulation when you need to verify a proposed odometer/claim, need deterministic results for testing chip-firing algorithms, or require all three outputs (stable config, toppling counts, sink chips) simultaneously.","instructions":null,"reviewSummary":null,"reviewSummaryHighlights":null,"reviewSummaryConcerns":null,"reviewSummaryGeneratedAt":null,"activationCount":0,"lastUsedAt":null,"lastSuccessfullyRanAt":null,"lastHealthCheckAt":"2026-11-04T06:40:57.626Z","isFirstParty":false,"canonicalSlug":"abelian-sandpile-sink-stabilization-odometer-4eac2a26"}