{"id":2201593,"recorded_at":"2026-11-02T19:13:26.805449Z","observed_at":"2026-11-02T19:13:26.805407Z","subject_kind":"source_record","subject":"x402_bazaar:https://math-geometry.x402tookit.com/cubic-solve","kind":"listing","method":"sync.x402_bazaar/1","body":{"endpoints":[["x402","https://math-geometry.x402tookit.com/cubic-solve"]],"name":"Algebra and Geometry Solvers","owner_address":"0xb531320805c5bed1d46aeadcf4f008fdf172dbda","raw":{"accepts":[{"amount":"20000","asset":"0x833589fCD6eDb6E08f4c7C32D4f71b54bdA02913","extra":{"name":"USD Coin","version":"2"},"maxTimeoutSeconds":300,"network":"eip155:8453","payTo":"0xb531320805C5BED1D46AEaDcF4F008FDF172DBDa","scheme":"exact"},{"amount":"20000","asset":"EPjFWdd5AufqSSqeM2qN1xzybapC8G4wEGGkZwyTDt1v","extra":{"feePayer":"D6ZhtNQ5nT9ZnTHUbqXZsTx5MH2rPFiBBggX4hY1WePM","transactionVersions":[0]},"maxTimeoutSeconds":300,"network":"solana:5eykt4UsFv8P8NJdTREpY1vzqKqZKvdp","payTo":"DUPiupXtuox38dcGoXUKer5mAydCzmaHjrbQ66qeEm8s","scheme":"exact"},{"amount":"20000","asset":"0x3c499c542cEF5E3811e1192ce70d8cC03d5c3359","extra":{"name":"USD Coin","version":"2"},"maxTimeoutSeconds":300,"network":"eip155:137","payTo":"0xb531320805C5BED1D46AEaDcF4F008FDF172DBDa","scheme":"exact"},{"amount":"20000","asset":"0xaf88d065e77c8cC2239327C5EDb3A432268e5831","extra":{"name":"USD Coin","version":"2"},"maxTimeoutSeconds":300,"network":"eip155:42161","payTo":"0xb531320805C5BED1D46AEaDcF4F008FDF172DBDa","scheme":"exact"}],"description":"Solve ax^3 + bx^2 + cx + d = 0: all three roots (real and complex) by Cardano and the trigonometric method.","extensions":{"bazaar":{"info":{"input":{"method":"GET","queryParams":{"a":1,"b":-6,"c":11,"d":-6},"type":"http"},"output":{"example":{"a":1,"asOf":"2026-10-11T08:51:18.592Z","b":-6,"c":11,"complexRoots":[],"d":-6,"degraded":false,"depressed":{"discriminant":-0.03703703704,"p":-1,"q":0},"disclaimer":"Screening signal computed from the named public source. Not financial, legal or investment advice; provided as is. Verify at the source before acting.","notChecked":["exact radical forms (results are decimals)","accuracy for extreme coefficient ratios beyond double precision"],"realRoots":[1,2],"reasons":["Reduced to a depressed cubic t^3 + pt + q = 0; the sign of q^2/4 + p^3/27 selects the method. Real roots are polished with Newton steps.","A cubic always has at least one real root."],"rootType":"three distinct real roots","roots":["1","2","…1 more"],"source":"computed locally","summary":"1x^3 + -6x^2 + 11x + -6 = 0: 1, 2, 3 (three distinct real roots).","verdict":"THREE_REAL_ROOTS"},"type":"json"}},"schema":{"$schema":"https://json-schema.org/draft/2020-12/schema","properties":{"input":{"additionalProperties":false,"properties":{"method":{"enum":["GET"],"type":"string"},"queryParams":{"properties":{"a":{"description":"Coefficient of x^3 (not 0)","type":"number"},"b":{"description":"Coefficient of x^2","type":"number"},"c":{"description":"Coefficient of x","type":"number"},"d":{"description":"Constant term","type":"number"}},"required":["a","b","c","d"],"type":"object"},"type":{"const":"http","type":"string"}},"required":["type","method"],"type":"object"},"output":{"properties":{"example":{"properties":{"a":{"type":["null","number"]},"asOf":{"type":["null","string"]},"b":{"type":["null","number"]},"c":{"type":["null","number"]},"complexRoots":{"type":["array","null"]},"d":{"type":["null","number"]},"degraded":{"type":["boolean","null"]},"depressed":{"properties":{"discriminant":{"type":["null","number"]},"p":{"type":["null","number"]},"q":{"type":["null","number"]}},"type":["null","object"]},"disclaimer":{"type":["null","string"]},"notChecked":{"items":{"type":"string"},"type":["array","null"]},"realRoots":{"items":{"type":"number"},"type":["array","null"]},"reasons":{"items":{"type":"string"},"type":["array","null"]},"rootType":{"type":["null","string"]},"roots":{"items":{"type":"string"},"type":["array","null"]},"source":{"type":["null","string"]},"summary":{"type":["null","string"]},"verdict":{"type":["null","string"]}},"type":"object"},"type":{"type":"string"}},"required":["type"],"type":"object"}},"required":["input"],"type":"object"}}},"lastUpdated":"2026-11-01T23:37:21.283Z","quality":{"l30DaysTotalCalls":2,"l30DaysUniquePayers":2,"lastCalledAt":"2026-11-01T23:37:21.114Z"},"resource":"https://math-geometry.x402tookit.com/cubic-solve","serviceName":"Algebra and Geometry Solvers","tags":["algebra","cubic","roots","calculator"],"type":"http","x402Version":2},"source":"x402_bazaar","summary":"Solve ax^3 + bx^2 + cx + d = 0: all three roots (real and complex) by Cardano and the trigonometric method."},"body_sha256":"c576f367c75526113cf8461e8c1db1b133d5a5be674b2383105dbf2a9bebade5","prev_id":null,"leaf":"0xb7c2f990ad58569dd17a68f491d02eb1c316d190a6b5d2d14c5639d6604c6f17","leaf_text":"{\"body\":\"c576f367c75526113cf8461e8c1db1b133d5a5be674b2383105dbf2a9bebade5\",\"id\":2201593,\"kind\":\"listing\",\"method\":\"sync.x402_bazaar/1\",\"observed_us\":1793646806805407,\"prev\":null,\"subject\":\"x402_bazaar:https://math-geometry.x402tookit.com/cubic-solve\",\"subject_kind\":\"source_record\"}","day":{"day":"2026-11-02","leaves":444186,"root":"0x78fecaabbe319e56f5c4b80fc02e2052e198ad24781da8832a475ff65f2002d1","chained":"0xdc35957db5d1371ca382b9152878ffece28ec7c5cb4f98fd71ddb367f8b999b2","anchor_chain":"eip155:5042002","anchor_tx":"0x56b814612eb2e3e544153df3e91e1f7199106d1e430c7d8c6b653feeb9ebe9af","anchor_block":70432815},"proof":["0xb7c30d5c292572d6ea4ae56d16b90f53b5dcc95e78c5841ecf5e9a8117667f9b","0x936e10251c33e051af277da5e62359bfdfaeb8a7554ffc38c20973a5db73c672","0xa5e0469e6752ee5c16359c835e50bf7e001762a7a62dc273786fdfe13c550e77","0x179a015e9923fa44bf4f959c488b27151649ed6901554029b86c147317db6014","0x57dc2d94c02e4d1ef4d58a33041da4e75d950974f098b1a4096432e56d341166","0xae5f709da36c833b0ac183774365290a81ddcafc2ef32867fe8862981eb7ae1a","0x805782e3ec4be95f9abd5ae032dacdd8461c1a299af5baaf5a5ccb8559c499b6","0x72a947f90b8c8c49403d214985af9a38744536f128295dd69add6097c25d88b2","0x1efecab01743ba6ae8e9e64ddd9e84ccb3ea802cd616e64189769bc062841ec7","0xf0b6bf793cc66a03909741a989c833367cfc76f3d77268884d6f3d1930d28961","0x2baaf56994f40f69d6e4622eada4b0cdaf5e4b3766e25b2769e9cdcb7eeebe1f","0x1e746a5fe19cb9ec0a19b0ddff5c240ad1117a5db0999c1e01fe8f1235d88e30","0x030e61e00342e920981555e2e665fa5ec4a741b10a078f282daa829896c87583","0x08da04eef748b7ac08271324db18913501d72c52afa240bf3f08b6da46e3b97f","0x834b6b9a36b42da183e2542785e8d2d7548ace455268a81922edbe6020cef644","0x2922573a524a0694086782ac45fa3083d3fc3f6a2a479b2105e1e2f06b2916f7","0x07ad80c0c234ecea379a2f4450dfd0804db049dbc62abe77af6306049ca6b6c2","0x98cbbf2c68ab4c0b4db782aeb88bea1f30b02178cf8b5d3d24a931d19492ea6d","0x252cce55f1a3d5391c16f82d7f62494429a5f69b03486d4cfcfb7b2c96d6c884"]}