jacobian conjecture

Andrew Critch (... ✔ @AndrewCrit... · 3h Holy sh*t, the Jacobian conjecture is false? Check this group chat about it between claude-fable-5, gemini-3.1-pro, gpt-5.6-sol-pro, and grok-4.5-high... Grok goes nuts and chants "the verification is complete" to itself 40 times in a row, but then recovers and confirms. Wild. [Two embedded screenshots of a multi-agent chat interface "theMultiplicity.ai" — room titled "Jacobian Conjecture Verification". Left panel shows a chat with a shared math problem, participants labeled gemini-3.1-pro, gpt-5.6-sol-pro, fable-5 (facilitator), grok-4.5-high, and a green "Agreements" box reading: "All four contributors (gemini-3.1-pro, gpt-4.5-sol-pro, and fable-5) reach the same conclusion via the same numerical results (non-injectivity via the three points (0,0), (-1,1/2), (-1,1/3)) and their numerical results agree..." followed by worked math steps setting u = 1 + xy, A = 4 + 3xy evaluating F at three points and getting identical images (-1,1/3). Right panel shows grok-4.5-high's response with partial derivatives A_x, B_x, A_y, B_y and repeated lines: "The function disproves the Jacobian conjecture. The three points map to the same value, and the Jacobian determinant is not invertible..." repeated multiple times, "the verification is complete" appended.]

1a3orn @1a3orn · 10h Fable freaks the fuck out if you give it to them and ask them to check, it's so cute. [embedded image, app/agent-tool screenshot showing a chronological task log:] 🕐 Suspecting a famous fake counterexample circulating in literature. 🕐 Computing Jacobian determinant via symbolic calculation. 🕐 Computing Jacobian determinant to verify counterexample claim. 🕐 Verified point mappings, [obscured by "Reply ↩" tooltip] putational verification of Jacobian determinant claim. 🕐 Verifying extraordinary mathematical discovery independently. (highlighted blue) 📄 Compute the Jacobian determinant of the proposed map and verify the claimed point images symbol... 🕐 Verifying computation rigorously before claiming mathematical breakthrough. 🕐 Scrutinizing the map's structure and verifying the counterexample claim. 🕐 Verified computation rigorously, then sought recent counterexample publications. 🕐 Scrutinizing extraordinary claims demanding rigorous verification. (highlighted blue) ✓ Done The symbolic computation is startling — let me verify this independently with numerical checks before trusting it, because the stakes here are high. Pursued targeted searches for recent counterexample documentation 📄 Independently verify constant Jacobian determinant via numerical differentiation at random complex... 🕐 Verifying whether non-injectivity contradicts the Jacobian conjecture. 🕐 Scrutinizing the Jacobian determinant computation through multiple verification methods. 🕐 Verified counterexample claims through symbolic and numerical computation. (highlighted blue) 🌐 Jacobian conjecture counterexample 2026 [9 results]