{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:QMLHIUS7WC56HUXY5HY4XD4RVM","short_pith_number":"pith:QMLHIUS7","canonical_record":{"source":{"id":"1702.06044","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2017-02-20T16:13:04Z","cross_cats_sorted":["math-ph","math.AP","math.MP"],"title_canon_sha256":"57d85f2a9745274bef1b4d6959bce813157d685c534d92388f2f172ab924b0ab","abstract_canon_sha256":"31c914eddb57b1aad38bfec1240c601d2be501c9fe53115985cbec28eae6b92f"},"schema_version":"1.0"},"canonical_sha256":"831674525fb0bbe3d2f8e9f1cb8f91ab16aa6b60bf980eab0d38d2ba6d2e3200","source":{"kind":"arxiv","id":"1702.06044","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1702.06044","created_at":"2026-05-18T00:50:24Z"},{"alias_kind":"arxiv_version","alias_value":"1702.06044v1","created_at":"2026-05-18T00:50:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1702.06044","created_at":"2026-05-18T00:50:24Z"},{"alias_kind":"pith_short_12","alias_value":"QMLHIUS7WC56","created_at":"2026-05-18T12:31:39Z"},{"alias_kind":"pith_short_16","alias_value":"QMLHIUS7WC56HUXY","created_at":"2026-05-18T12:31:39Z"},{"alias_kind":"pith_short_8","alias_value":"QMLHIUS7","created_at":"2026-05-18T12:31:39Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:QMLHIUS7WC56HUXY5HY4XD4RVM","target":"record","payload":{"canonical_record":{"source":{"id":"1702.06044","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2017-02-20T16:13:04Z","cross_cats_sorted":["math-ph","math.AP","math.MP"],"title_canon_sha256":"57d85f2a9745274bef1b4d6959bce813157d685c534d92388f2f172ab924b0ab","abstract_canon_sha256":"31c914eddb57b1aad38bfec1240c601d2be501c9fe53115985cbec28eae6b92f"},"schema_version":"1.0"},"canonical_sha256":"831674525fb0bbe3d2f8e9f1cb8f91ab16aa6b60bf980eab0d38d2ba6d2e3200","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:50:24.491878Z","signature_b64":"ZYP+S9R66ulDx9UrRmM4fUbEh0e8huuEc+gg1R1bdcKuq4dKKOxPRtUZ798BRcnfcRGdU+EeM0xNz/HaOcYmDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"831674525fb0bbe3d2f8e9f1cb8f91ab16aa6b60bf980eab0d38d2ba6d2e3200","last_reissued_at":"2026-05-18T00:50:24.491187Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:50:24.491187Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1702.06044","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:50:24Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Fg0cjWzDu4fD+GwzS/XeAcZMMyQSYf7ldMumDKPCLadKWzbK4WO+s4Rm2T9NXDtgH4BhvPXngjOUpEE+klV3DA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-07T03:54:38.584906Z"},"content_sha256":"5de1d40b2aa06a2f095b6f09f9721d9a229e1d7aa89be2dd25a41f460019768e","schema_version":"1.0","event_id":"sha256:5de1d40b2aa06a2f095b6f09f9721d9a229e1d7aa89be2dd25a41f460019768e"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:QMLHIUS7WC56HUXY5HY4XD4RVM","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The Kontsevich tetrahedral flow in 2D: a toy model","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.AP","math.MP"],"primary_cat":"math.DG","authors_text":"Anass Bouisaghouane","submitted_at":"2017-02-20T16:13:04Z","abstract_excerpt":"In the paper \"Formality conjecture\" (1996) Kontsevich designed a universal flow $\\dot{\\mathcal{P}}=\\mathcal{Q}_{a:b}(\\mathcal{P})=a\\Gamma_{1}+b\\Gamma_{2}$ on the spaces of Poisson structures $\\mathcal{P}$ on all affine manifolds of dimension $n \\geqslant 2$. We prove a claim from $\\textit{loc. cit.}$ stating that if $n=2$, the flow $\\mathcal{Q}_{1:0}=\\Gamma_{1}(\\mathcal{P})$ is Poisson-cohomology trivial: $\\Gamma_{1}(\\mathcal{P})$ is the Schouten bracket of $\\mathcal{P}$ with $\\mathcal{X}$, for some vector field $\\mathcal{X}$; we examine the structure of the space of solutions $\\mathcal{X}$. B"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1702.06044","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:50:24Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"bP9jeUxtz66S78GP4Dmq3zNRICA/YlQqdTBRobyjBBrCpiH3VF+X0l/s1FGmOLD0JHCPyrT7L4sfcMZifb4zBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-07T03:54:38.585241Z"},"content_sha256":"69a1e6b21de07ae34f362d988c170ac1e29d958cec650be661297c8b8dc1b84c","schema_version":"1.0","event_id":"sha256:69a1e6b21de07ae34f362d988c170ac1e29d958cec650be661297c8b8dc1b84c"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/QMLHIUS7WC56HUXY5HY4XD4RVM/bundle.json","state_url":"https://pith.science/pith/QMLHIUS7WC56HUXY5HY4XD4RVM/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/QMLHIUS7WC56HUXY5HY4XD4RVM/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-07-07T03:54:38Z","links":{"resolver":"https://pith.science/pith/QMLHIUS7WC56HUXY5HY4XD4RVM","bundle":"https://pith.science/pith/QMLHIUS7WC56HUXY5HY4XD4RVM/bundle.json","state":"https://pith.science/pith/QMLHIUS7WC56HUXY5HY4XD4RVM/state.json","well_known_bundle":"https://pith.science/.well-known/pith/QMLHIUS7WC56HUXY5HY4XD4RVM/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:QMLHIUS7WC56HUXY5HY4XD4RVM","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"31c914eddb57b1aad38bfec1240c601d2be501c9fe53115985cbec28eae6b92f","cross_cats_sorted":["math-ph","math.AP","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2017-02-20T16:13:04Z","title_canon_sha256":"57d85f2a9745274bef1b4d6959bce813157d685c534d92388f2f172ab924b0ab"},"schema_version":"1.0","source":{"id":"1702.06044","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1702.06044","created_at":"2026-05-18T00:50:24Z"},{"alias_kind":"arxiv_version","alias_value":"1702.06044v1","created_at":"2026-05-18T00:50:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1702.06044","created_at":"2026-05-18T00:50:24Z"},{"alias_kind":"pith_short_12","alias_value":"QMLHIUS7WC56","created_at":"2026-05-18T12:31:39Z"},{"alias_kind":"pith_short_16","alias_value":"QMLHIUS7WC56HUXY","created_at":"2026-05-18T12:31:39Z"},{"alias_kind":"pith_short_8","alias_value":"QMLHIUS7","created_at":"2026-05-18T12:31:39Z"}],"graph_snapshots":[{"event_id":"sha256:69a1e6b21de07ae34f362d988c170ac1e29d958cec650be661297c8b8dc1b84c","target":"graph","created_at":"2026-05-18T00:50:24Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"In the paper \"Formality conjecture\" (1996) Kontsevich designed a universal flow $\\dot{\\mathcal{P}}=\\mathcal{Q}_{a:b}(\\mathcal{P})=a\\Gamma_{1}+b\\Gamma_{2}$ on the spaces of Poisson structures $\\mathcal{P}$ on all affine manifolds of dimension $n \\geqslant 2$. We prove a claim from $\\textit{loc. cit.}$ stating that if $n=2$, the flow $\\mathcal{Q}_{1:0}=\\Gamma_{1}(\\mathcal{P})$ is Poisson-cohomology trivial: $\\Gamma_{1}(\\mathcal{P})$ is the Schouten bracket of $\\mathcal{P}$ with $\\mathcal{X}$, for some vector field $\\mathcal{X}$; we examine the structure of the space of solutions $\\mathcal{X}$. B","authors_text":"Anass Bouisaghouane","cross_cats":["math-ph","math.AP","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2017-02-20T16:13:04Z","title":"The Kontsevich tetrahedral flow in 2D: a toy model"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1702.06044","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:5de1d40b2aa06a2f095b6f09f9721d9a229e1d7aa89be2dd25a41f460019768e","target":"record","created_at":"2026-05-18T00:50:24Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"31c914eddb57b1aad38bfec1240c601d2be501c9fe53115985cbec28eae6b92f","cross_cats_sorted":["math-ph","math.AP","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2017-02-20T16:13:04Z","title_canon_sha256":"57d85f2a9745274bef1b4d6959bce813157d685c534d92388f2f172ab924b0ab"},"schema_version":"1.0","source":{"id":"1702.06044","kind":"arxiv","version":1}},"canonical_sha256":"831674525fb0bbe3d2f8e9f1cb8f91ab16aa6b60bf980eab0d38d2ba6d2e3200","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"831674525fb0bbe3d2f8e9f1cb8f91ab16aa6b60bf980eab0d38d2ba6d2e3200","first_computed_at":"2026-05-18T00:50:24.491187Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:50:24.491187Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ZYP+S9R66ulDx9UrRmM4fUbEh0e8huuEc+gg1R1bdcKuq4dKKOxPRtUZ798BRcnfcRGdU+EeM0xNz/HaOcYmDA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:50:24.491878Z","signed_message":"canonical_sha256_bytes"},"source_id":"1702.06044","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5de1d40b2aa06a2f095b6f09f9721d9a229e1d7aa89be2dd25a41f460019768e","sha256:69a1e6b21de07ae34f362d988c170ac1e29d958cec650be661297c8b8dc1b84c"],"state_sha256":"639c47d8ca3470a7af1431ecbcde47677549bf28da5fea34529d5c52a83ff243"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"so4ldIqCJQyN7kkkolSIZXevHx291nQQPiR4L1dy+CfbZsiSLEURvkAIz7ShoxD81TH5MR75TzJbE3zVVQ5tCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-07T03:54:38.587059Z","bundle_sha256":"d594779a422fed82715ac3621562aba68bf802eb8d8d4685e63e23e3e714d343"}}