{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:UNY7K5QW5G2DMDHUASGKMLNHXX","short_pith_number":"pith:UNY7K5QW","canonical_record":{"source":{"id":"1812.01413","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2018-12-04T13:56:50Z","cross_cats_sorted":["math.MP","nlin.SI"],"title_canon_sha256":"7d9aeff029badfd5a694d624e1cc2790a79fe7b41bbc586153f0d68f3c3135f2","abstract_canon_sha256":"770e6dfab7341b4abb1b9b20c6b2d5f355d6749a65da598f80c8144897418e8a"},"schema_version":"1.0"},"canonical_sha256":"a371f57616e9b4360cf4048ca62da7bdf966a1126c0382d6ac6c0e979eca891e","source":{"kind":"arxiv","id":"1812.01413","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1812.01413","created_at":"2026-05-17T23:46:09Z"},{"alias_kind":"arxiv_version","alias_value":"1812.01413v1","created_at":"2026-05-17T23:46:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1812.01413","created_at":"2026-05-17T23:46:09Z"},{"alias_kind":"pith_short_12","alias_value":"UNY7K5QW5G2D","created_at":"2026-05-18T12:32:56Z"},{"alias_kind":"pith_short_16","alias_value":"UNY7K5QW5G2DMDHU","created_at":"2026-05-18T12:32:56Z"},{"alias_kind":"pith_short_8","alias_value":"UNY7K5QW","created_at":"2026-05-18T12:32:56Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:UNY7K5QW5G2DMDHUASGKMLNHXX","target":"record","payload":{"canonical_record":{"source":{"id":"1812.01413","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2018-12-04T13:56:50Z","cross_cats_sorted":["math.MP","nlin.SI"],"title_canon_sha256":"7d9aeff029badfd5a694d624e1cc2790a79fe7b41bbc586153f0d68f3c3135f2","abstract_canon_sha256":"770e6dfab7341b4abb1b9b20c6b2d5f355d6749a65da598f80c8144897418e8a"},"schema_version":"1.0"},"canonical_sha256":"a371f57616e9b4360cf4048ca62da7bdf966a1126c0382d6ac6c0e979eca891e","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:46:09.317777Z","signature_b64":"D7GA8fjnhym2KyyMGD4Q0u8fvl/eTsMAEze5WSy5M4UT+vW/AuDZvA07vquaGjST+xEGcvfQA2Q2xnseGNZ9CQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a371f57616e9b4360cf4048ca62da7bdf966a1126c0382d6ac6c0e979eca891e","last_reissued_at":"2026-05-17T23:46:09.317258Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:46:09.317258Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1812.01413","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":"2026-05-17T23:46:09Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"wJxSyeqn/cb6NErYypCYMqxbPCklDD73jNFN8AUw7XQhvRSjFjuaWvxlsamICTbsqi4JwyquLVKmv0g73sIXBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-12T05:20:12.934885Z"},"content_sha256":"5262339566f781e7b512a5614dcfc3d91627772deb27ae07f972a4479b33f2c1","schema_version":"1.0","event_id":"sha256:5262339566f781e7b512a5614dcfc3d91627772deb27ae07f972a4479b33f2c1"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:UNY7K5QW5G2DMDHUASGKMLNHXX","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Bi-Hamiltonian structure of the Oriented Associativity Equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP","nlin.SI"],"primary_cat":"math-ph","authors_text":"M.V. Pavlov, R.F. Vitolo","submitted_at":"2018-12-04T13:56:50Z","abstract_excerpt":"The Oriented Associativity equation plays a fundamental role in the theory of Integrable Systems. In this paper we prove that the equation, besides being Hamiltonian with respect to a first-order Hamiltonian operator, has a third-order non-local homogeneous Hamiltonian operator belonging to a class which has been recently studied, thus providing a highly non-trivial example in that class and showing intriguing connections with algebraic geometry."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1812.01413","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":"2026-05-17T23:46:09Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"5WfEjNnnUcbXQIFtuRjht+e9rgx1tmbScfHePa9gIPN08sOJVei695vm7JaUusXyKSSRLckjthuxmS/sPWWCCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-12T05:20:12.935447Z"},"content_sha256":"bee317c326cc53bc9ab081857da12c3be0b00b4a948c2a7b704377f9a4f117c8","schema_version":"1.0","event_id":"sha256:bee317c326cc53bc9ab081857da12c3be0b00b4a948c2a7b704377f9a4f117c8"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/UNY7K5QW5G2DMDHUASGKMLNHXX/bundle.json","state_url":"https://pith.science/pith/UNY7K5QW5G2DMDHUASGKMLNHXX/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/UNY7K5QW5G2DMDHUASGKMLNHXX/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":"2026-06-12T05:20:12Z","links":{"resolver":"https://pith.science/pith/UNY7K5QW5G2DMDHUASGKMLNHXX","bundle":"https://pith.science/pith/UNY7K5QW5G2DMDHUASGKMLNHXX/bundle.json","state":"https://pith.science/pith/UNY7K5QW5G2DMDHUASGKMLNHXX/state.json","well_known_bundle":"https://pith.science/.well-known/pith/UNY7K5QW5G2DMDHUASGKMLNHXX/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:UNY7K5QW5G2DMDHUASGKMLNHXX","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":"770e6dfab7341b4abb1b9b20c6b2d5f355d6749a65da598f80c8144897418e8a","cross_cats_sorted":["math.MP","nlin.SI"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2018-12-04T13:56:50Z","title_canon_sha256":"7d9aeff029badfd5a694d624e1cc2790a79fe7b41bbc586153f0d68f3c3135f2"},"schema_version":"1.0","source":{"id":"1812.01413","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1812.01413","created_at":"2026-05-17T23:46:09Z"},{"alias_kind":"arxiv_version","alias_value":"1812.01413v1","created_at":"2026-05-17T23:46:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1812.01413","created_at":"2026-05-17T23:46:09Z"},{"alias_kind":"pith_short_12","alias_value":"UNY7K5QW5G2D","created_at":"2026-05-18T12:32:56Z"},{"alias_kind":"pith_short_16","alias_value":"UNY7K5QW5G2DMDHU","created_at":"2026-05-18T12:32:56Z"},{"alias_kind":"pith_short_8","alias_value":"UNY7K5QW","created_at":"2026-05-18T12:32:56Z"}],"graph_snapshots":[{"event_id":"sha256:bee317c326cc53bc9ab081857da12c3be0b00b4a948c2a7b704377f9a4f117c8","target":"graph","created_at":"2026-05-17T23:46:09Z","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":"The Oriented Associativity equation plays a fundamental role in the theory of Integrable Systems. In this paper we prove that the equation, besides being Hamiltonian with respect to a first-order Hamiltonian operator, has a third-order non-local homogeneous Hamiltonian operator belonging to a class which has been recently studied, thus providing a highly non-trivial example in that class and showing intriguing connections with algebraic geometry.","authors_text":"M.V. Pavlov, R.F. Vitolo","cross_cats":["math.MP","nlin.SI"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2018-12-04T13:56:50Z","title":"Bi-Hamiltonian structure of the Oriented Associativity Equation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1812.01413","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":"sha256:5262339566f781e7b512a5614dcfc3d91627772deb27ae07f972a4479b33f2c1","target":"record","created_at":"2026-05-17T23:46:09Z","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":"770e6dfab7341b4abb1b9b20c6b2d5f355d6749a65da598f80c8144897418e8a","cross_cats_sorted":["math.MP","nlin.SI"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2018-12-04T13:56:50Z","title_canon_sha256":"7d9aeff029badfd5a694d624e1cc2790a79fe7b41bbc586153f0d68f3c3135f2"},"schema_version":"1.0","source":{"id":"1812.01413","kind":"arxiv","version":1}},"canonical_sha256":"a371f57616e9b4360cf4048ca62da7bdf966a1126c0382d6ac6c0e979eca891e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a371f57616e9b4360cf4048ca62da7bdf966a1126c0382d6ac6c0e979eca891e","first_computed_at":"2026-05-17T23:46:09.317258Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:46:09.317258Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"D7GA8fjnhym2KyyMGD4Q0u8fvl/eTsMAEze5WSy5M4UT+vW/AuDZvA07vquaGjST+xEGcvfQA2Q2xnseGNZ9CQ==","signature_status":"signed_v1","signed_at":"2026-05-17T23:46:09.317777Z","signed_message":"canonical_sha256_bytes"},"source_id":"1812.01413","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5262339566f781e7b512a5614dcfc3d91627772deb27ae07f972a4479b33f2c1","sha256:bee317c326cc53bc9ab081857da12c3be0b00b4a948c2a7b704377f9a4f117c8"],"state_sha256":"232f8ce43c27c7bd848e4474128525c4adc785f00d11d5d43ac3e64e1caa0437"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"BNfbasPOYghnur/YnkZ/uYu4rOX5QyOHcRvvMaWb0lqGXwKSH/zbvylwSbcUnCP40ucknrR1QA+3lC2YBSIuDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-12T05:20:12.938162Z","bundle_sha256":"94885a2c9aa8b6728388be640478f5ef3d26b19d2ee4966f94ab76579eb79b14"}}