{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:4QP2ADZ4ISWNXUN4ML2TI5FYHK","short_pith_number":"pith:4QP2ADZ4","canonical_record":{"source":{"id":"1410.2936","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2014-10-11T01:03:20Z","cross_cats_sorted":["math.DS","math.MP","math.SG","physics.flu-dyn"],"title_canon_sha256":"ccc1df3bd2bc5b7e7427b1f2b0b12f4af18e3613a204d4e3be7e0a4a801bf8ef","abstract_canon_sha256":"7da913cdca563e276afd878fbddb20e5cc69bf2e4211273f66aa7597711872dc"},"schema_version":"1.0"},"canonical_sha256":"e41fa00f3c44acdbd1bc62f53474b83a8fdfcf65d04f9bc26ec135a926014abf","source":{"kind":"arxiv","id":"1410.2936","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1410.2936","created_at":"2026-05-18T00:28:02Z"},{"alias_kind":"arxiv_version","alias_value":"1410.2936v3","created_at":"2026-05-18T00:28:02Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1410.2936","created_at":"2026-05-18T00:28:02Z"},{"alias_kind":"pith_short_12","alias_value":"4QP2ADZ4ISWN","created_at":"2026-05-18T12:28:14Z"},{"alias_kind":"pith_short_16","alias_value":"4QP2ADZ4ISWNXUN4","created_at":"2026-05-18T12:28:14Z"},{"alias_kind":"pith_short_8","alias_value":"4QP2ADZ4","created_at":"2026-05-18T12:28:14Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:4QP2ADZ4ISWNXUN4ML2TI5FYHK","target":"record","payload":{"canonical_record":{"source":{"id":"1410.2936","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2014-10-11T01:03:20Z","cross_cats_sorted":["math.DS","math.MP","math.SG","physics.flu-dyn"],"title_canon_sha256":"ccc1df3bd2bc5b7e7427b1f2b0b12f4af18e3613a204d4e3be7e0a4a801bf8ef","abstract_canon_sha256":"7da913cdca563e276afd878fbddb20e5cc69bf2e4211273f66aa7597711872dc"},"schema_version":"1.0"},"canonical_sha256":"e41fa00f3c44acdbd1bc62f53474b83a8fdfcf65d04f9bc26ec135a926014abf","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:28:02.983309Z","signature_b64":"spOFxBf8iza6OhHEShu4q+lFxReY2Xfe3z/ZxxXPJy7GdciXhxwHkBn1tqi8LPTCEgD7fSkd21ZlwN9TmIj9AQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e41fa00f3c44acdbd1bc62f53474b83a8fdfcf65d04f9bc26ec135a926014abf","last_reissued_at":"2026-05-18T00:28:02.982390Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:28:02.982390Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1410.2936","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:28:02Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/56MobiMuXCES2niLltOMZtCw6sdmGBwwOReHLllHU1ZQeV/6AJMJOo1j4/2BRxOzPc73ebdnQBxm9tMeMyJDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T05:07:45.771774Z"},"content_sha256":"c2b5f5be31b6e17af1acdf5b56b1075626ce43f4c3371a6de9d74cfad5e27abe","schema_version":"1.0","event_id":"sha256:c2b5f5be31b6e17af1acdf5b56b1075626ce43f4c3371a6de9d74cfad5e27abe"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:4QP2ADZ4ISWNXUN4ML2TI5FYHK","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Hierarchical structure of noncanonical Hamiltonian systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DS","math.MP","math.SG","physics.flu-dyn"],"primary_cat":"math-ph","authors_text":"P. J. Morrison, Z. Yoshida","submitted_at":"2014-10-11T01:03:20Z","abstract_excerpt":"Topological constraints play a key role in the self-organizing processes that create structures in macro systems. In fact, if all possible degrees of freedom are actualized on equal footing without constraint, the state of \"equipartition\" may bear no specific structure. Fluid turbulence is a typical example - while turbulent mixing seems to increase entropy, a variety of sustained vortical structures can emerge. In Hamiltonian formalism, some topological constraints are represented by Casimir invariants (for example, helicities of a fluid or a plasma), and then, the effective phase space is re"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1410.2936","kind":"arxiv","version":3},"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":"2026-05-18T00:28:02Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"jK190YLaeXAM5L9b6+d+vx1Qd+UFt/D9OzS21DF650f0n3OKJ4Xl+MlSslFX39uyAviMWZC3zkwAc0b0FJ8nAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T05:07:45.772124Z"},"content_sha256":"77bc00b4fee164a3b4f08c448afa3877ea55a511a39e233856dda371fb4f935f","schema_version":"1.0","event_id":"sha256:77bc00b4fee164a3b4f08c448afa3877ea55a511a39e233856dda371fb4f935f"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/4QP2ADZ4ISWNXUN4ML2TI5FYHK/bundle.json","state_url":"https://pith.science/pith/4QP2ADZ4ISWNXUN4ML2TI5FYHK/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/4QP2ADZ4ISWNXUN4ML2TI5FYHK/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":"2026-05-30T05:07:45Z","links":{"resolver":"https://pith.science/pith/4QP2ADZ4ISWNXUN4ML2TI5FYHK","bundle":"https://pith.science/pith/4QP2ADZ4ISWNXUN4ML2TI5FYHK/bundle.json","state":"https://pith.science/pith/4QP2ADZ4ISWNXUN4ML2TI5FYHK/state.json","well_known_bundle":"https://pith.science/.well-known/pith/4QP2ADZ4ISWNXUN4ML2TI5FYHK/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:4QP2ADZ4ISWNXUN4ML2TI5FYHK","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":"7da913cdca563e276afd878fbddb20e5cc69bf2e4211273f66aa7597711872dc","cross_cats_sorted":["math.DS","math.MP","math.SG","physics.flu-dyn"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2014-10-11T01:03:20Z","title_canon_sha256":"ccc1df3bd2bc5b7e7427b1f2b0b12f4af18e3613a204d4e3be7e0a4a801bf8ef"},"schema_version":"1.0","source":{"id":"1410.2936","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1410.2936","created_at":"2026-05-18T00:28:02Z"},{"alias_kind":"arxiv_version","alias_value":"1410.2936v3","created_at":"2026-05-18T00:28:02Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1410.2936","created_at":"2026-05-18T00:28:02Z"},{"alias_kind":"pith_short_12","alias_value":"4QP2ADZ4ISWN","created_at":"2026-05-18T12:28:14Z"},{"alias_kind":"pith_short_16","alias_value":"4QP2ADZ4ISWNXUN4","created_at":"2026-05-18T12:28:14Z"},{"alias_kind":"pith_short_8","alias_value":"4QP2ADZ4","created_at":"2026-05-18T12:28:14Z"}],"graph_snapshots":[{"event_id":"sha256:77bc00b4fee164a3b4f08c448afa3877ea55a511a39e233856dda371fb4f935f","target":"graph","created_at":"2026-05-18T00:28:02Z","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":"Topological constraints play a key role in the self-organizing processes that create structures in macro systems. In fact, if all possible degrees of freedom are actualized on equal footing without constraint, the state of \"equipartition\" may bear no specific structure. Fluid turbulence is a typical example - while turbulent mixing seems to increase entropy, a variety of sustained vortical structures can emerge. In Hamiltonian formalism, some topological constraints are represented by Casimir invariants (for example, helicities of a fluid or a plasma), and then, the effective phase space is re","authors_text":"P. J. Morrison, Z. Yoshida","cross_cats":["math.DS","math.MP","math.SG","physics.flu-dyn"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2014-10-11T01:03:20Z","title":"Hierarchical structure of noncanonical Hamiltonian systems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1410.2936","kind":"arxiv","version":3},"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:c2b5f5be31b6e17af1acdf5b56b1075626ce43f4c3371a6de9d74cfad5e27abe","target":"record","created_at":"2026-05-18T00:28:02Z","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":"7da913cdca563e276afd878fbddb20e5cc69bf2e4211273f66aa7597711872dc","cross_cats_sorted":["math.DS","math.MP","math.SG","physics.flu-dyn"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2014-10-11T01:03:20Z","title_canon_sha256":"ccc1df3bd2bc5b7e7427b1f2b0b12f4af18e3613a204d4e3be7e0a4a801bf8ef"},"schema_version":"1.0","source":{"id":"1410.2936","kind":"arxiv","version":3}},"canonical_sha256":"e41fa00f3c44acdbd1bc62f53474b83a8fdfcf65d04f9bc26ec135a926014abf","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e41fa00f3c44acdbd1bc62f53474b83a8fdfcf65d04f9bc26ec135a926014abf","first_computed_at":"2026-05-18T00:28:02.982390Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:28:02.982390Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"spOFxBf8iza6OhHEShu4q+lFxReY2Xfe3z/ZxxXPJy7GdciXhxwHkBn1tqi8LPTCEgD7fSkd21ZlwN9TmIj9AQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:28:02.983309Z","signed_message":"canonical_sha256_bytes"},"source_id":"1410.2936","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c2b5f5be31b6e17af1acdf5b56b1075626ce43f4c3371a6de9d74cfad5e27abe","sha256:77bc00b4fee164a3b4f08c448afa3877ea55a511a39e233856dda371fb4f935f"],"state_sha256":"88ca539956cb86dfe6fb4a3d370db0784738c39e7a61d39e516adaa20a505792"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"3rfgdqfgD75ZJOVehy/616mnK2TX37Na/3DRO4aGx4Y109LcprGGoANIs56mey7WD97JTxijYb0re1Axai8WDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-30T05:07:45.775155Z","bundle_sha256":"466fa866b089776e88774139a361cc51d1cacfb41839d272abf5e83eda83cbb1"}}