{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2006:IOTM5C7PW2TELJB53NR2FKR3CO","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":"177520d18bb0ceb63c76c68d874b015e83e39e073de173bed65c4e0265763288","cross_cats_sorted":["math.SG"],"license":"","primary_cat":"math.DS","submitted_at":"2006-01-18T11:39:59Z","title_canon_sha256":"143e88aa63b831a840892bc830225bb514d628a50b2ac596d605d2f7239337eb"},"schema_version":"1.0","source":{"id":"math/0601434","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0601434","created_at":"2026-05-18T01:38:24Z"},{"alias_kind":"arxiv_version","alias_value":"math/0601434v1","created_at":"2026-05-18T01:38:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0601434","created_at":"2026-05-18T01:38:24Z"},{"alias_kind":"pith_short_12","alias_value":"IOTM5C7PW2TE","created_at":"2026-05-18T12:25:54Z"},{"alias_kind":"pith_short_16","alias_value":"IOTM5C7PW2TELJB5","created_at":"2026-05-18T12:25:54Z"},{"alias_kind":"pith_short_8","alias_value":"IOTM5C7P","created_at":"2026-05-18T12:25:54Z"}],"graph_snapshots":[{"event_id":"sha256:59e112125313216917e769ebf270ccdf5334b06018e316e576cad04ae7184274","target":"graph","created_at":"2026-05-18T01:38:24Z","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":"We investigate the problem of symmetry breaking in the framework of dynamical systems with symmetry on a smooth manifold. Two cases will be analyzed: general and Hamiltonian dynamical systems. We give sufficient conditions for symmetry breaking in both cases.","authors_text":"Mircea Puta, Petre Birtea, R\\u{a}zvan Micu Tudoran, Tudor S. Ratiu","cross_cats":["math.SG"],"headline":"","license":"","primary_cat":"math.DS","submitted_at":"2006-01-18T11:39:59Z","title":"On the symmetry breaking phenomenon"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0601434","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":"sha256:9c19375345515ebc37b68ccd1c658da7a457f3a609798f9119d99476bf40dde8","target":"record","created_at":"2026-05-18T01:38:24Z","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":"177520d18bb0ceb63c76c68d874b015e83e39e073de173bed65c4e0265763288","cross_cats_sorted":["math.SG"],"license":"","primary_cat":"math.DS","submitted_at":"2006-01-18T11:39:59Z","title_canon_sha256":"143e88aa63b831a840892bc830225bb514d628a50b2ac596d605d2f7239337eb"},"schema_version":"1.0","source":{"id":"math/0601434","kind":"arxiv","version":1}},"canonical_sha256":"43a6ce8befb6a645a43ddb63a2aa3b13b06ad0de33ea05d3a20bf68e3366d6b3","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"43a6ce8befb6a645a43ddb63a2aa3b13b06ad0de33ea05d3a20bf68e3366d6b3","first_computed_at":"2026-05-18T01:38:24.494763Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:38:24.494763Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"OJszSMYNdlO0xHU4Aw4AvGAhpS5oGIQ6THXzl5871/8aJzLjNIq+mkj54YydYsbaM3z06PaDEVemwPXmmUZ8Cg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:38:24.495482Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/0601434","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9c19375345515ebc37b68ccd1c658da7a457f3a609798f9119d99476bf40dde8","sha256:59e112125313216917e769ebf270ccdf5334b06018e316e576cad04ae7184274"],"state_sha256":"feb1420ebcb9a0d4795197cd99977a01f43acc4af4b25307340bc99694403c4d"}