{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:QULX4WOAQXQL7LCJOS2XYHEVCZ","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":"ab240e136106b44ad9109b676223f793bd7c147cc127925fe6d9cbc33473394f","cross_cats_sorted":["physics.bio-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2015-01-30T18:46:14Z","title_canon_sha256":"b9279ee1a9c51017226a102e4150dc35d6f3cf4d1943ef6f9839fb7c0c051cf5"},"schema_version":"1.0","source":{"id":"1501.07879","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1501.07879","created_at":"2026-05-18T01:37:49Z"},{"alias_kind":"arxiv_version","alias_value":"1501.07879v2","created_at":"2026-05-18T01:37:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1501.07879","created_at":"2026-05-18T01:37:49Z"},{"alias_kind":"pith_short_12","alias_value":"QULX4WOAQXQL","created_at":"2026-05-18T12:29:39Z"},{"alias_kind":"pith_short_16","alias_value":"QULX4WOAQXQL7LCJ","created_at":"2026-05-18T12:29:39Z"},{"alias_kind":"pith_short_8","alias_value":"QULX4WOA","created_at":"2026-05-18T12:29:39Z"}],"graph_snapshots":[{"event_id":"sha256:7b90ec543aea76972fe25a6f0747296a5f8c12666bf84638d4847fb6f441362e","target":"graph","created_at":"2026-05-18T01:37:49Z","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":"When animal groups move coherently in the form of a flock, their trajectories are not all parallel, the individuals exchange their position in the group. In this Letter we introduce a measure of this mixing dynamics, which we quantify as the winding of the braid formed from the particle trajectories. Building on a paradigmatic flocking model we numerically and theoretically explain the winding statistics, and show that it is predominantly set by the global twist of the trajectories as a consequence of a spontaneous symmetry breaking.","authors_text":"Denis Bartolo, Jean-Baptiste Caussin","cross_cats":["physics.bio-ph"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2015-01-30T18:46:14Z","title":"Braiding a flock: winding statistics of interacting flying spins"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1501.07879","kind":"arxiv","version":2},"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":"sha256:5470cda045239b424e4821b7b2a65d7bec09384aa7e9cd50ad5108809d46d68f","target":"record","created_at":"2026-05-18T01:37:49Z","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":"ab240e136106b44ad9109b676223f793bd7c147cc127925fe6d9cbc33473394f","cross_cats_sorted":["physics.bio-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2015-01-30T18:46:14Z","title_canon_sha256":"b9279ee1a9c51017226a102e4150dc35d6f3cf4d1943ef6f9839fb7c0c051cf5"},"schema_version":"1.0","source":{"id":"1501.07879","kind":"arxiv","version":2}},"canonical_sha256":"85177e59c085e0bfac4974b57c1c9516632b48b80c725911c41fbc5d2da715e2","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"85177e59c085e0bfac4974b57c1c9516632b48b80c725911c41fbc5d2da715e2","first_computed_at":"2026-05-18T01:37:49.113338Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:37:49.113338Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"gR7wiTbpkEM0K7mxGSp/szQwhZLrkP1Qfr0QGIl45orluKFlNCPR0hh/Pw1RfrTQwf81/202HRx5d7uB1CSeAw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:37:49.113806Z","signed_message":"canonical_sha256_bytes"},"source_id":"1501.07879","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5470cda045239b424e4821b7b2a65d7bec09384aa7e9cd50ad5108809d46d68f","sha256:7b90ec543aea76972fe25a6f0747296a5f8c12666bf84638d4847fb6f441362e"],"state_sha256":"245703c3cd7670f31e847a1eb30a78a006c975a0f1b398cd6e3f24ed9b780491"}