{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:KRQURMX5EMSQBPLSIDN4NRY5BC","short_pith_number":"pith:KRQURMX5","canonical_record":{"source":{"id":"1205.2047","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/publicdomain/","primary_cat":"nlin.PS","submitted_at":"2012-05-09T17:46:46Z","cross_cats_sorted":[],"title_canon_sha256":"0568a2ec9ce2dd4ba0155bd5c9a63ff4058878dc39f386a13411e6bad49b0011","abstract_canon_sha256":"efab3b82ee404f09c47ef4ddc04f226436bd8961bdf42324215da1d7f933ea27"},"schema_version":"1.0"},"canonical_sha256":"546148b2fd232500bd7240dbc6c71d089450e26baf0ed659444d6f6c479344a2","source":{"kind":"arxiv","id":"1205.2047","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1205.2047","created_at":"2026-05-18T01:57:35Z"},{"alias_kind":"arxiv_version","alias_value":"1205.2047v1","created_at":"2026-05-18T01:57:35Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1205.2047","created_at":"2026-05-18T01:57:35Z"},{"alias_kind":"pith_short_12","alias_value":"KRQURMX5EMSQ","created_at":"2026-05-18T12:27:11Z"},{"alias_kind":"pith_short_16","alias_value":"KRQURMX5EMSQBPLS","created_at":"2026-05-18T12:27:11Z"},{"alias_kind":"pith_short_8","alias_value":"KRQURMX5","created_at":"2026-05-18T12:27:11Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:KRQURMX5EMSQBPLSIDN4NRY5BC","target":"record","payload":{"canonical_record":{"source":{"id":"1205.2047","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/publicdomain/","primary_cat":"nlin.PS","submitted_at":"2012-05-09T17:46:46Z","cross_cats_sorted":[],"title_canon_sha256":"0568a2ec9ce2dd4ba0155bd5c9a63ff4058878dc39f386a13411e6bad49b0011","abstract_canon_sha256":"efab3b82ee404f09c47ef4ddc04f226436bd8961bdf42324215da1d7f933ea27"},"schema_version":"1.0"},"canonical_sha256":"546148b2fd232500bd7240dbc6c71d089450e26baf0ed659444d6f6c479344a2","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:57:35.992763Z","signature_b64":"nSGUrh5paYoly6lMziBMg1/5JhPl2T/+eUBhkJOdUfINmh4Wp/ooKSEmzLdAD5Q4WthAWAiQxu0LwlqDQucfDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"546148b2fd232500bd7240dbc6c71d089450e26baf0ed659444d6f6c479344a2","last_reissued_at":"2026-05-18T01:57:35.992152Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:57:35.992152Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1205.2047","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":"2026-05-18T01:57:35Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"bb2LCludkf+uOM6N2ty4jli00A9Q6ynUuknSjhpNTRBy1IG1ToZ3PUe7eOnyT3DRFSfx+3qcOhT8xlFHlQecBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T11:21:05.848637Z"},"content_sha256":"a09b422dbb35c99276e3e6c27d99581edf022e41fd9bd8bb400cd66270b7a2e7","schema_version":"1.0","event_id":"sha256:a09b422dbb35c99276e3e6c27d99581edf022e41fd9bd8bb400cd66270b7a2e7"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:KRQURMX5EMSQBPLSIDN4NRY5BC","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Statistical multi-moment bifurcations in random delay coupled swarms","license":"http://creativecommons.org/licenses/publicdomain/","headline":"","cross_cats":[],"primary_cat":"nlin.PS","authors_text":"Brandon Lindley, Ira B. Schwartz, Luis Mier-y-Teran-Romero","submitted_at":"2012-05-09T17:46:46Z","abstract_excerpt":"We study the effects of discrete, randomly distributed time delays on the dynamics of a coupled system of self-propelling particles. Bifurcation analysis on a mean field approximation of the system reveals that the system possesses patterns with certain universal characteristics that depend on distinguished moments of the time delay distribution. Specifically, we show both theoretically and numerically that although bifurcations of simple patterns, such as translations, change stability only as a function of the first moment of the time delay distribution, more complex patterns arising from Ho"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1205.2047","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":"2026-05-18T01:57:35Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"WgnHAi0ey9/5/KvEUZ50x3vaTTlDLrJIfCDk0LG9rfm5R9awFMVvDK1yofpNjb28n8ge6x896IjlPnGaUqIcBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T11:21:05.849340Z"},"content_sha256":"4bb93be15625ddd9da1f7c5deead2c7f539b4ee5a786d923a085f06bc4bd2182","schema_version":"1.0","event_id":"sha256:4bb93be15625ddd9da1f7c5deead2c7f539b4ee5a786d923a085f06bc4bd2182"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/KRQURMX5EMSQBPLSIDN4NRY5BC/bundle.json","state_url":"https://pith.science/pith/KRQURMX5EMSQBPLSIDN4NRY5BC/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/KRQURMX5EMSQBPLSIDN4NRY5BC/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":"2026-05-27T11:21:05Z","links":{"resolver":"https://pith.science/pith/KRQURMX5EMSQBPLSIDN4NRY5BC","bundle":"https://pith.science/pith/KRQURMX5EMSQBPLSIDN4NRY5BC/bundle.json","state":"https://pith.science/pith/KRQURMX5EMSQBPLSIDN4NRY5BC/state.json","well_known_bundle":"https://pith.science/.well-known/pith/KRQURMX5EMSQBPLSIDN4NRY5BC/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:KRQURMX5EMSQBPLSIDN4NRY5BC","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":"efab3b82ee404f09c47ef4ddc04f226436bd8961bdf42324215da1d7f933ea27","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/publicdomain/","primary_cat":"nlin.PS","submitted_at":"2012-05-09T17:46:46Z","title_canon_sha256":"0568a2ec9ce2dd4ba0155bd5c9a63ff4058878dc39f386a13411e6bad49b0011"},"schema_version":"1.0","source":{"id":"1205.2047","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1205.2047","created_at":"2026-05-18T01:57:35Z"},{"alias_kind":"arxiv_version","alias_value":"1205.2047v1","created_at":"2026-05-18T01:57:35Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1205.2047","created_at":"2026-05-18T01:57:35Z"},{"alias_kind":"pith_short_12","alias_value":"KRQURMX5EMSQ","created_at":"2026-05-18T12:27:11Z"},{"alias_kind":"pith_short_16","alias_value":"KRQURMX5EMSQBPLS","created_at":"2026-05-18T12:27:11Z"},{"alias_kind":"pith_short_8","alias_value":"KRQURMX5","created_at":"2026-05-18T12:27:11Z"}],"graph_snapshots":[{"event_id":"sha256:4bb93be15625ddd9da1f7c5deead2c7f539b4ee5a786d923a085f06bc4bd2182","target":"graph","created_at":"2026-05-18T01:57:35Z","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 study the effects of discrete, randomly distributed time delays on the dynamics of a coupled system of self-propelling particles. Bifurcation analysis on a mean field approximation of the system reveals that the system possesses patterns with certain universal characteristics that depend on distinguished moments of the time delay distribution. Specifically, we show both theoretically and numerically that although bifurcations of simple patterns, such as translations, change stability only as a function of the first moment of the time delay distribution, more complex patterns arising from Ho","authors_text":"Brandon Lindley, Ira B. Schwartz, Luis Mier-y-Teran-Romero","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/publicdomain/","primary_cat":"nlin.PS","submitted_at":"2012-05-09T17:46:46Z","title":"Statistical multi-moment bifurcations in random delay coupled swarms"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1205.2047","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:a09b422dbb35c99276e3e6c27d99581edf022e41fd9bd8bb400cd66270b7a2e7","target":"record","created_at":"2026-05-18T01:57:35Z","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":"efab3b82ee404f09c47ef4ddc04f226436bd8961bdf42324215da1d7f933ea27","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/publicdomain/","primary_cat":"nlin.PS","submitted_at":"2012-05-09T17:46:46Z","title_canon_sha256":"0568a2ec9ce2dd4ba0155bd5c9a63ff4058878dc39f386a13411e6bad49b0011"},"schema_version":"1.0","source":{"id":"1205.2047","kind":"arxiv","version":1}},"canonical_sha256":"546148b2fd232500bd7240dbc6c71d089450e26baf0ed659444d6f6c479344a2","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"546148b2fd232500bd7240dbc6c71d089450e26baf0ed659444d6f6c479344a2","first_computed_at":"2026-05-18T01:57:35.992152Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:57:35.992152Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"nSGUrh5paYoly6lMziBMg1/5JhPl2T/+eUBhkJOdUfINmh4Wp/ooKSEmzLdAD5Q4WthAWAiQxu0LwlqDQucfDA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:57:35.992763Z","signed_message":"canonical_sha256_bytes"},"source_id":"1205.2047","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a09b422dbb35c99276e3e6c27d99581edf022e41fd9bd8bb400cd66270b7a2e7","sha256:4bb93be15625ddd9da1f7c5deead2c7f539b4ee5a786d923a085f06bc4bd2182"],"state_sha256":"0fde4ee9b8465c2140d5423cf68cae012906f322f00da8e5f4717c9d2f504ef3"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"k7UhiyKrPVw2N+Yd9hOGkSNE9uES44KuFF9FIO1Gx/O3JqeQX5C6vro1JmWn6stIDvLj9F3v2s9YZ4hCHeKZBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-27T11:21:05.852985Z","bundle_sha256":"e05749599602525ffc9508e189a7fa28a530d61821be501680f9df8b34280c3b"}}