{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:CBR46WWUTT3YBJNQVIZ7E5E5F5","short_pith_number":"pith:CBR46WWU","canonical_record":{"source":{"id":"1503.04539","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2015-03-16T06:52:31Z","cross_cats_sorted":["nlin.CD"],"title_canon_sha256":"349994d76a6647f6e2f59e639fad3be10eaeca16d93a578ee217f0bbcf970667","abstract_canon_sha256":"3d27d30cc4310f84884f07aa56f30441fabbb7ca1293fb85cfef158d3ac7ac0b"},"schema_version":"1.0"},"canonical_sha256":"1063cf5ad49cf780a5b0aa33f2749d2f7f84349542f53aae12ca7bd4a4a52157","source":{"kind":"arxiv","id":"1503.04539","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1503.04539","created_at":"2026-05-18T01:21:13Z"},{"alias_kind":"arxiv_version","alias_value":"1503.04539v1","created_at":"2026-05-18T01:21:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1503.04539","created_at":"2026-05-18T01:21:13Z"},{"alias_kind":"pith_short_12","alias_value":"CBR46WWUTT3Y","created_at":"2026-05-18T12:29:14Z"},{"alias_kind":"pith_short_16","alias_value":"CBR46WWUTT3YBJNQ","created_at":"2026-05-18T12:29:14Z"},{"alias_kind":"pith_short_8","alias_value":"CBR46WWU","created_at":"2026-05-18T12:29:14Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:CBR46WWUTT3YBJNQVIZ7E5E5F5","target":"record","payload":{"canonical_record":{"source":{"id":"1503.04539","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2015-03-16T06:52:31Z","cross_cats_sorted":["nlin.CD"],"title_canon_sha256":"349994d76a6647f6e2f59e639fad3be10eaeca16d93a578ee217f0bbcf970667","abstract_canon_sha256":"3d27d30cc4310f84884f07aa56f30441fabbb7ca1293fb85cfef158d3ac7ac0b"},"schema_version":"1.0"},"canonical_sha256":"1063cf5ad49cf780a5b0aa33f2749d2f7f84349542f53aae12ca7bd4a4a52157","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:21:13.480420Z","signature_b64":"KQM5eTeuYWqrsN0EF/gQ3Ns2HUNwWSpqlr3gT2usDYnDF19mb1oWQoeh/vqxDNU290lvh+tb6F8rXmGQlYbIBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1063cf5ad49cf780a5b0aa33f2749d2f7f84349542f53aae12ca7bd4a4a52157","last_reissued_at":"2026-05-18T01:21:13.479730Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:21:13.479730Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1503.04539","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":"2026-05-18T01:21:13Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"gYNOG+JFWaoNKxv+Q4AMKqsX66Xm8gjDsxzZSvGNKYLynn50+BMqu6cCmi0vO2EmqLfYnJriLxeLIC2luB9MBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T02:19:22.281343Z"},"content_sha256":"c75de8fe803af4245cc1419309b9dc7bebcee962a934679213568e9913963c5b","schema_version":"1.0","event_id":"sha256:c75de8fe803af4245cc1419309b9dc7bebcee962a934679213568e9913963c5b"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:CBR46WWUTT3YBJNQVIZ7E5E5F5","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The Hamiltonian Mean Field model: effect of network structure on synchronization dynamics","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["nlin.CD"],"primary_cat":"cond-mat.stat-mech","authors_text":"James D. Meiss, Juan G. Restrepo, Yogesh S. Virkar","submitted_at":"2015-03-16T06:52:31Z","abstract_excerpt":"The Hamiltonian Mean Field (HMF) model of coupled inertial, Hamiltonian rotors is a prototype for conservative dynamics in systems with long-range interactions. We consider the case where the interactions between the rotors are governed by a network described by a weighted adjacency matrix. By studying the linear stability of the incoherent state, we find that the transition to synchrony occurs at a coupling constant $K$ inversely proportional to the largest eigenvalue of the adjacency matrix. We derive a closed system of equations for a set of local order parameters and use these equations to"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1503.04539","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":"2026-05-18T01:21:13Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"tzQStdrmRRg+eqvjULUOoXSlogXvI11z9JldnJqF3fK2+XcSWPImZ1slb7/PImELb6LkxpF/00oslcp+bcisAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T02:19:22.281995Z"},"content_sha256":"705dc9ec284ba7cfb9435ca765c04eea29f86708d2eb42dbbab863e97c88bf2f","schema_version":"1.0","event_id":"sha256:705dc9ec284ba7cfb9435ca765c04eea29f86708d2eb42dbbab863e97c88bf2f"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/CBR46WWUTT3YBJNQVIZ7E5E5F5/bundle.json","state_url":"https://pith.science/pith/CBR46WWUTT3YBJNQVIZ7E5E5F5/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/CBR46WWUTT3YBJNQVIZ7E5E5F5/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":"2026-05-31T02:19:22Z","links":{"resolver":"https://pith.science/pith/CBR46WWUTT3YBJNQVIZ7E5E5F5","bundle":"https://pith.science/pith/CBR46WWUTT3YBJNQVIZ7E5E5F5/bundle.json","state":"https://pith.science/pith/CBR46WWUTT3YBJNQVIZ7E5E5F5/state.json","well_known_bundle":"https://pith.science/.well-known/pith/CBR46WWUTT3YBJNQVIZ7E5E5F5/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:CBR46WWUTT3YBJNQVIZ7E5E5F5","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":"3d27d30cc4310f84884f07aa56f30441fabbb7ca1293fb85cfef158d3ac7ac0b","cross_cats_sorted":["nlin.CD"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2015-03-16T06:52:31Z","title_canon_sha256":"349994d76a6647f6e2f59e639fad3be10eaeca16d93a578ee217f0bbcf970667"},"schema_version":"1.0","source":{"id":"1503.04539","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1503.04539","created_at":"2026-05-18T01:21:13Z"},{"alias_kind":"arxiv_version","alias_value":"1503.04539v1","created_at":"2026-05-18T01:21:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1503.04539","created_at":"2026-05-18T01:21:13Z"},{"alias_kind":"pith_short_12","alias_value":"CBR46WWUTT3Y","created_at":"2026-05-18T12:29:14Z"},{"alias_kind":"pith_short_16","alias_value":"CBR46WWUTT3YBJNQ","created_at":"2026-05-18T12:29:14Z"},{"alias_kind":"pith_short_8","alias_value":"CBR46WWU","created_at":"2026-05-18T12:29:14Z"}],"graph_snapshots":[{"event_id":"sha256:705dc9ec284ba7cfb9435ca765c04eea29f86708d2eb42dbbab863e97c88bf2f","target":"graph","created_at":"2026-05-18T01:21:13Z","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 Hamiltonian Mean Field (HMF) model of coupled inertial, Hamiltonian rotors is a prototype for conservative dynamics in systems with long-range interactions. We consider the case where the interactions between the rotors are governed by a network described by a weighted adjacency matrix. By studying the linear stability of the incoherent state, we find that the transition to synchrony occurs at a coupling constant $K$ inversely proportional to the largest eigenvalue of the adjacency matrix. We derive a closed system of equations for a set of local order parameters and use these equations to","authors_text":"James D. Meiss, Juan G. Restrepo, Yogesh S. Virkar","cross_cats":["nlin.CD"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2015-03-16T06:52:31Z","title":"The Hamiltonian Mean Field model: effect of network structure on synchronization dynamics"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1503.04539","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:c75de8fe803af4245cc1419309b9dc7bebcee962a934679213568e9913963c5b","target":"record","created_at":"2026-05-18T01:21:13Z","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":"3d27d30cc4310f84884f07aa56f30441fabbb7ca1293fb85cfef158d3ac7ac0b","cross_cats_sorted":["nlin.CD"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2015-03-16T06:52:31Z","title_canon_sha256":"349994d76a6647f6e2f59e639fad3be10eaeca16d93a578ee217f0bbcf970667"},"schema_version":"1.0","source":{"id":"1503.04539","kind":"arxiv","version":1}},"canonical_sha256":"1063cf5ad49cf780a5b0aa33f2749d2f7f84349542f53aae12ca7bd4a4a52157","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1063cf5ad49cf780a5b0aa33f2749d2f7f84349542f53aae12ca7bd4a4a52157","first_computed_at":"2026-05-18T01:21:13.479730Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:21:13.479730Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"KQM5eTeuYWqrsN0EF/gQ3Ns2HUNwWSpqlr3gT2usDYnDF19mb1oWQoeh/vqxDNU290lvh+tb6F8rXmGQlYbIBg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:21:13.480420Z","signed_message":"canonical_sha256_bytes"},"source_id":"1503.04539","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c75de8fe803af4245cc1419309b9dc7bebcee962a934679213568e9913963c5b","sha256:705dc9ec284ba7cfb9435ca765c04eea29f86708d2eb42dbbab863e97c88bf2f"],"state_sha256":"ea766f6dc6c85c71094f1de4afb7e5271fc9bf30a6f57c3e87fd56e6411711ed"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"1mJf0ri2u/ceF2Fu7lL6fvqk1nq1mnlXAPpwjBgFzP4bQIJjt/TXEVkiLGzunWNr1LJo2224vlPpTZd33L8sCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-31T02:19:22.284919Z","bundle_sha256":"e0edc6f87b063a1e7573a4a30d208193153ac8d42723084a635a096f6bd5e740"}}