{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2008:RML2Z3VOV4U6IRXXFQOTJUJ5TC","short_pith_number":"pith:RML2Z3VO","canonical_record":{"source":{"id":"0812.4374","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.AO","submitted_at":"2008-12-23T11:52:03Z","cross_cats_sorted":["nlin.PS"],"title_canon_sha256":"ba8edc5a4a57a33ce63dc483e425a4aae3191f89df72a74525dd773286349513","abstract_canon_sha256":"c1fc1d9c198744f15da85b25737d5fb92972959fbfe6f7e6179f21901aae2515"},"schema_version":"1.0"},"canonical_sha256":"8b17aceeaeaf29e446f72c1d34d13d98b2eb8863a6cf890998c93990df586320","source":{"kind":"arxiv","id":"0812.4374","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0812.4374","created_at":"2026-05-18T02:15:03Z"},{"alias_kind":"arxiv_version","alias_value":"0812.4374v1","created_at":"2026-05-18T02:15:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0812.4374","created_at":"2026-05-18T02:15:03Z"},{"alias_kind":"pith_short_12","alias_value":"RML2Z3VOV4U6","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_16","alias_value":"RML2Z3VOV4U6IRXX","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_8","alias_value":"RML2Z3VO","created_at":"2026-05-18T12:25:58Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2008:RML2Z3VOV4U6IRXXFQOTJUJ5TC","target":"record","payload":{"canonical_record":{"source":{"id":"0812.4374","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.AO","submitted_at":"2008-12-23T11:52:03Z","cross_cats_sorted":["nlin.PS"],"title_canon_sha256":"ba8edc5a4a57a33ce63dc483e425a4aae3191f89df72a74525dd773286349513","abstract_canon_sha256":"c1fc1d9c198744f15da85b25737d5fb92972959fbfe6f7e6179f21901aae2515"},"schema_version":"1.0"},"canonical_sha256":"8b17aceeaeaf29e446f72c1d34d13d98b2eb8863a6cf890998c93990df586320","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:15:03.939476Z","signature_b64":"rVmJYeJ6HjApfKnFs1dL2BGNKdpPpetWspJBSkui4otuXNp0fZ7nz7N9JV1xgRqX+TSAL0V3PKE3Hs+1O7EWAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8b17aceeaeaf29e446f72c1d34d13d98b2eb8863a6cf890998c93990df586320","last_reissued_at":"2026-05-18T02:15:03.939083Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:15:03.939083Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"0812.4374","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":"2026-05-18T02:15:03Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"5m8TuIUOg46U94yFVI5ZYsF17mt94BPIQT7EX/AUNiEc8PRlOdI30lzqNda6WgR63HQoNqPljb16plZU8lqIBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T18:42:16.258798Z"},"content_sha256":"6f3773a9ad7703e0f4b5f358d17b5a4834a5be6b5e71f86f3767217983ec409c","schema_version":"1.0","event_id":"sha256:6f3773a9ad7703e0f4b5f358d17b5a4834a5be6b5e71f86f3767217983ec409c"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2008:RML2Z3VOV4U6IRXXFQOTJUJ5TC","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Transition to amplitude death in scale-free networks","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["nlin.PS"],"primary_cat":"nlin.AO","authors_text":"Choy Heng Lai, Shuguang Guan, Weiqing Liu, Xingang Wang","submitted_at":"2008-12-23T11:52:03Z","abstract_excerpt":"Transition to amplitude death in scale-free networks of nonlinear oscillators is investigated. As the coupling strength increases, the network will undergo three stages in approaching to the state of complete amplitude death. The first stage is featured by a \\emph{\"stair-like\"} distribution of the node amplitude, and the transition is accomplished by a \\emph{hierarchical death} of the amplitude stairs. The second and third stages are characterized by, respectively, a continuing elimination of the synchronous clusters and a fast death of the non-synchronized nodes."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0812.4374","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":"2026-05-18T02:15:03Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"kHjxz4RNAvok6uNCueZeFBx5tNyHujswUJwnHNxWrg56pgyfeve5NUgVZ8vHkcc0LsdrwDYgQzWR3WhI+JtaAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T18:42:16.259148Z"},"content_sha256":"bb747096766ed7fe82b10f5ee231916a46cf6bdb5243d6a0a48a8bee6d8c5348","schema_version":"1.0","event_id":"sha256:bb747096766ed7fe82b10f5ee231916a46cf6bdb5243d6a0a48a8bee6d8c5348"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/RML2Z3VOV4U6IRXXFQOTJUJ5TC/bundle.json","state_url":"https://pith.science/pith/RML2Z3VOV4U6IRXXFQOTJUJ5TC/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/RML2Z3VOV4U6IRXXFQOTJUJ5TC/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":"2026-06-01T18:42:16Z","links":{"resolver":"https://pith.science/pith/RML2Z3VOV4U6IRXXFQOTJUJ5TC","bundle":"https://pith.science/pith/RML2Z3VOV4U6IRXXFQOTJUJ5TC/bundle.json","state":"https://pith.science/pith/RML2Z3VOV4U6IRXXFQOTJUJ5TC/state.json","well_known_bundle":"https://pith.science/.well-known/pith/RML2Z3VOV4U6IRXXFQOTJUJ5TC/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2008:RML2Z3VOV4U6IRXXFQOTJUJ5TC","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":"c1fc1d9c198744f15da85b25737d5fb92972959fbfe6f7e6179f21901aae2515","cross_cats_sorted":["nlin.PS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.AO","submitted_at":"2008-12-23T11:52:03Z","title_canon_sha256":"ba8edc5a4a57a33ce63dc483e425a4aae3191f89df72a74525dd773286349513"},"schema_version":"1.0","source":{"id":"0812.4374","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0812.4374","created_at":"2026-05-18T02:15:03Z"},{"alias_kind":"arxiv_version","alias_value":"0812.4374v1","created_at":"2026-05-18T02:15:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0812.4374","created_at":"2026-05-18T02:15:03Z"},{"alias_kind":"pith_short_12","alias_value":"RML2Z3VOV4U6","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_16","alias_value":"RML2Z3VOV4U6IRXX","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_8","alias_value":"RML2Z3VO","created_at":"2026-05-18T12:25:58Z"}],"graph_snapshots":[{"event_id":"sha256:bb747096766ed7fe82b10f5ee231916a46cf6bdb5243d6a0a48a8bee6d8c5348","target":"graph","created_at":"2026-05-18T02:15:03Z","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":"Transition to amplitude death in scale-free networks of nonlinear oscillators is investigated. As the coupling strength increases, the network will undergo three stages in approaching to the state of complete amplitude death. The first stage is featured by a \\emph{\"stair-like\"} distribution of the node amplitude, and the transition is accomplished by a \\emph{hierarchical death} of the amplitude stairs. The second and third stages are characterized by, respectively, a continuing elimination of the synchronous clusters and a fast death of the non-synchronized nodes.","authors_text":"Choy Heng Lai, Shuguang Guan, Weiqing Liu, Xingang Wang","cross_cats":["nlin.PS"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.AO","submitted_at":"2008-12-23T11:52:03Z","title":"Transition to amplitude death in scale-free networks"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0812.4374","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":"sha256:6f3773a9ad7703e0f4b5f358d17b5a4834a5be6b5e71f86f3767217983ec409c","target":"record","created_at":"2026-05-18T02:15:03Z","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":"c1fc1d9c198744f15da85b25737d5fb92972959fbfe6f7e6179f21901aae2515","cross_cats_sorted":["nlin.PS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.AO","submitted_at":"2008-12-23T11:52:03Z","title_canon_sha256":"ba8edc5a4a57a33ce63dc483e425a4aae3191f89df72a74525dd773286349513"},"schema_version":"1.0","source":{"id":"0812.4374","kind":"arxiv","version":1}},"canonical_sha256":"8b17aceeaeaf29e446f72c1d34d13d98b2eb8863a6cf890998c93990df586320","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8b17aceeaeaf29e446f72c1d34d13d98b2eb8863a6cf890998c93990df586320","first_computed_at":"2026-05-18T02:15:03.939083Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:15:03.939083Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"rVmJYeJ6HjApfKnFs1dL2BGNKdpPpetWspJBSkui4otuXNp0fZ7nz7N9JV1xgRqX+TSAL0V3PKE3Hs+1O7EWAw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:15:03.939476Z","signed_message":"canonical_sha256_bytes"},"source_id":"0812.4374","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6f3773a9ad7703e0f4b5f358d17b5a4834a5be6b5e71f86f3767217983ec409c","sha256:bb747096766ed7fe82b10f5ee231916a46cf6bdb5243d6a0a48a8bee6d8c5348"],"state_sha256":"611c82fffe727bc82902d61e5d64d58f8bfb2a3734d09a369481d175bc45321f"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"YyNw+m24umFktPH8jVCUPy+6WqJ2j4Y4UUi20rqckSdTMB1FHMBsdUPkyT5uRKftdyoIhov5KZp6ft8S0YibDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-01T18:42:16.261117Z","bundle_sha256":"df7795f75207fbfa4dfce4a7b3c3138acd5794611bd148cb54db7fe58b0d0ac7"}}