{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:HTJL5A655BWUIKLP3EM2AZ42NK","short_pith_number":"pith:HTJL5A65","canonical_record":{"source":{"id":"1610.08437","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2016-10-26T17:55:55Z","cross_cats_sorted":[],"title_canon_sha256":"d290127342d99ead90e0734964b313d86a3586c965821d266fa288a2497836b5","abstract_canon_sha256":"ab958dd3d98591e580d698931931cc4be112e2521fa82efd67f9abb4165bbbc2"},"schema_version":"1.0"},"canonical_sha256":"3cd2be83dde86d44296fd919a0679a6aacc0a6e990f76e68b3bc6311c5b4cd8d","source":{"kind":"arxiv","id":"1610.08437","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1610.08437","created_at":"2026-05-18T01:01:09Z"},{"alias_kind":"arxiv_version","alias_value":"1610.08437v1","created_at":"2026-05-18T01:01:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1610.08437","created_at":"2026-05-18T01:01:09Z"},{"alias_kind":"pith_short_12","alias_value":"HTJL5A655BWU","created_at":"2026-05-18T12:30:22Z"},{"alias_kind":"pith_short_16","alias_value":"HTJL5A655BWUIKLP","created_at":"2026-05-18T12:30:22Z"},{"alias_kind":"pith_short_8","alias_value":"HTJL5A65","created_at":"2026-05-18T12:30:22Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:HTJL5A655BWUIKLP3EM2AZ42NK","target":"record","payload":{"canonical_record":{"source":{"id":"1610.08437","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2016-10-26T17:55:55Z","cross_cats_sorted":[],"title_canon_sha256":"d290127342d99ead90e0734964b313d86a3586c965821d266fa288a2497836b5","abstract_canon_sha256":"ab958dd3d98591e580d698931931cc4be112e2521fa82efd67f9abb4165bbbc2"},"schema_version":"1.0"},"canonical_sha256":"3cd2be83dde86d44296fd919a0679a6aacc0a6e990f76e68b3bc6311c5b4cd8d","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:01:09.662776Z","signature_b64":"zM9YL8tTnp0Y0Bd6tAAIiZuY23wXjMkIrcv6eSL7CMgmsk3/T6r6YO59i1Nw/oFyS121NAFqs/Mhc0rWPO8bAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3cd2be83dde86d44296fd919a0679a6aacc0a6e990f76e68b3bc6311c5b4cd8d","last_reissued_at":"2026-05-18T01:01:09.662169Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:01:09.662169Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1610.08437","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":"2026-05-18T01:01:09Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"M7w+nqH1yJYCLNDWgkXS97zoe6oWYDZEcj4oOsacLyn3HZC5TKFoCL8XLCtW2zyOTIW0F47LKMUFGk2RbdyuDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T11:00:23.440192Z"},"content_sha256":"a49625bcdba2cb56574daaf55244aa607fcceb41d2ad636b02742bc77406038f","schema_version":"1.0","event_id":"sha256:a49625bcdba2cb56574daaf55244aa607fcceb41d2ad636b02742bc77406038f"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:HTJL5A655BWUIKLP3EM2AZ42NK","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On the region of attraction of phase-locked states for swing equations on connected graphs with inhomogeneous dampings","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Young-Pil Choi, Zhuchun Li","submitted_at":"2016-10-26T17:55:55Z","abstract_excerpt":"We consider the synchronization problem of swing equations, a second-order Kuramoto-type model, on connected networks with inhomogeneous dampings. This was largely motivated by its relevance to the dynamics of power grids. We focus on the estimate of the region of attraction of synchronous states which is a central problem in the transient stability of power grids. In the recent literature, D\\\"{o}rfler, Chertkov, and Bullo [Proc. Natl. Acad. Sci. USA, 110 (2013), pp. 2005-2010] found a condition for the synchronization in smart grids. They pointed out that the region of attraction is an import"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.08437","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":"2026-05-18T01:01:09Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"MynOLG8qNZTSZhK+Y20sLlOA3Uz/gAddGyZjP6R25YgH0Me1pc+KUCctfgYwNiuspd0aSns2I93/+Kfb3KdnCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T11:00:23.440554Z"},"content_sha256":"b144ba5a5edce0d534c72613e8a25c89f7ae12e37aa95f70ababb494ec6d21c0","schema_version":"1.0","event_id":"sha256:b144ba5a5edce0d534c72613e8a25c89f7ae12e37aa95f70ababb494ec6d21c0"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/HTJL5A655BWUIKLP3EM2AZ42NK/bundle.json","state_url":"https://pith.science/pith/HTJL5A655BWUIKLP3EM2AZ42NK/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/HTJL5A655BWUIKLP3EM2AZ42NK/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":"2026-06-07T11:00:23Z","links":{"resolver":"https://pith.science/pith/HTJL5A655BWUIKLP3EM2AZ42NK","bundle":"https://pith.science/pith/HTJL5A655BWUIKLP3EM2AZ42NK/bundle.json","state":"https://pith.science/pith/HTJL5A655BWUIKLP3EM2AZ42NK/state.json","well_known_bundle":"https://pith.science/.well-known/pith/HTJL5A655BWUIKLP3EM2AZ42NK/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:HTJL5A655BWUIKLP3EM2AZ42NK","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":"ab958dd3d98591e580d698931931cc4be112e2521fa82efd67f9abb4165bbbc2","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2016-10-26T17:55:55Z","title_canon_sha256":"d290127342d99ead90e0734964b313d86a3586c965821d266fa288a2497836b5"},"schema_version":"1.0","source":{"id":"1610.08437","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1610.08437","created_at":"2026-05-18T01:01:09Z"},{"alias_kind":"arxiv_version","alias_value":"1610.08437v1","created_at":"2026-05-18T01:01:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1610.08437","created_at":"2026-05-18T01:01:09Z"},{"alias_kind":"pith_short_12","alias_value":"HTJL5A655BWU","created_at":"2026-05-18T12:30:22Z"},{"alias_kind":"pith_short_16","alias_value":"HTJL5A655BWUIKLP","created_at":"2026-05-18T12:30:22Z"},{"alias_kind":"pith_short_8","alias_value":"HTJL5A65","created_at":"2026-05-18T12:30:22Z"}],"graph_snapshots":[{"event_id":"sha256:b144ba5a5edce0d534c72613e8a25c89f7ae12e37aa95f70ababb494ec6d21c0","target":"graph","created_at":"2026-05-18T01:01:09Z","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 consider the synchronization problem of swing equations, a second-order Kuramoto-type model, on connected networks with inhomogeneous dampings. This was largely motivated by its relevance to the dynamics of power grids. We focus on the estimate of the region of attraction of synchronous states which is a central problem in the transient stability of power grids. In the recent literature, D\\\"{o}rfler, Chertkov, and Bullo [Proc. Natl. Acad. Sci. USA, 110 (2013), pp. 2005-2010] found a condition for the synchronization in smart grids. They pointed out that the region of attraction is an import","authors_text":"Young-Pil Choi, Zhuchun Li","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2016-10-26T17:55:55Z","title":"On the region of attraction of phase-locked states for swing equations on connected graphs with inhomogeneous dampings"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.08437","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:a49625bcdba2cb56574daaf55244aa607fcceb41d2ad636b02742bc77406038f","target":"record","created_at":"2026-05-18T01:01:09Z","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":"ab958dd3d98591e580d698931931cc4be112e2521fa82efd67f9abb4165bbbc2","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2016-10-26T17:55:55Z","title_canon_sha256":"d290127342d99ead90e0734964b313d86a3586c965821d266fa288a2497836b5"},"schema_version":"1.0","source":{"id":"1610.08437","kind":"arxiv","version":1}},"canonical_sha256":"3cd2be83dde86d44296fd919a0679a6aacc0a6e990f76e68b3bc6311c5b4cd8d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3cd2be83dde86d44296fd919a0679a6aacc0a6e990f76e68b3bc6311c5b4cd8d","first_computed_at":"2026-05-18T01:01:09.662169Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:01:09.662169Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"zM9YL8tTnp0Y0Bd6tAAIiZuY23wXjMkIrcv6eSL7CMgmsk3/T6r6YO59i1Nw/oFyS121NAFqs/Mhc0rWPO8bAw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:01:09.662776Z","signed_message":"canonical_sha256_bytes"},"source_id":"1610.08437","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a49625bcdba2cb56574daaf55244aa607fcceb41d2ad636b02742bc77406038f","sha256:b144ba5a5edce0d534c72613e8a25c89f7ae12e37aa95f70ababb494ec6d21c0"],"state_sha256":"c88a84f7935a2ec4d1742fce9f0aced158c0200522bc9eaf9925aa4038c20710"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Asr64neAgIjyu8WDgT2wXRD5mfloQQW0oO8G83T5cpC4D0kkECLSF3VNqfpWBCLoganYc99CRph1mkvu1rziCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-07T11:00:23.442580Z","bundle_sha256":"e95d23cf811c2b9826a15e743db84f734c7d39792cb4e0f0520bd937f90969be"}}