{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:Z3FQS43MNJNNIUXK5SNJNY74G5","short_pith_number":"pith:Z3FQS43M","canonical_record":{"source":{"id":"1707.07351","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2017-07-23T21:27:20Z","cross_cats_sorted":["cs.SY","eess.SY"],"title_canon_sha256":"21bee1af7a58a3e61c886ea9da0c81c9689e2e4ae493bba3f5929246a67fb41d","abstract_canon_sha256":"e7b27b1c3ee7e72beadd5bfdbe4e97645794b79393c58d30f36630507d9ea713"},"schema_version":"1.0"},"canonical_sha256":"cecb09736c6a5ad452eaec9a96e3fc376b3e4696ba8b9aa971e84d77fd1e2ccd","source":{"kind":"arxiv","id":"1707.07351","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1707.07351","created_at":"2026-06-04T18:11:11Z"},{"alias_kind":"arxiv_version","alias_value":"1707.07351v2","created_at":"2026-06-04T18:11:11Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1707.07351","created_at":"2026-06-04T18:11:11Z"},{"alias_kind":"pith_short_12","alias_value":"Z3FQS43MNJNN","created_at":"2026-06-04T18:11:11Z"},{"alias_kind":"pith_short_16","alias_value":"Z3FQS43MNJNNIUXK","created_at":"2026-06-04T18:11:11Z"},{"alias_kind":"pith_short_8","alias_value":"Z3FQS43M","created_at":"2026-06-04T18:11:11Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:Z3FQS43MNJNNIUXK5SNJNY74G5","target":"record","payload":{"canonical_record":{"source":{"id":"1707.07351","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2017-07-23T21:27:20Z","cross_cats_sorted":["cs.SY","eess.SY"],"title_canon_sha256":"21bee1af7a58a3e61c886ea9da0c81c9689e2e4ae493bba3f5929246a67fb41d","abstract_canon_sha256":"e7b27b1c3ee7e72beadd5bfdbe4e97645794b79393c58d30f36630507d9ea713"},"schema_version":"1.0"},"canonical_sha256":"cecb09736c6a5ad452eaec9a96e3fc376b3e4696ba8b9aa971e84d77fd1e2ccd","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-04T18:11:11.178513Z","signature_b64":"0BYItn1G1vqqzQwEpCCI0mJdiXpEqYiJrJixJDMxXZVdSbGAj3mUuwLIUSRru67N6Ia6AOkGWh9exUAsTK0bDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"cecb09736c6a5ad452eaec9a96e3fc376b3e4696ba8b9aa971e84d77fd1e2ccd","last_reissued_at":"2026-06-04T18:11:11.178001Z","signature_status":"signed_v1","first_computed_at":"2026-06-04T18:11:11.178001Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1707.07351","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-06-04T18:11:11Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"4Di/di+HA/AJJCfmqN8UPfx5UqnKDdR5vKjWNYu8V5qOLWOoJFeIjUW8OGkAPABgCniBptZRkcfnnQROkFYyCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-26T14:32:46.124754Z"},"content_sha256":"350118362fe9a5dee18816b68c7a6b687d26e97060305e1003fe4ad1844b9a9f","schema_version":"1.0","event_id":"sha256:350118362fe9a5dee18816b68c7a6b687d26e97060305e1003fe4ad1844b9a9f"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:Z3FQS43MNJNNIUXK5SNJNY74G5","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Stability and instability in saddle point dynamics Part II: The subgradient method","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.SY","eess.SY"],"primary_cat":"math.OC","authors_text":"Ioannis Lestas, Thomas Holding","submitted_at":"2017-07-23T21:27:20Z","abstract_excerpt":"In part I we considered the problem of convergence to a saddle point of a concave-convex function via gradient dynamics and an exact characterization was given to their asymptotic behaviour. In part II we consider a general class of subgradient dynamics that provide a restriction in an arbitrary convex domain. We show that despite the nonlinear and non-smooth character of these dynamics their $\\omega$-limit set is comprised of solutions to only linear ODEs. In particular, we show that the latter are solutions to subgradient dynamics on affine subspaces which is a smooth class of dynamics the a"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1707.07351","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/1707.07351/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-06-04T18:11:11Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"6fkaBU1zcF6ZUOB0Cu8rCBCvQwSnRMOcAtP7Ql2KB5eac5oK5cPcC15hK4s0W8vcHYFWoWWr6yE79KVrz66LCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-26T14:32:46.125132Z"},"content_sha256":"26837a5b6fb14416061a4007187d034d5306a1317181e518c326886af353b70a","schema_version":"1.0","event_id":"sha256:26837a5b6fb14416061a4007187d034d5306a1317181e518c326886af353b70a"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/Z3FQS43MNJNNIUXK5SNJNY74G5/bundle.json","state_url":"https://pith.science/pith/Z3FQS43MNJNNIUXK5SNJNY74G5/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/Z3FQS43MNJNNIUXK5SNJNY74G5/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":"2026-06-26T14:32:46Z","links":{"resolver":"https://pith.science/pith/Z3FQS43MNJNNIUXK5SNJNY74G5","bundle":"https://pith.science/pith/Z3FQS43MNJNNIUXK5SNJNY74G5/bundle.json","state":"https://pith.science/pith/Z3FQS43MNJNNIUXK5SNJNY74G5/state.json","well_known_bundle":"https://pith.science/.well-known/pith/Z3FQS43MNJNNIUXK5SNJNY74G5/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:Z3FQS43MNJNNIUXK5SNJNY74G5","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":"e7b27b1c3ee7e72beadd5bfdbe4e97645794b79393c58d30f36630507d9ea713","cross_cats_sorted":["cs.SY","eess.SY"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2017-07-23T21:27:20Z","title_canon_sha256":"21bee1af7a58a3e61c886ea9da0c81c9689e2e4ae493bba3f5929246a67fb41d"},"schema_version":"1.0","source":{"id":"1707.07351","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1707.07351","created_at":"2026-06-04T18:11:11Z"},{"alias_kind":"arxiv_version","alias_value":"1707.07351v2","created_at":"2026-06-04T18:11:11Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1707.07351","created_at":"2026-06-04T18:11:11Z"},{"alias_kind":"pith_short_12","alias_value":"Z3FQS43MNJNN","created_at":"2026-06-04T18:11:11Z"},{"alias_kind":"pith_short_16","alias_value":"Z3FQS43MNJNNIUXK","created_at":"2026-06-04T18:11:11Z"},{"alias_kind":"pith_short_8","alias_value":"Z3FQS43M","created_at":"2026-06-04T18:11:11Z"}],"graph_snapshots":[{"event_id":"sha256:26837a5b6fb14416061a4007187d034d5306a1317181e518c326886af353b70a","target":"graph","created_at":"2026-06-04T18:11:11Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/1707.07351/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In part I we considered the problem of convergence to a saddle point of a concave-convex function via gradient dynamics and an exact characterization was given to their asymptotic behaviour. In part II we consider a general class of subgradient dynamics that provide a restriction in an arbitrary convex domain. We show that despite the nonlinear and non-smooth character of these dynamics their $\\omega$-limit set is comprised of solutions to only linear ODEs. In particular, we show that the latter are solutions to subgradient dynamics on affine subspaces which is a smooth class of dynamics the a","authors_text":"Ioannis Lestas, Thomas Holding","cross_cats":["cs.SY","eess.SY"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2017-07-23T21:27:20Z","title":"Stability and instability in saddle point dynamics Part II: The subgradient method"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1707.07351","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":"sha256:350118362fe9a5dee18816b68c7a6b687d26e97060305e1003fe4ad1844b9a9f","target":"record","created_at":"2026-06-04T18:11:11Z","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":"e7b27b1c3ee7e72beadd5bfdbe4e97645794b79393c58d30f36630507d9ea713","cross_cats_sorted":["cs.SY","eess.SY"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2017-07-23T21:27:20Z","title_canon_sha256":"21bee1af7a58a3e61c886ea9da0c81c9689e2e4ae493bba3f5929246a67fb41d"},"schema_version":"1.0","source":{"id":"1707.07351","kind":"arxiv","version":2}},"canonical_sha256":"cecb09736c6a5ad452eaec9a96e3fc376b3e4696ba8b9aa971e84d77fd1e2ccd","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"cecb09736c6a5ad452eaec9a96e3fc376b3e4696ba8b9aa971e84d77fd1e2ccd","first_computed_at":"2026-06-04T18:11:11.178001Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-04T18:11:11.178001Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"0BYItn1G1vqqzQwEpCCI0mJdiXpEqYiJrJixJDMxXZVdSbGAj3mUuwLIUSRru67N6Ia6AOkGWh9exUAsTK0bDg==","signature_status":"signed_v1","signed_at":"2026-06-04T18:11:11.178513Z","signed_message":"canonical_sha256_bytes"},"source_id":"1707.07351","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:350118362fe9a5dee18816b68c7a6b687d26e97060305e1003fe4ad1844b9a9f","sha256:26837a5b6fb14416061a4007187d034d5306a1317181e518c326886af353b70a"],"state_sha256":"938369601fae356458d3a6584dca88bd045a0a4a5d35397596d04bf1ff28a9cd"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ZcSSUUWk0y2COpDs8sUtTy5l4xClaUzKxCM/3AWUheACK2t8eQYz9dHwkl2/3yfeI+k9WgzEZ16w1Z8oN5RvDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-26T14:32:46.127167Z","bundle_sha256":"55f58cac81b9d04e8f440d867f4f47c4b5c10c74a82e00a3f60c3a40b26cfba5"}}