{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:HCVS2533IA4OJA4VDBUJRVXIPB","short_pith_number":"pith:HCVS2533","canonical_record":{"source":{"id":"1708.03391","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"math.OC","submitted_at":"2017-08-10T21:28:45Z","cross_cats_sorted":[],"title_canon_sha256":"143643a2a87cbcce8515fe084d8dca6a0849883645c6930d68fe19331f9fb0a5","abstract_canon_sha256":"ef618de24847b2658116a5d649deaa112ff791724c1190104659871a52713060"},"schema_version":"1.0"},"canonical_sha256":"38ab2d777b4038e48395186898d6e8786d29b68c463f3e56be4c642822fe66ee","source":{"kind":"arxiv","id":"1708.03391","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1708.03391","created_at":"2026-05-18T00:38:13Z"},{"alias_kind":"arxiv_version","alias_value":"1708.03391v1","created_at":"2026-05-18T00:38:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1708.03391","created_at":"2026-05-18T00:38:13Z"},{"alias_kind":"pith_short_12","alias_value":"HCVS2533IA4O","created_at":"2026-05-18T12:31:18Z"},{"alias_kind":"pith_short_16","alias_value":"HCVS2533IA4OJA4V","created_at":"2026-05-18T12:31:18Z"},{"alias_kind":"pith_short_8","alias_value":"HCVS2533","created_at":"2026-05-18T12:31:18Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:HCVS2533IA4OJA4VDBUJRVXIPB","target":"record","payload":{"canonical_record":{"source":{"id":"1708.03391","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"math.OC","submitted_at":"2017-08-10T21:28:45Z","cross_cats_sorted":[],"title_canon_sha256":"143643a2a87cbcce8515fe084d8dca6a0849883645c6930d68fe19331f9fb0a5","abstract_canon_sha256":"ef618de24847b2658116a5d649deaa112ff791724c1190104659871a52713060"},"schema_version":"1.0"},"canonical_sha256":"38ab2d777b4038e48395186898d6e8786d29b68c463f3e56be4c642822fe66ee","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:38:13.218251Z","signature_b64":"hlDoJ0P2Aq9GG466eltxrGwjNUq8vtDGUC8imD/KwvqbqXV2nu1KD4LqkiA0pqdeUYcsnZOXSyPMuXmQo2mbAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"38ab2d777b4038e48395186898d6e8786d29b68c463f3e56be4c642822fe66ee","last_reissued_at":"2026-05-18T00:38:13.217546Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:38:13.217546Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1708.03391","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":"2026-05-18T00:38:13Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"2B8WTqs+tlY1OrWVYfzgwpAZeT+UStzx5C9Ueh8k7A7sz0OVrX2tNGbTw7i737dzhZYOWZQ/4pvV28yeEG//Dw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T12:08:33.589471Z"},"content_sha256":"5b5fefc8f422128cd03a92dadcf6bbef45e5c0a6e0896dd5b3c58d13b749aea7","schema_version":"1.0","event_id":"sha256:5b5fefc8f422128cd03a92dadcf6bbef45e5c0a6e0896dd5b3c58d13b749aea7"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:HCVS2533IA4OJA4VDBUJRVXIPB","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Permutation invariant proper polyhedral cones and their Lyapunov rank","license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Juyoung Jeong, M. Seetharama Gowda","submitted_at":"2017-08-10T21:28:45Z","abstract_excerpt":"The Lyapunov rank of a proper cone $K$ in a finite dimensional real Hilbert space is defined as the dimension of the space of all Lyapunov-like transformations on $K$, or equivalently, the dimension of the Lie algebra of the automorphism group of $K$. This (rank) measures the number of linearly independent bilinear relations needed to express a complementarity system on $K$ (that arises, for example, from a linear program or a complementarity problem on the cone). Motivated by the problem of describing spectral/proper cones where the complementarity system can be expressed as a square system ("},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1708.03391","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":"2026-05-18T00:38:13Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"jewX9jK7HSarLUYslWO+tGRfXMPsUrhrx8XZRsgmCQcTYhnxVwE2F0s2mX/YUy3uyqh4C8Nwmgj6hDjekDK2AA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T12:08:33.589802Z"},"content_sha256":"c801fd1429a625a8c494dcabb7b46470ab358802cab0e5b54ae728e6644193c5","schema_version":"1.0","event_id":"sha256:c801fd1429a625a8c494dcabb7b46470ab358802cab0e5b54ae728e6644193c5"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/HCVS2533IA4OJA4VDBUJRVXIPB/bundle.json","state_url":"https://pith.science/pith/HCVS2533IA4OJA4VDBUJRVXIPB/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/HCVS2533IA4OJA4VDBUJRVXIPB/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":"2026-06-01T12:08:33Z","links":{"resolver":"https://pith.science/pith/HCVS2533IA4OJA4VDBUJRVXIPB","bundle":"https://pith.science/pith/HCVS2533IA4OJA4VDBUJRVXIPB/bundle.json","state":"https://pith.science/pith/HCVS2533IA4OJA4VDBUJRVXIPB/state.json","well_known_bundle":"https://pith.science/.well-known/pith/HCVS2533IA4OJA4VDBUJRVXIPB/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:HCVS2533IA4OJA4VDBUJRVXIPB","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":"ef618de24847b2658116a5d649deaa112ff791724c1190104659871a52713060","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"math.OC","submitted_at":"2017-08-10T21:28:45Z","title_canon_sha256":"143643a2a87cbcce8515fe084d8dca6a0849883645c6930d68fe19331f9fb0a5"},"schema_version":"1.0","source":{"id":"1708.03391","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1708.03391","created_at":"2026-05-18T00:38:13Z"},{"alias_kind":"arxiv_version","alias_value":"1708.03391v1","created_at":"2026-05-18T00:38:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1708.03391","created_at":"2026-05-18T00:38:13Z"},{"alias_kind":"pith_short_12","alias_value":"HCVS2533IA4O","created_at":"2026-05-18T12:31:18Z"},{"alias_kind":"pith_short_16","alias_value":"HCVS2533IA4OJA4V","created_at":"2026-05-18T12:31:18Z"},{"alias_kind":"pith_short_8","alias_value":"HCVS2533","created_at":"2026-05-18T12:31:18Z"}],"graph_snapshots":[{"event_id":"sha256:c801fd1429a625a8c494dcabb7b46470ab358802cab0e5b54ae728e6644193c5","target":"graph","created_at":"2026-05-18T00:38:13Z","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 Lyapunov rank of a proper cone $K$ in a finite dimensional real Hilbert space is defined as the dimension of the space of all Lyapunov-like transformations on $K$, or equivalently, the dimension of the Lie algebra of the automorphism group of $K$. This (rank) measures the number of linearly independent bilinear relations needed to express a complementarity system on $K$ (that arises, for example, from a linear program or a complementarity problem on the cone). Motivated by the problem of describing spectral/proper cones where the complementarity system can be expressed as a square system (","authors_text":"Juyoung Jeong, M. Seetharama Gowda","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"math.OC","submitted_at":"2017-08-10T21:28:45Z","title":"Permutation invariant proper polyhedral cones and their Lyapunov rank"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1708.03391","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":"sha256:5b5fefc8f422128cd03a92dadcf6bbef45e5c0a6e0896dd5b3c58d13b749aea7","target":"record","created_at":"2026-05-18T00:38:13Z","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":"ef618de24847b2658116a5d649deaa112ff791724c1190104659871a52713060","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"math.OC","submitted_at":"2017-08-10T21:28:45Z","title_canon_sha256":"143643a2a87cbcce8515fe084d8dca6a0849883645c6930d68fe19331f9fb0a5"},"schema_version":"1.0","source":{"id":"1708.03391","kind":"arxiv","version":1}},"canonical_sha256":"38ab2d777b4038e48395186898d6e8786d29b68c463f3e56be4c642822fe66ee","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"38ab2d777b4038e48395186898d6e8786d29b68c463f3e56be4c642822fe66ee","first_computed_at":"2026-05-18T00:38:13.217546Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:38:13.217546Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"hlDoJ0P2Aq9GG466eltxrGwjNUq8vtDGUC8imD/KwvqbqXV2nu1KD4LqkiA0pqdeUYcsnZOXSyPMuXmQo2mbAA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:38:13.218251Z","signed_message":"canonical_sha256_bytes"},"source_id":"1708.03391","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5b5fefc8f422128cd03a92dadcf6bbef45e5c0a6e0896dd5b3c58d13b749aea7","sha256:c801fd1429a625a8c494dcabb7b46470ab358802cab0e5b54ae728e6644193c5"],"state_sha256":"69c6bb43231f75c42026d1584799d4c10084c7e51ce78228b110518d79867f55"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"biVnFrT7tku+rv4Upl8rHaXpo1Hfgv3lmfJHxQVfD5B+BFqM8S/CIopQagy/2ONsd62jAFVMkIFyA+rwPTxtBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-01T12:08:33.592095Z","bundle_sha256":"ca7c9e98955f935ed63cbbb6c6a01c0f445bc535b2ddd3647f8f8c654becb2c9"}}