{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:3JEUZBXP2A2UY3SKVUJEJOWJ3L","short_pith_number":"pith:3JEUZBXP","canonical_record":{"source":{"id":"1509.05085","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2015-09-16T23:55:57Z","cross_cats_sorted":[],"title_canon_sha256":"4e2a151e5734b385c250a0a10c5d4c912e88690808d1c3cf4ca1b47967cdea0e","abstract_canon_sha256":"0f8f2844408c202538fa27f19afe9ba5fbd64383860c873fadea69571c3ac9b0"},"schema_version":"1.0"},"canonical_sha256":"da494c86efd0354c6e4aad1244bac9dac6e1da5b3234750079907cfb3e56cc72","source":{"kind":"arxiv","id":"1509.05085","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1509.05085","created_at":"2026-05-18T01:32:49Z"},{"alias_kind":"arxiv_version","alias_value":"1509.05085v1","created_at":"2026-05-18T01:32:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1509.05085","created_at":"2026-05-18T01:32:49Z"},{"alias_kind":"pith_short_12","alias_value":"3JEUZBXP2A2U","created_at":"2026-05-18T12:29:02Z"},{"alias_kind":"pith_short_16","alias_value":"3JEUZBXP2A2UY3SK","created_at":"2026-05-18T12:29:02Z"},{"alias_kind":"pith_short_8","alias_value":"3JEUZBXP","created_at":"2026-05-18T12:29:02Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:3JEUZBXP2A2UY3SKVUJEJOWJ3L","target":"record","payload":{"canonical_record":{"source":{"id":"1509.05085","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2015-09-16T23:55:57Z","cross_cats_sorted":[],"title_canon_sha256":"4e2a151e5734b385c250a0a10c5d4c912e88690808d1c3cf4ca1b47967cdea0e","abstract_canon_sha256":"0f8f2844408c202538fa27f19afe9ba5fbd64383860c873fadea69571c3ac9b0"},"schema_version":"1.0"},"canonical_sha256":"da494c86efd0354c6e4aad1244bac9dac6e1da5b3234750079907cfb3e56cc72","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:32:49.953229Z","signature_b64":"lBSzRlgHTWGPqaKalvPT1jnAtcYttH+WHdEExJQeRO16E3GNq+7OW0DzscFjwfH9yJn7zZDeRsZ1aVG92G89CQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"da494c86efd0354c6e4aad1244bac9dac6e1da5b3234750079907cfb3e56cc72","last_reissued_at":"2026-05-18T01:32:49.952771Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:32:49.952771Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1509.05085","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":"2026-05-18T01:32:49Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"CmCyY+Mri/WesYgCaWZFJ4bi/bLeTPegTUvn/80nyUbZV25Vwi/qv/KZd5y5onXXxZGOJAzq7F8snF5gVnjrCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-25T23:23:53.226911Z"},"content_sha256":"ebacc287e2be8ab5aec683b6a8b068b7992a052f50132d3e5968a08b0f03ca31","schema_version":"1.0","event_id":"sha256:ebacc287e2be8ab5aec683b6a8b068b7992a052f50132d3e5968a08b0f03ca31"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:3JEUZBXP2A2UY3SKVUJEJOWJ3L","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Weighted Orthogonal Polynomials-Based Generalization of Wirtinger-Type Integral Inequalities for Delayed Continuous-Time Systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Cheng Gong, Xian Zhang, Yantao Wang, Yuanyuan Han","submitted_at":"2015-09-16T23:55:57Z","abstract_excerpt":"In the past three years, many researchers have proven and/or employed some Wirtinger-type integral inequalities to establish less conservative stability criteria for delayed continu\\-ous-time systems. In this present paper, we will investigate weighted orthogonal polynomials-based integral inequalities which is a generalization of the existing Jensen's inequalities and Wirtinger-type integral inequalities."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1509.05085","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":"2026-05-18T01:32:49Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"8VTvAXHy6In14tRNmYabgrKilG2QceUyKwiosBvMMLKh7tmzJvBStEXMaDtJ5GYXcII8fyp2Sf1zY8/j9M9RBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-25T23:23:53.227249Z"},"content_sha256":"15d835ec0cb4d33b9143db956d4d2af2e078bfb26be5e25b8c470831cdc45bc4","schema_version":"1.0","event_id":"sha256:15d835ec0cb4d33b9143db956d4d2af2e078bfb26be5e25b8c470831cdc45bc4"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/3JEUZBXP2A2UY3SKVUJEJOWJ3L/bundle.json","state_url":"https://pith.science/pith/3JEUZBXP2A2UY3SKVUJEJOWJ3L/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/3JEUZBXP2A2UY3SKVUJEJOWJ3L/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":"2026-06-25T23:23:53Z","links":{"resolver":"https://pith.science/pith/3JEUZBXP2A2UY3SKVUJEJOWJ3L","bundle":"https://pith.science/pith/3JEUZBXP2A2UY3SKVUJEJOWJ3L/bundle.json","state":"https://pith.science/pith/3JEUZBXP2A2UY3SKVUJEJOWJ3L/state.json","well_known_bundle":"https://pith.science/.well-known/pith/3JEUZBXP2A2UY3SKVUJEJOWJ3L/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:3JEUZBXP2A2UY3SKVUJEJOWJ3L","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":"0f8f2844408c202538fa27f19afe9ba5fbd64383860c873fadea69571c3ac9b0","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2015-09-16T23:55:57Z","title_canon_sha256":"4e2a151e5734b385c250a0a10c5d4c912e88690808d1c3cf4ca1b47967cdea0e"},"schema_version":"1.0","source":{"id":"1509.05085","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1509.05085","created_at":"2026-05-18T01:32:49Z"},{"alias_kind":"arxiv_version","alias_value":"1509.05085v1","created_at":"2026-05-18T01:32:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1509.05085","created_at":"2026-05-18T01:32:49Z"},{"alias_kind":"pith_short_12","alias_value":"3JEUZBXP2A2U","created_at":"2026-05-18T12:29:02Z"},{"alias_kind":"pith_short_16","alias_value":"3JEUZBXP2A2UY3SK","created_at":"2026-05-18T12:29:02Z"},{"alias_kind":"pith_short_8","alias_value":"3JEUZBXP","created_at":"2026-05-18T12:29:02Z"}],"graph_snapshots":[{"event_id":"sha256:15d835ec0cb4d33b9143db956d4d2af2e078bfb26be5e25b8c470831cdc45bc4","target":"graph","created_at":"2026-05-18T01:32:49Z","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":"In the past three years, many researchers have proven and/or employed some Wirtinger-type integral inequalities to establish less conservative stability criteria for delayed continu\\-ous-time systems. In this present paper, we will investigate weighted orthogonal polynomials-based integral inequalities which is a generalization of the existing Jensen's inequalities and Wirtinger-type integral inequalities.","authors_text":"Cheng Gong, Xian Zhang, Yantao Wang, Yuanyuan Han","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2015-09-16T23:55:57Z","title":"Weighted Orthogonal Polynomials-Based Generalization of Wirtinger-Type Integral Inequalities for Delayed Continuous-Time Systems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1509.05085","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:ebacc287e2be8ab5aec683b6a8b068b7992a052f50132d3e5968a08b0f03ca31","target":"record","created_at":"2026-05-18T01:32:49Z","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":"0f8f2844408c202538fa27f19afe9ba5fbd64383860c873fadea69571c3ac9b0","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2015-09-16T23:55:57Z","title_canon_sha256":"4e2a151e5734b385c250a0a10c5d4c912e88690808d1c3cf4ca1b47967cdea0e"},"schema_version":"1.0","source":{"id":"1509.05085","kind":"arxiv","version":1}},"canonical_sha256":"da494c86efd0354c6e4aad1244bac9dac6e1da5b3234750079907cfb3e56cc72","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"da494c86efd0354c6e4aad1244bac9dac6e1da5b3234750079907cfb3e56cc72","first_computed_at":"2026-05-18T01:32:49.952771Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:32:49.952771Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"lBSzRlgHTWGPqaKalvPT1jnAtcYttH+WHdEExJQeRO16E3GNq+7OW0DzscFjwfH9yJn7zZDeRsZ1aVG92G89CQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:32:49.953229Z","signed_message":"canonical_sha256_bytes"},"source_id":"1509.05085","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ebacc287e2be8ab5aec683b6a8b068b7992a052f50132d3e5968a08b0f03ca31","sha256:15d835ec0cb4d33b9143db956d4d2af2e078bfb26be5e25b8c470831cdc45bc4"],"state_sha256":"6213b500261a13baa803aeaa0074ed89abbde10f8c40f8453a47645f083dfad0"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"P/TYP2F/cUmhhdWn27ND+6WFZ+NLjciAk9IfXoYtAuTLOG3VtCe7A9xLT4EYaiGyHezcraGQf9BEx27vI1NjDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-25T23:23:53.229194Z","bundle_sha256":"29c8605235f814df4d9cf8cc382e5ac2a2f4bf70e990d48cc9de3a373939d964"}}