{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:WPE2ABER3SHZQIFJA56HWAT347","short_pith_number":"pith:WPE2ABER","canonical_record":{"source":{"id":"1411.1611","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2014-11-06T13:45:10Z","cross_cats_sorted":["cs.SY"],"title_canon_sha256":"cdf4d7589d0457af5f0c7e9bfed90a03c6cb5ebdcdfa88d86dac97ede9feaf45","abstract_canon_sha256":"7e52d979f5d2d1289e0c935b28049dfcd04919c0f5a96b9c64fe11df4154dd22"},"schema_version":"1.0"},"canonical_sha256":"b3c9a00491dc8f9820a9077c7b027be7d92bcaca443f5c2846b063b9585e920f","source":{"kind":"arxiv","id":"1411.1611","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1411.1611","created_at":"2026-05-18T00:54:53Z"},{"alias_kind":"arxiv_version","alias_value":"1411.1611v3","created_at":"2026-05-18T00:54:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1411.1611","created_at":"2026-05-18T00:54:53Z"},{"alias_kind":"pith_short_12","alias_value":"WPE2ABER3SHZ","created_at":"2026-05-18T12:28:54Z"},{"alias_kind":"pith_short_16","alias_value":"WPE2ABER3SHZQIFJ","created_at":"2026-05-18T12:28:54Z"},{"alias_kind":"pith_short_8","alias_value":"WPE2ABER","created_at":"2026-05-18T12:28:54Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:WPE2ABER3SHZQIFJA56HWAT347","target":"record","payload":{"canonical_record":{"source":{"id":"1411.1611","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2014-11-06T13:45:10Z","cross_cats_sorted":["cs.SY"],"title_canon_sha256":"cdf4d7589d0457af5f0c7e9bfed90a03c6cb5ebdcdfa88d86dac97ede9feaf45","abstract_canon_sha256":"7e52d979f5d2d1289e0c935b28049dfcd04919c0f5a96b9c64fe11df4154dd22"},"schema_version":"1.0"},"canonical_sha256":"b3c9a00491dc8f9820a9077c7b027be7d92bcaca443f5c2846b063b9585e920f","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:54:53.091075Z","signature_b64":"JFAaW2HhEFSbWgH3Jjv/Kv/DKiXWDKY/1i+3oZ3woUN7AUi1zvEnuVwGm4g4f7DwuoX02FQkSSxtKimNJW0yBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b3c9a00491dc8f9820a9077c7b027be7d92bcaca443f5c2846b063b9585e920f","last_reissued_at":"2026-05-18T00:54:53.090691Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:54:53.090691Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1411.1611","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:54:53Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"SQQ4kNDJL/kQrcYg4y6aKmjFsPj6oxOqAysoiU8jP8j90Q4PyqPkEfCdVm9Tdxeq45Qb/qVCLCt/RlaF87l3Bw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-27T12:00:04.171329Z"},"content_sha256":"1642fb8c01d486808c32897ac52edc4ed4540430bbd0520470ac03290f27befa","schema_version":"1.0","event_id":"sha256:1642fb8c01d486808c32897ac52edc4ed4540430bbd0520470ac03290f27befa"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:WPE2ABER3SHZQIFJA56HWAT347","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Variations on Barbalat's Lemma","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.SY"],"primary_cat":"math.OC","authors_text":"B\\'alint Farkas, Sven-Ake Wegner","submitted_at":"2014-11-06T13:45:10Z","abstract_excerpt":"It is not hard to prove that a uniformly continuous real function, whose integral up to infinity exists, vanishes at infinity, and it is probably little known that this statement runs under the name \"Barbalat's Lemma.\" In fact, the latter name is frequently used in control theory, where the lemma is used to obtain Lyapunov-like stability theorems for non-linear and non-autonomous systems. Barbalat's Lemma is qualitative in the sense that it asserts that a function has certain properties, here convergence to zero. Such qualitative statements can typically be proved by \"soft analysis\", such as i"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1411.1611","kind":"arxiv","version":3},"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":"2026-05-18T00:54:53Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"6ocertLWehDVo6wI/9WUoU8c39SbTRyKkOZWGnNXr7WlAs8pg4KvxCX8gh2NlOT/i6ATbyrG84c0Cb5ToyDVBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-27T12:00:04.171675Z"},"content_sha256":"c1cd83238214e37217f50471e0894c8d409ae3b0b19a476ba3d034de0bdd3ced","schema_version":"1.0","event_id":"sha256:c1cd83238214e37217f50471e0894c8d409ae3b0b19a476ba3d034de0bdd3ced"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/WPE2ABER3SHZQIFJA56HWAT347/bundle.json","state_url":"https://pith.science/pith/WPE2ABER3SHZQIFJA56HWAT347/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/WPE2ABER3SHZQIFJA56HWAT347/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":"2026-06-27T12:00:04Z","links":{"resolver":"https://pith.science/pith/WPE2ABER3SHZQIFJA56HWAT347","bundle":"https://pith.science/pith/WPE2ABER3SHZQIFJA56HWAT347/bundle.json","state":"https://pith.science/pith/WPE2ABER3SHZQIFJA56HWAT347/state.json","well_known_bundle":"https://pith.science/.well-known/pith/WPE2ABER3SHZQIFJA56HWAT347/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:WPE2ABER3SHZQIFJA56HWAT347","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":"7e52d979f5d2d1289e0c935b28049dfcd04919c0f5a96b9c64fe11df4154dd22","cross_cats_sorted":["cs.SY"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2014-11-06T13:45:10Z","title_canon_sha256":"cdf4d7589d0457af5f0c7e9bfed90a03c6cb5ebdcdfa88d86dac97ede9feaf45"},"schema_version":"1.0","source":{"id":"1411.1611","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1411.1611","created_at":"2026-05-18T00:54:53Z"},{"alias_kind":"arxiv_version","alias_value":"1411.1611v3","created_at":"2026-05-18T00:54:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1411.1611","created_at":"2026-05-18T00:54:53Z"},{"alias_kind":"pith_short_12","alias_value":"WPE2ABER3SHZ","created_at":"2026-05-18T12:28:54Z"},{"alias_kind":"pith_short_16","alias_value":"WPE2ABER3SHZQIFJ","created_at":"2026-05-18T12:28:54Z"},{"alias_kind":"pith_short_8","alias_value":"WPE2ABER","created_at":"2026-05-18T12:28:54Z"}],"graph_snapshots":[{"event_id":"sha256:c1cd83238214e37217f50471e0894c8d409ae3b0b19a476ba3d034de0bdd3ced","target":"graph","created_at":"2026-05-18T00:54:53Z","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":"It is not hard to prove that a uniformly continuous real function, whose integral up to infinity exists, vanishes at infinity, and it is probably little known that this statement runs under the name \"Barbalat's Lemma.\" In fact, the latter name is frequently used in control theory, where the lemma is used to obtain Lyapunov-like stability theorems for non-linear and non-autonomous systems. Barbalat's Lemma is qualitative in the sense that it asserts that a function has certain properties, here convergence to zero. Such qualitative statements can typically be proved by \"soft analysis\", such as i","authors_text":"B\\'alint Farkas, Sven-Ake Wegner","cross_cats":["cs.SY"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2014-11-06T13:45:10Z","title":"Variations on Barbalat's Lemma"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1411.1611","kind":"arxiv","version":3},"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":"sha256:1642fb8c01d486808c32897ac52edc4ed4540430bbd0520470ac03290f27befa","target":"record","created_at":"2026-05-18T00:54:53Z","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":"7e52d979f5d2d1289e0c935b28049dfcd04919c0f5a96b9c64fe11df4154dd22","cross_cats_sorted":["cs.SY"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2014-11-06T13:45:10Z","title_canon_sha256":"cdf4d7589d0457af5f0c7e9bfed90a03c6cb5ebdcdfa88d86dac97ede9feaf45"},"schema_version":"1.0","source":{"id":"1411.1611","kind":"arxiv","version":3}},"canonical_sha256":"b3c9a00491dc8f9820a9077c7b027be7d92bcaca443f5c2846b063b9585e920f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b3c9a00491dc8f9820a9077c7b027be7d92bcaca443f5c2846b063b9585e920f","first_computed_at":"2026-05-18T00:54:53.090691Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:54:53.090691Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"JFAaW2HhEFSbWgH3Jjv/Kv/DKiXWDKY/1i+3oZ3woUN7AUi1zvEnuVwGm4g4f7DwuoX02FQkSSxtKimNJW0yBg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:54:53.091075Z","signed_message":"canonical_sha256_bytes"},"source_id":"1411.1611","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1642fb8c01d486808c32897ac52edc4ed4540430bbd0520470ac03290f27befa","sha256:c1cd83238214e37217f50471e0894c8d409ae3b0b19a476ba3d034de0bdd3ced"],"state_sha256":"c6d069a76ca057b0ed17d6805d4404d3a62d069981a8a3a96d395d9b3aeca5bd"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"cOFaDNGn3O/ev4I/YqARHjnQrBHA2VmhoJU3x7XaPyesTQ6WHBSj46qMHwLUhFwBifQ2oISQXxcjwnW2HqhxCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-27T12:00:04.173762Z","bundle_sha256":"4ef8285723d8e26bbb4bda6f968efa444ca3e7ae09341a66032fb1ce49718495"}}