{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2023:KGKGZQPPN5YMP4T4YWMBP2RMLE","short_pith_number":"pith:KGKGZQPP","canonical_record":{"source":{"id":"2307.10775","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/publicdomain/zero/1.0/","primary_cat":"math.NA","submitted_at":"2023-07-20T11:17:59Z","cross_cats_sorted":["cs.NA"],"title_canon_sha256":"edf77226c6d6f3e79529958db38c36182937aa2f08c039af24f5ec5377396282","abstract_canon_sha256":"6d6272c83aec028ea18b8f60b66402c7d1626fad641ce3496bcec166702378f1"},"schema_version":"1.0"},"canonical_sha256":"51946cc1ef6f70c7f27cc59817ea2c592a7b6477ad2a87619b4dc5f9a774d9bf","source":{"kind":"arxiv","id":"2307.10775","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2307.10775","created_at":"2026-07-05T06:33:09Z"},{"alias_kind":"arxiv_version","alias_value":"2307.10775v1","created_at":"2026-07-05T06:33:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2307.10775","created_at":"2026-07-05T06:33:09Z"},{"alias_kind":"pith_short_12","alias_value":"KGKGZQPPN5YM","created_at":"2026-07-05T06:33:09Z"},{"alias_kind":"pith_short_16","alias_value":"KGKGZQPPN5YMP4T4","created_at":"2026-07-05T06:33:09Z"},{"alias_kind":"pith_short_8","alias_value":"KGKGZQPP","created_at":"2026-07-05T06:33:09Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2023:KGKGZQPPN5YMP4T4YWMBP2RMLE","target":"record","payload":{"canonical_record":{"source":{"id":"2307.10775","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/publicdomain/zero/1.0/","primary_cat":"math.NA","submitted_at":"2023-07-20T11:17:59Z","cross_cats_sorted":["cs.NA"],"title_canon_sha256":"edf77226c6d6f3e79529958db38c36182937aa2f08c039af24f5ec5377396282","abstract_canon_sha256":"6d6272c83aec028ea18b8f60b66402c7d1626fad641ce3496bcec166702378f1"},"schema_version":"1.0"},"canonical_sha256":"51946cc1ef6f70c7f27cc59817ea2c592a7b6477ad2a87619b4dc5f9a774d9bf","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T06:33:09.877486Z","signature_b64":"cW8gKbfStE7w27MMgI9znnnJgla+Ym/Zh54jKl1lFdgh4DE+oYzJAbc4q3IYW7nF3IbjgC2Tt1VVgOCUhD6dBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"51946cc1ef6f70c7f27cc59817ea2c592a7b6477ad2a87619b4dc5f9a774d9bf","last_reissued_at":"2026-07-05T06:33:09.877089Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T06:33:09.877089Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2307.10775","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":"2026-07-05T06:33:09Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"g+bjVdR1SZbspDGZ9bwUxyTkmRyXBp+4qf8MjMRdBZndJ447cveVvQtSmXC/bPI2qlkkYUruXfWuZ3b5qm70Dw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-15T19:52:06.048156Z"},"content_sha256":"9a4ffff98dfd437f2b4dde38ae98082683a62a28c685f5a2a4be9f6638b4a696","schema_version":"1.0","event_id":"sha256:9a4ffff98dfd437f2b4dde38ae98082683a62a28c685f5a2a4be9f6638b4a696"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2023:KGKGZQPPN5YMP4T4YWMBP2RMLE","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Perturbation bounds for the largest C-eigenvalue of piezoelectric-type tensors","license":"http://creativecommons.org/publicdomain/zero/1.0/","headline":"","cross_cats":["cs.NA"],"primary_cat":"math.NA","authors_text":"Dongdong Liu, Xifu Liu, Yaping Shi","submitted_at":"2023-07-20T11:17:59Z","abstract_excerpt":"In this paper, we focus on the perturbation analysis of the largest C-eigenvalue of the piezoelectric-type tensor which has concrete physical meaning which determines the highest piezoelectric coupling constant. Three perturbation bounds are presented, theoretical analysis and numerical examples show that the third perturbation bound has high accuracy when the norm of the perturbation tensor is small."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2307.10775","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2307.10775/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":"2026-07-05T06:33:09Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"y35CfrKzi5JgeqeeSLVgjuXFTPkWhoW0IAQoeJFXpTXbsROug7LgUzqrWVw2FO6gU3i0H2/cZ0bxb7KSZxO5DQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-15T19:52:06.049121Z"},"content_sha256":"04694ac2af4f661ef9dc5771abed5b6905f812bf55c40a3547c834c993c6262c","schema_version":"1.0","event_id":"sha256:04694ac2af4f661ef9dc5771abed5b6905f812bf55c40a3547c834c993c6262c"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/KGKGZQPPN5YMP4T4YWMBP2RMLE/bundle.json","state_url":"https://pith.science/pith/KGKGZQPPN5YMP4T4YWMBP2RMLE/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/KGKGZQPPN5YMP4T4YWMBP2RMLE/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":"2026-08-15T19:52:06Z","links":{"resolver":"https://pith.science/pith/KGKGZQPPN5YMP4T4YWMBP2RMLE","bundle":"https://pith.science/pith/KGKGZQPPN5YMP4T4YWMBP2RMLE/bundle.json","state":"https://pith.science/pith/KGKGZQPPN5YMP4T4YWMBP2RMLE/state.json","well_known_bundle":"https://pith.science/.well-known/pith/KGKGZQPPN5YMP4T4YWMBP2RMLE/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2023:KGKGZQPPN5YMP4T4YWMBP2RMLE","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":"6d6272c83aec028ea18b8f60b66402c7d1626fad641ce3496bcec166702378f1","cross_cats_sorted":["cs.NA"],"license":"http://creativecommons.org/publicdomain/zero/1.0/","primary_cat":"math.NA","submitted_at":"2023-07-20T11:17:59Z","title_canon_sha256":"edf77226c6d6f3e79529958db38c36182937aa2f08c039af24f5ec5377396282"},"schema_version":"1.0","source":{"id":"2307.10775","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2307.10775","created_at":"2026-07-05T06:33:09Z"},{"alias_kind":"arxiv_version","alias_value":"2307.10775v1","created_at":"2026-07-05T06:33:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2307.10775","created_at":"2026-07-05T06:33:09Z"},{"alias_kind":"pith_short_12","alias_value":"KGKGZQPPN5YM","created_at":"2026-07-05T06:33:09Z"},{"alias_kind":"pith_short_16","alias_value":"KGKGZQPPN5YMP4T4","created_at":"2026-07-05T06:33:09Z"},{"alias_kind":"pith_short_8","alias_value":"KGKGZQPP","created_at":"2026-07-05T06:33:09Z"}],"graph_snapshots":[{"event_id":"sha256:04694ac2af4f661ef9dc5771abed5b6905f812bf55c40a3547c834c993c6262c","target":"graph","created_at":"2026-07-05T06:33:09Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2307.10775/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In this paper, we focus on the perturbation analysis of the largest C-eigenvalue of the piezoelectric-type tensor which has concrete physical meaning which determines the highest piezoelectric coupling constant. Three perturbation bounds are presented, theoretical analysis and numerical examples show that the third perturbation bound has high accuracy when the norm of the perturbation tensor is small.","authors_text":"Dongdong Liu, Xifu Liu, Yaping Shi","cross_cats":["cs.NA"],"headline":"","license":"http://creativecommons.org/publicdomain/zero/1.0/","primary_cat":"math.NA","submitted_at":"2023-07-20T11:17:59Z","title":"Perturbation bounds for the largest C-eigenvalue of piezoelectric-type tensors"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2307.10775","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":"sha256:9a4ffff98dfd437f2b4dde38ae98082683a62a28c685f5a2a4be9f6638b4a696","target":"record","created_at":"2026-07-05T06:33:09Z","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":"6d6272c83aec028ea18b8f60b66402c7d1626fad641ce3496bcec166702378f1","cross_cats_sorted":["cs.NA"],"license":"http://creativecommons.org/publicdomain/zero/1.0/","primary_cat":"math.NA","submitted_at":"2023-07-20T11:17:59Z","title_canon_sha256":"edf77226c6d6f3e79529958db38c36182937aa2f08c039af24f5ec5377396282"},"schema_version":"1.0","source":{"id":"2307.10775","kind":"arxiv","version":1}},"canonical_sha256":"51946cc1ef6f70c7f27cc59817ea2c592a7b6477ad2a87619b4dc5f9a774d9bf","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"51946cc1ef6f70c7f27cc59817ea2c592a7b6477ad2a87619b4dc5f9a774d9bf","first_computed_at":"2026-07-05T06:33:09.877089Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T06:33:09.877089Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"cW8gKbfStE7w27MMgI9znnnJgla+Ym/Zh54jKl1lFdgh4DE+oYzJAbc4q3IYW7nF3IbjgC2Tt1VVgOCUhD6dBA==","signature_status":"signed_v1","signed_at":"2026-07-05T06:33:09.877486Z","signed_message":"canonical_sha256_bytes"},"source_id":"2307.10775","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9a4ffff98dfd437f2b4dde38ae98082683a62a28c685f5a2a4be9f6638b4a696","sha256:04694ac2af4f661ef9dc5771abed5b6905f812bf55c40a3547c834c993c6262c"],"state_sha256":"dc37af0884f5d06a30cf1d3a5e374e213ed5a3a6eb7b1ed71c58f41be11261a6"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"nENbtd8u41A/89zo2+ruWUU8PaWJhMhxX0XMFG+pKJZAUXk1lSnBDDLJigR2OhPy1mORqRk2WDrM26n55bF2Dg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-15T19:52:06.056036Z","bundle_sha256":"6aba233dbd2d36391881e440be1942d16ed4a3e2f06faa378831c9548f95c350"}}