{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2025:WD3OZGMPLYRJN4SXAZPIJBJLA5","short_pith_number":"pith:WD3OZGMP","canonical_record":{"source":{"id":"2501.03719","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2025-01-07T11:58:20Z","cross_cats_sorted":["cs.NA","math.AP","math.DG"],"title_canon_sha256":"805171dd7edc1a684ba7a15f83eb8e5207be8808e328751371474d2b1679efdf","abstract_canon_sha256":"b471a6bb83d94cf8f23dcc5ca61fc63fc18e3a1dce93e5ecdcba9becf688021f"},"schema_version":"1.0"},"canonical_sha256":"b0f6ec998f5e2296f257065e84852b075228a07828ec6d184676236a7b47dcbf","source":{"kind":"arxiv","id":"2501.03719","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2501.03719","created_at":"2026-07-05T10:36:34Z"},{"alias_kind":"arxiv_version","alias_value":"2501.03719v2","created_at":"2026-07-05T10:36:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2501.03719","created_at":"2026-07-05T10:36:34Z"},{"alias_kind":"pith_short_12","alias_value":"WD3OZGMPLYRJ","created_at":"2026-07-05T10:36:34Z"},{"alias_kind":"pith_short_16","alias_value":"WD3OZGMPLYRJN4SX","created_at":"2026-07-05T10:36:34Z"},{"alias_kind":"pith_short_8","alias_value":"WD3OZGMP","created_at":"2026-07-05T10:36:34Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2025:WD3OZGMPLYRJN4SXAZPIJBJLA5","target":"record","payload":{"canonical_record":{"source":{"id":"2501.03719","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2025-01-07T11:58:20Z","cross_cats_sorted":["cs.NA","math.AP","math.DG"],"title_canon_sha256":"805171dd7edc1a684ba7a15f83eb8e5207be8808e328751371474d2b1679efdf","abstract_canon_sha256":"b471a6bb83d94cf8f23dcc5ca61fc63fc18e3a1dce93e5ecdcba9becf688021f"},"schema_version":"1.0"},"canonical_sha256":"b0f6ec998f5e2296f257065e84852b075228a07828ec6d184676236a7b47dcbf","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T10:36:34.019552Z","signature_b64":"I1Eo9Co0/ALzxU1o8aKHGHMrBI7g2d8f2ihymZtZcswSK14tuEDh1CqEZoIcB4wTPblCu8kenwLth7nTftxYBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b0f6ec998f5e2296f257065e84852b075228a07828ec6d184676236a7b47dcbf","last_reissued_at":"2026-07-05T10:36:34.018881Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T10:36:34.018881Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2501.03719","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":"2026-07-05T10:36:34Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+f5dkPERLT0t6qbgoZ8x0qNxQUsrMB1CA2Ceo5PsoifDqja4OBsD2E8DeRGvdRYHXDs3jTyWBUE+0Lt4xk+YCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-05T08:34:27.831043Z"},"content_sha256":"245a1ce8440837330daec5a2c1da637e86c6005b647c4979d76f9538ae9b52c3","schema_version":"1.0","event_id":"sha256:245a1ce8440837330daec5a2c1da637e86c6005b647c4979d76f9538ae9b52c3"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2025:WD3OZGMPLYRJN4SXAZPIJBJLA5","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Shape Taylor expansion for wave scattering problems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.NA","math.AP","math.DG"],"primary_cat":"math.NA","authors_text":"Gang Bao, Haoran Ma, Jingzhi Li, Jun Lai","submitted_at":"2025-01-07T11:58:20Z","abstract_excerpt":"The Taylor expansion of wave fields with respect to shape parameters has a wide range of applications in wave scattering problems, including inverse scattering, optimal design, and uncertainty quantification. However, deriving the high order shape derivatives required for this expansion poses significant challenges with conventional methods. This paper addresses these difficulties by introducing elegant recurrence formulas for computing high order shape derivatives. The derivation employs tools from exterior differential forms, Lie derivatives, and material derivatives. The work establishes a "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2501.03719","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/2501.03719/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":"2026-07-05T10:36:34Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"KxJ52DN35Q5q+JOlcbLGdfKjFavlxQSJWxfeLnz8vQsNKcD6BUC8b15LeQmy1ciG4TxvNn0uo56Y9a0TCDY9Bg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-05T08:34:27.831548Z"},"content_sha256":"075621eb5e38f7f69ff129e82aa7ea4673f52dcc17157fe468d10c1d28fe4452","schema_version":"1.0","event_id":"sha256:075621eb5e38f7f69ff129e82aa7ea4673f52dcc17157fe468d10c1d28fe4452"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/WD3OZGMPLYRJN4SXAZPIJBJLA5/bundle.json","state_url":"https://pith.science/pith/WD3OZGMPLYRJN4SXAZPIJBJLA5/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/WD3OZGMPLYRJN4SXAZPIJBJLA5/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":"2026-08-05T08:34:27Z","links":{"resolver":"https://pith.science/pith/WD3OZGMPLYRJN4SXAZPIJBJLA5","bundle":"https://pith.science/pith/WD3OZGMPLYRJN4SXAZPIJBJLA5/bundle.json","state":"https://pith.science/pith/WD3OZGMPLYRJN4SXAZPIJBJLA5/state.json","well_known_bundle":"https://pith.science/.well-known/pith/WD3OZGMPLYRJN4SXAZPIJBJLA5/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:WD3OZGMPLYRJN4SXAZPIJBJLA5","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":"b471a6bb83d94cf8f23dcc5ca61fc63fc18e3a1dce93e5ecdcba9becf688021f","cross_cats_sorted":["cs.NA","math.AP","math.DG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2025-01-07T11:58:20Z","title_canon_sha256":"805171dd7edc1a684ba7a15f83eb8e5207be8808e328751371474d2b1679efdf"},"schema_version":"1.0","source":{"id":"2501.03719","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2501.03719","created_at":"2026-07-05T10:36:34Z"},{"alias_kind":"arxiv_version","alias_value":"2501.03719v2","created_at":"2026-07-05T10:36:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2501.03719","created_at":"2026-07-05T10:36:34Z"},{"alias_kind":"pith_short_12","alias_value":"WD3OZGMPLYRJ","created_at":"2026-07-05T10:36:34Z"},{"alias_kind":"pith_short_16","alias_value":"WD3OZGMPLYRJN4SX","created_at":"2026-07-05T10:36:34Z"},{"alias_kind":"pith_short_8","alias_value":"WD3OZGMP","created_at":"2026-07-05T10:36:34Z"}],"graph_snapshots":[{"event_id":"sha256:075621eb5e38f7f69ff129e82aa7ea4673f52dcc17157fe468d10c1d28fe4452","target":"graph","created_at":"2026-07-05T10:36:34Z","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/2501.03719/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"The Taylor expansion of wave fields with respect to shape parameters has a wide range of applications in wave scattering problems, including inverse scattering, optimal design, and uncertainty quantification. However, deriving the high order shape derivatives required for this expansion poses significant challenges with conventional methods. This paper addresses these difficulties by introducing elegant recurrence formulas for computing high order shape derivatives. The derivation employs tools from exterior differential forms, Lie derivatives, and material derivatives. The work establishes a ","authors_text":"Gang Bao, Haoran Ma, Jingzhi Li, Jun Lai","cross_cats":["cs.NA","math.AP","math.DG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2025-01-07T11:58:20Z","title":"Shape Taylor expansion for wave scattering problems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2501.03719","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":"sha256:245a1ce8440837330daec5a2c1da637e86c6005b647c4979d76f9538ae9b52c3","target":"record","created_at":"2026-07-05T10:36:34Z","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":"b471a6bb83d94cf8f23dcc5ca61fc63fc18e3a1dce93e5ecdcba9becf688021f","cross_cats_sorted":["cs.NA","math.AP","math.DG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2025-01-07T11:58:20Z","title_canon_sha256":"805171dd7edc1a684ba7a15f83eb8e5207be8808e328751371474d2b1679efdf"},"schema_version":"1.0","source":{"id":"2501.03719","kind":"arxiv","version":2}},"canonical_sha256":"b0f6ec998f5e2296f257065e84852b075228a07828ec6d184676236a7b47dcbf","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b0f6ec998f5e2296f257065e84852b075228a07828ec6d184676236a7b47dcbf","first_computed_at":"2026-07-05T10:36:34.018881Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T10:36:34.018881Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"I1Eo9Co0/ALzxU1o8aKHGHMrBI7g2d8f2ihymZtZcswSK14tuEDh1CqEZoIcB4wTPblCu8kenwLth7nTftxYBA==","signature_status":"signed_v1","signed_at":"2026-07-05T10:36:34.019552Z","signed_message":"canonical_sha256_bytes"},"source_id":"2501.03719","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:245a1ce8440837330daec5a2c1da637e86c6005b647c4979d76f9538ae9b52c3","sha256:075621eb5e38f7f69ff129e82aa7ea4673f52dcc17157fe468d10c1d28fe4452"],"state_sha256":"faefbff18dc7d62a83dda7337e9fef7f49187837fdc0f95a23796cdb63fd5651"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"0ig6/ztUNntiWFgcx23hs2r81WMndq2qOIqR45mrx4DUnYVh+ZBRYSNLthDccdauCb5fuwprsRMZuF0MjHsqAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-05T08:34:27.848138Z","bundle_sha256":"4b156ab789a815dc96f17b381b46d93b2543c1a3211928e1563e381e0df9694b"}}