{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:LXX3VXNKVSDUM5EJFWMIMZ6XRA","short_pith_number":"pith:LXX3VXNK","canonical_record":{"source":{"id":"1704.03171","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2017-04-11T07:09:54Z","cross_cats_sorted":[],"title_canon_sha256":"cf093db00b46bcbabdf075a4708d4d66777abc147f5696b27d85fe6087285209","abstract_canon_sha256":"0ce7579d8c0c4806b1a24c87a6d0f8429b574d85b68432ed1ac83241cfedadab"},"schema_version":"1.0"},"canonical_sha256":"5defbaddaaac874674892d988667d788285897ccc1c6580a2b3e6652e124503d","source":{"kind":"arxiv","id":"1704.03171","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1704.03171","created_at":"2026-05-18T00:46:33Z"},{"alias_kind":"arxiv_version","alias_value":"1704.03171v1","created_at":"2026-05-18T00:46:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1704.03171","created_at":"2026-05-18T00:46:33Z"},{"alias_kind":"pith_short_12","alias_value":"LXX3VXNKVSDU","created_at":"2026-05-18T12:31:28Z"},{"alias_kind":"pith_short_16","alias_value":"LXX3VXNKVSDUM5EJ","created_at":"2026-05-18T12:31:28Z"},{"alias_kind":"pith_short_8","alias_value":"LXX3VXNK","created_at":"2026-05-18T12:31:28Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:LXX3VXNKVSDUM5EJFWMIMZ6XRA","target":"record","payload":{"canonical_record":{"source":{"id":"1704.03171","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2017-04-11T07:09:54Z","cross_cats_sorted":[],"title_canon_sha256":"cf093db00b46bcbabdf075a4708d4d66777abc147f5696b27d85fe6087285209","abstract_canon_sha256":"0ce7579d8c0c4806b1a24c87a6d0f8429b574d85b68432ed1ac83241cfedadab"},"schema_version":"1.0"},"canonical_sha256":"5defbaddaaac874674892d988667d788285897ccc1c6580a2b3e6652e124503d","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:46:33.317614Z","signature_b64":"DZ+pCeNn5vnEnw5UGVjH6sIe0DAxG+7QQtuvQd2l5fYXFO711AK3ilwsxF3/Np9mE+XvqL6QNPS+rwU6POLaAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5defbaddaaac874674892d988667d788285897ccc1c6580a2b3e6652e124503d","last_reissued_at":"2026-05-18T00:46:33.317056Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:46:33.317056Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1704.03171","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":"2026-05-18T00:46:33Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"8yu6LcLe/TFmHBdu4x+2Gw38Vpyf0Z6tzEDoD46C1uq/gdlu6Fidtyvu22aQlnMwgZWPXSm+0ZYjLvg0R3+nCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-10T12:03:10.377213Z"},"content_sha256":"92bcc1bffdbe2d562557c4060541bf6e6f0697c79583d34c31ae2e6b4a3c71d7","schema_version":"1.0","event_id":"sha256:92bcc1bffdbe2d562557c4060541bf6e6f0697c79583d34c31ae2e6b4a3c71d7"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:LXX3VXNKVSDUM5EJFWMIMZ6XRA","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"An efficient spectral-Galerkin approximation and error analysis for Maxwell transmission eigenvalue problems in spherical geometries","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Jing An, Zhimin Zhang","submitted_at":"2017-04-11T07:09:54Z","abstract_excerpt":"We propose and analyze an efficient spectral-Galerkin approximation for the Maxwell transmission eigenvalue problem in spherical geometry. Using a vector spherical harmonic expansion, we reduce the problem to a sequence of equivalent one-dimensional TE and TM modes that can be solved individually in parallel. For the TE mode, we derive associated generalized eigenvalue problems and corresponding pole conditions. Then we introduce weighted Sobolev spaces based on the pole condition and prove error estimates for the generalized eigenvalue problem. The TM mode is a coupled system with four unknow"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1704.03171","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":"2026-05-18T00:46:33Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ChFS8nfFNHuIqah6GEI2Pm4iwvFrdMsbME2kG1POB9X0/FzYWtPFnoytQvDqER3nQbAMmkz9xPqQqUU4b1IoCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-10T12:03:10.377877Z"},"content_sha256":"b7eb319cc09898b99cd192b31301405a3bf7caf9c037646512644c8be96062e6","schema_version":"1.0","event_id":"sha256:b7eb319cc09898b99cd192b31301405a3bf7caf9c037646512644c8be96062e6"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/LXX3VXNKVSDUM5EJFWMIMZ6XRA/bundle.json","state_url":"https://pith.science/pith/LXX3VXNKVSDUM5EJFWMIMZ6XRA/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/LXX3VXNKVSDUM5EJFWMIMZ6XRA/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":"2026-06-10T12:03:10Z","links":{"resolver":"https://pith.science/pith/LXX3VXNKVSDUM5EJFWMIMZ6XRA","bundle":"https://pith.science/pith/LXX3VXNKVSDUM5EJFWMIMZ6XRA/bundle.json","state":"https://pith.science/pith/LXX3VXNKVSDUM5EJFWMIMZ6XRA/state.json","well_known_bundle":"https://pith.science/.well-known/pith/LXX3VXNKVSDUM5EJFWMIMZ6XRA/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:LXX3VXNKVSDUM5EJFWMIMZ6XRA","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":"0ce7579d8c0c4806b1a24c87a6d0f8429b574d85b68432ed1ac83241cfedadab","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2017-04-11T07:09:54Z","title_canon_sha256":"cf093db00b46bcbabdf075a4708d4d66777abc147f5696b27d85fe6087285209"},"schema_version":"1.0","source":{"id":"1704.03171","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1704.03171","created_at":"2026-05-18T00:46:33Z"},{"alias_kind":"arxiv_version","alias_value":"1704.03171v1","created_at":"2026-05-18T00:46:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1704.03171","created_at":"2026-05-18T00:46:33Z"},{"alias_kind":"pith_short_12","alias_value":"LXX3VXNKVSDU","created_at":"2026-05-18T12:31:28Z"},{"alias_kind":"pith_short_16","alias_value":"LXX3VXNKVSDUM5EJ","created_at":"2026-05-18T12:31:28Z"},{"alias_kind":"pith_short_8","alias_value":"LXX3VXNK","created_at":"2026-05-18T12:31:28Z"}],"graph_snapshots":[{"event_id":"sha256:b7eb319cc09898b99cd192b31301405a3bf7caf9c037646512644c8be96062e6","target":"graph","created_at":"2026-05-18T00:46:33Z","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":"We propose and analyze an efficient spectral-Galerkin approximation for the Maxwell transmission eigenvalue problem in spherical geometry. Using a vector spherical harmonic expansion, we reduce the problem to a sequence of equivalent one-dimensional TE and TM modes that can be solved individually in parallel. For the TE mode, we derive associated generalized eigenvalue problems and corresponding pole conditions. Then we introduce weighted Sobolev spaces based on the pole condition and prove error estimates for the generalized eigenvalue problem. The TM mode is a coupled system with four unknow","authors_text":"Jing An, Zhimin Zhang","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2017-04-11T07:09:54Z","title":"An efficient spectral-Galerkin approximation and error analysis for Maxwell transmission eigenvalue problems in spherical geometries"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1704.03171","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":"sha256:92bcc1bffdbe2d562557c4060541bf6e6f0697c79583d34c31ae2e6b4a3c71d7","target":"record","created_at":"2026-05-18T00:46:33Z","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":"0ce7579d8c0c4806b1a24c87a6d0f8429b574d85b68432ed1ac83241cfedadab","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2017-04-11T07:09:54Z","title_canon_sha256":"cf093db00b46bcbabdf075a4708d4d66777abc147f5696b27d85fe6087285209"},"schema_version":"1.0","source":{"id":"1704.03171","kind":"arxiv","version":1}},"canonical_sha256":"5defbaddaaac874674892d988667d788285897ccc1c6580a2b3e6652e124503d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5defbaddaaac874674892d988667d788285897ccc1c6580a2b3e6652e124503d","first_computed_at":"2026-05-18T00:46:33.317056Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:46:33.317056Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"DZ+pCeNn5vnEnw5UGVjH6sIe0DAxG+7QQtuvQd2l5fYXFO711AK3ilwsxF3/Np9mE+XvqL6QNPS+rwU6POLaAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:46:33.317614Z","signed_message":"canonical_sha256_bytes"},"source_id":"1704.03171","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:92bcc1bffdbe2d562557c4060541bf6e6f0697c79583d34c31ae2e6b4a3c71d7","sha256:b7eb319cc09898b99cd192b31301405a3bf7caf9c037646512644c8be96062e6"],"state_sha256":"678498fffa3a534fb3c7dc3ac7541b7ad71cd4dd49bb6e0e3981114ee98d7d23"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"5RNs+4YzZc8UANHq5IJrvvXXGTgGm7tyItH90IsjEOMt5dCP4vPWi9WkzvzBd53xtaN/T3VNFkITc/g1KgeoCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-10T12:03:10.381452Z","bundle_sha256":"583447b2f31fa4abb1bfd8f530833c502bbd97e359eb140c21dfd427fd886fe1"}}