{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:E5VYK6PFFT7S4TZH7GJOJEASYS","short_pith_number":"pith:E5VYK6PF","canonical_record":{"source":{"id":"2607.08848","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NA","submitted_at":"2026-07-09T18:14:38Z","cross_cats_sorted":["cs.NA","physics.comp-ph"],"title_canon_sha256":"fe1433d1b0f2ab4b551cbfe6c24d83ecf0a9eb56e49ddcc6b94e47509897f8d0","abstract_canon_sha256":"54919811885ca55c7cb02411bb6eb4a1ebd24d0fe39b1bda946788c64d58fa5b"},"schema_version":"1.0"},"canonical_sha256":"276b8579e52cff2e4f27f992e49012c48880d4c71062990894b62e42f872fb0b","source":{"kind":"arxiv","id":"2607.08848","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2607.08848","created_at":"2026-07-13T00:17:21Z"},{"alias_kind":"arxiv_version","alias_value":"2607.08848v1","created_at":"2026-07-13T00:17:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.08848","created_at":"2026-07-13T00:17:21Z"},{"alias_kind":"pith_short_12","alias_value":"E5VYK6PFFT7S","created_at":"2026-07-13T00:17:21Z"},{"alias_kind":"pith_short_16","alias_value":"E5VYK6PFFT7S4TZH","created_at":"2026-07-13T00:17:21Z"},{"alias_kind":"pith_short_8","alias_value":"E5VYK6PF","created_at":"2026-07-13T00:17:21Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:E5VYK6PFFT7S4TZH7GJOJEASYS","target":"record","payload":{"canonical_record":{"source":{"id":"2607.08848","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NA","submitted_at":"2026-07-09T18:14:38Z","cross_cats_sorted":["cs.NA","physics.comp-ph"],"title_canon_sha256":"fe1433d1b0f2ab4b551cbfe6c24d83ecf0a9eb56e49ddcc6b94e47509897f8d0","abstract_canon_sha256":"54919811885ca55c7cb02411bb6eb4a1ebd24d0fe39b1bda946788c64d58fa5b"},"schema_version":"1.0"},"canonical_sha256":"276b8579e52cff2e4f27f992e49012c48880d4c71062990894b62e42f872fb0b","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-13T00:17:21.843810Z","signature_b64":"/6WVtNsn5xan6csKd9WkvZf68+fEXYYt+G0p1ChIl3+c26UdvV12My1MCmJB7/AIRsJCYFrG+6Ui911Z5EtpBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"276b8579e52cff2e4f27f992e49012c48880d4c71062990894b62e42f872fb0b","last_reissued_at":"2026-07-13T00:17:21.842628Z","signature_status":"signed_v1","first_computed_at":"2026-07-13T00:17:21.842628Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2607.08848","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":"2026-07-13T00:17:21Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"1PGc6w3qyciey0WvfQJ3FkVHShj7NMJqC/1id+ThQ6+/T7sws817Q0KsWEO8tGBlfjAdLEaJNmDNW7z6kWQ0Dg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-03T16:32:17.769932Z"},"content_sha256":"c165cc9d5d964891b3a413b15161d95ee189a1a25308e9040840a3b31e82599f","schema_version":"1.0","event_id":"sha256:c165cc9d5d964891b3a413b15161d95ee189a1a25308e9040840a3b31e82599f"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:E5VYK6PFFT7S4TZH7GJOJEASYS","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"An Explicit Higher-Order Dual Basis for a Multiplicatively Calder\\'on Preconditioned Electric Field Integral Equation","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.NA","physics.comp-ph"],"primary_cat":"math.NA","authors_text":"Bernd Hofmann, Francesco P. Andriulli, Simon B. Adrian, Thomas F. Eibert","submitted_at":"2026-07-09T18:14:38Z","abstract_excerpt":"One of the most effective means to precondition the electric field integral equation (EFIE) discretized with Rao-Wilton-Glisson (RWG) functions is the multiplicative Calder\\'on preconditioner employing Buffa-Christiansen (BC) functions as a basis dual to the RWG basis. It results in a formulation that is free from the dense-discretization and the low-frequency breakdown. To generalize the multiplicative Calder\\'on preconditioner from the low-order BC and RWG basis to higher orders, we utilize B-spline-based basis functions and establish the first explicit high-order dual basis. It can be regar"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.08848","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/2607.08848/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":"2026-07-13T00:17:21Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ZAXlUeRy9UdngzE+3gourpMpK6bYtrNrN8zgeu3kw5UMJIb3Juq/DY52n5yaC+/+lOUnGqPvIyxBRDpwFYbMAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-03T16:32:17.770460Z"},"content_sha256":"982ad773007c112cb969499714f694209e987e04193bd599bed9ec11655e4661","schema_version":"1.0","event_id":"sha256:982ad773007c112cb969499714f694209e987e04193bd599bed9ec11655e4661"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/E5VYK6PFFT7S4TZH7GJOJEASYS/bundle.json","state_url":"https://pith.science/pith/E5VYK6PFFT7S4TZH7GJOJEASYS/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/E5VYK6PFFT7S4TZH7GJOJEASYS/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":"2026-08-03T16:32:17Z","links":{"resolver":"https://pith.science/pith/E5VYK6PFFT7S4TZH7GJOJEASYS","bundle":"https://pith.science/pith/E5VYK6PFFT7S4TZH7GJOJEASYS/bundle.json","state":"https://pith.science/pith/E5VYK6PFFT7S4TZH7GJOJEASYS/state.json","well_known_bundle":"https://pith.science/.well-known/pith/E5VYK6PFFT7S4TZH7GJOJEASYS/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:E5VYK6PFFT7S4TZH7GJOJEASYS","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":"54919811885ca55c7cb02411bb6eb4a1ebd24d0fe39b1bda946788c64d58fa5b","cross_cats_sorted":["cs.NA","physics.comp-ph"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NA","submitted_at":"2026-07-09T18:14:38Z","title_canon_sha256":"fe1433d1b0f2ab4b551cbfe6c24d83ecf0a9eb56e49ddcc6b94e47509897f8d0"},"schema_version":"1.0","source":{"id":"2607.08848","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2607.08848","created_at":"2026-07-13T00:17:21Z"},{"alias_kind":"arxiv_version","alias_value":"2607.08848v1","created_at":"2026-07-13T00:17:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.08848","created_at":"2026-07-13T00:17:21Z"},{"alias_kind":"pith_short_12","alias_value":"E5VYK6PFFT7S","created_at":"2026-07-13T00:17:21Z"},{"alias_kind":"pith_short_16","alias_value":"E5VYK6PFFT7S4TZH","created_at":"2026-07-13T00:17:21Z"},{"alias_kind":"pith_short_8","alias_value":"E5VYK6PF","created_at":"2026-07-13T00:17:21Z"}],"graph_snapshots":[{"event_id":"sha256:982ad773007c112cb969499714f694209e987e04193bd599bed9ec11655e4661","target":"graph","created_at":"2026-07-13T00:17:21Z","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/2607.08848/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"One of the most effective means to precondition the electric field integral equation (EFIE) discretized with Rao-Wilton-Glisson (RWG) functions is the multiplicative Calder\\'on preconditioner employing Buffa-Christiansen (BC) functions as a basis dual to the RWG basis. It results in a formulation that is free from the dense-discretization and the low-frequency breakdown. To generalize the multiplicative Calder\\'on preconditioner from the low-order BC and RWG basis to higher orders, we utilize B-spline-based basis functions and establish the first explicit high-order dual basis. It can be regar","authors_text":"Bernd Hofmann, Francesco P. Andriulli, Simon B. Adrian, Thomas F. Eibert","cross_cats":["cs.NA","physics.comp-ph"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NA","submitted_at":"2026-07-09T18:14:38Z","title":"An Explicit Higher-Order Dual Basis for a Multiplicatively Calder\\'on Preconditioned Electric Field Integral Equation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.08848","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:c165cc9d5d964891b3a413b15161d95ee189a1a25308e9040840a3b31e82599f","target":"record","created_at":"2026-07-13T00:17:21Z","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":"54919811885ca55c7cb02411bb6eb4a1ebd24d0fe39b1bda946788c64d58fa5b","cross_cats_sorted":["cs.NA","physics.comp-ph"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NA","submitted_at":"2026-07-09T18:14:38Z","title_canon_sha256":"fe1433d1b0f2ab4b551cbfe6c24d83ecf0a9eb56e49ddcc6b94e47509897f8d0"},"schema_version":"1.0","source":{"id":"2607.08848","kind":"arxiv","version":1}},"canonical_sha256":"276b8579e52cff2e4f27f992e49012c48880d4c71062990894b62e42f872fb0b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"276b8579e52cff2e4f27f992e49012c48880d4c71062990894b62e42f872fb0b","first_computed_at":"2026-07-13T00:17:21.842628Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-13T00:17:21.842628Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"/6WVtNsn5xan6csKd9WkvZf68+fEXYYt+G0p1ChIl3+c26UdvV12My1MCmJB7/AIRsJCYFrG+6Ui911Z5EtpBQ==","signature_status":"signed_v1","signed_at":"2026-07-13T00:17:21.843810Z","signed_message":"canonical_sha256_bytes"},"source_id":"2607.08848","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c165cc9d5d964891b3a413b15161d95ee189a1a25308e9040840a3b31e82599f","sha256:982ad773007c112cb969499714f694209e987e04193bd599bed9ec11655e4661"],"state_sha256":"949d4c88bcb73791b7c0ed2ed3597f3125be4a1b61239bba22c79a28e245b221"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Vy3aBL9/k2DR8JxzQvskovGrY+q4O2QGHi2wtTEV6idQLoHJ0hiKCBBkujTMFsVXSOx5sHbQDBPa9+ttuvmbAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-03T16:32:17.777839Z","bundle_sha256":"078b28dfd457f58864537cbf335138e921f2a14b3f176eab0cfbfa3be75d558b"}}