{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:KKCZ6H324MSWORYIQ3OMEIOD2T","short_pith_number":"pith:KKCZ6H32","canonical_record":{"source":{"id":"2601.13823","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NA","submitted_at":"2026-01-20T10:31:27Z","cross_cats_sorted":["cs.NA","math-ph","math.MP"],"title_canon_sha256":"a5f75a58f64823e60862540c1affed3fee274b6b6de3ad123f92c13839f1f040","abstract_canon_sha256":"70d02a1c8eadbf1ea43b81379415d016560711de1b315825f0c3dd640ae2f082"},"schema_version":"1.0"},"canonical_sha256":"52859f1f7ae32567470886dcc221c3d4da10369bc14c0c2c197737f46d686989","source":{"kind":"arxiv","id":"2601.13823","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2601.13823","created_at":"2026-06-12T01:09:20Z"},{"alias_kind":"arxiv_version","alias_value":"2601.13823v2","created_at":"2026-06-12T01:09:20Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2601.13823","created_at":"2026-06-12T01:09:20Z"},{"alias_kind":"pith_short_12","alias_value":"KKCZ6H324MSW","created_at":"2026-06-12T01:09:20Z"},{"alias_kind":"pith_short_16","alias_value":"KKCZ6H324MSWORYI","created_at":"2026-06-12T01:09:20Z"},{"alias_kind":"pith_short_8","alias_value":"KKCZ6H32","created_at":"2026-06-12T01:09:20Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:KKCZ6H324MSWORYIQ3OMEIOD2T","target":"record","payload":{"canonical_record":{"source":{"id":"2601.13823","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NA","submitted_at":"2026-01-20T10:31:27Z","cross_cats_sorted":["cs.NA","math-ph","math.MP"],"title_canon_sha256":"a5f75a58f64823e60862540c1affed3fee274b6b6de3ad123f92c13839f1f040","abstract_canon_sha256":"70d02a1c8eadbf1ea43b81379415d016560711de1b315825f0c3dd640ae2f082"},"schema_version":"1.0"},"canonical_sha256":"52859f1f7ae32567470886dcc221c3d4da10369bc14c0c2c197737f46d686989","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-12T01:09:20.465095Z","signature_b64":"LkkrNumAY2HpwxHMe1cRW9AXnmPQDFtIVGF07NrajaqA47ve4gOrMzp3YMs0Fno00tHOqBpW8VOraQym1drNBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"52859f1f7ae32567470886dcc221c3d4da10369bc14c0c2c197737f46d686989","last_reissued_at":"2026-06-12T01:09:20.464311Z","signature_status":"signed_v1","first_computed_at":"2026-06-12T01:09:20.464311Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2601.13823","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":"2026-06-12T01:09:20Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"cnkbdWa4HT6UMzInYng3jG/yBEJBcmo4qVG2gf3sdT1nI/FPgX9yFPf4poL8D4qP6vughpeK+WOu10pygX1bAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-20T19:11:00.015917Z"},"content_sha256":"0c122cc661e86dd31e4c7ab444961dc74f5885b3969c88b7d6db63c4087610ec","schema_version":"1.0","event_id":"sha256:0c122cc661e86dd31e4c7ab444961dc74f5885b3969c88b7d6db63c4087610ec"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:KKCZ6H324MSWORYIQ3OMEIOD2T","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Multitrace M\\\"uller Boundary Integral Equation for Electromagnetic Scattering by Composite Objects","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.NA","math-ph","math.MP"],"primary_cat":"math.NA","authors_text":"Kristof Cools, Van Chien Le","submitted_at":"2026-01-20T10:31:27Z","abstract_excerpt":"This paper introduces a boundary integral equation for time-harmonic electromagnetic scattering by composite dielectric objects. The formulation extends the classical M\\\"uller equation to composite structures through the global multitrace method. The key ingredient enabling this extension is the use of the Stratton-Chu representation in complementary region, also known as the extinction property, which augments the off-diagonal blocks of the interior representation operator. The resulting block system is composed entirely of second-kind operators. A Petrov-Galerkin (mixed) discretization using"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2601.13823","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/2601.13823/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":"2026-06-12T01:09:20Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"QjvYkg6PVU4CHPcQ9rlQFBZ4J9pnLieMTxFQlmB+fDl/tDghLG5PypXvetib0M6GTvPr8KBLk31Oto6zBE4rCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-20T19:11:00.016306Z"},"content_sha256":"5f9e78d454db7377e6b93f2ee1ad0e744f09ec8edcfc1fd40f5ac4ac98bbbd2a","schema_version":"1.0","event_id":"sha256:5f9e78d454db7377e6b93f2ee1ad0e744f09ec8edcfc1fd40f5ac4ac98bbbd2a"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/KKCZ6H324MSWORYIQ3OMEIOD2T/bundle.json","state_url":"https://pith.science/pith/KKCZ6H324MSWORYIQ3OMEIOD2T/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/KKCZ6H324MSWORYIQ3OMEIOD2T/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":"2026-06-20T19:11:00Z","links":{"resolver":"https://pith.science/pith/KKCZ6H324MSWORYIQ3OMEIOD2T","bundle":"https://pith.science/pith/KKCZ6H324MSWORYIQ3OMEIOD2T/bundle.json","state":"https://pith.science/pith/KKCZ6H324MSWORYIQ3OMEIOD2T/state.json","well_known_bundle":"https://pith.science/.well-known/pith/KKCZ6H324MSWORYIQ3OMEIOD2T/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:KKCZ6H324MSWORYIQ3OMEIOD2T","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":"70d02a1c8eadbf1ea43b81379415d016560711de1b315825f0c3dd640ae2f082","cross_cats_sorted":["cs.NA","math-ph","math.MP"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NA","submitted_at":"2026-01-20T10:31:27Z","title_canon_sha256":"a5f75a58f64823e60862540c1affed3fee274b6b6de3ad123f92c13839f1f040"},"schema_version":"1.0","source":{"id":"2601.13823","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2601.13823","created_at":"2026-06-12T01:09:20Z"},{"alias_kind":"arxiv_version","alias_value":"2601.13823v2","created_at":"2026-06-12T01:09:20Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2601.13823","created_at":"2026-06-12T01:09:20Z"},{"alias_kind":"pith_short_12","alias_value":"KKCZ6H324MSW","created_at":"2026-06-12T01:09:20Z"},{"alias_kind":"pith_short_16","alias_value":"KKCZ6H324MSWORYI","created_at":"2026-06-12T01:09:20Z"},{"alias_kind":"pith_short_8","alias_value":"KKCZ6H32","created_at":"2026-06-12T01:09:20Z"}],"graph_snapshots":[{"event_id":"sha256:5f9e78d454db7377e6b93f2ee1ad0e744f09ec8edcfc1fd40f5ac4ac98bbbd2a","target":"graph","created_at":"2026-06-12T01:09:20Z","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/2601.13823/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"This paper introduces a boundary integral equation for time-harmonic electromagnetic scattering by composite dielectric objects. The formulation extends the classical M\\\"uller equation to composite structures through the global multitrace method. The key ingredient enabling this extension is the use of the Stratton-Chu representation in complementary region, also known as the extinction property, which augments the off-diagonal blocks of the interior representation operator. The resulting block system is composed entirely of second-kind operators. A Petrov-Galerkin (mixed) discretization using","authors_text":"Kristof Cools, Van Chien Le","cross_cats":["cs.NA","math-ph","math.MP"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NA","submitted_at":"2026-01-20T10:31:27Z","title":"Multitrace M\\\"uller Boundary Integral Equation for Electromagnetic Scattering by Composite Objects"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2601.13823","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":"sha256:0c122cc661e86dd31e4c7ab444961dc74f5885b3969c88b7d6db63c4087610ec","target":"record","created_at":"2026-06-12T01:09:20Z","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":"70d02a1c8eadbf1ea43b81379415d016560711de1b315825f0c3dd640ae2f082","cross_cats_sorted":["cs.NA","math-ph","math.MP"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NA","submitted_at":"2026-01-20T10:31:27Z","title_canon_sha256":"a5f75a58f64823e60862540c1affed3fee274b6b6de3ad123f92c13839f1f040"},"schema_version":"1.0","source":{"id":"2601.13823","kind":"arxiv","version":2}},"canonical_sha256":"52859f1f7ae32567470886dcc221c3d4da10369bc14c0c2c197737f46d686989","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"52859f1f7ae32567470886dcc221c3d4da10369bc14c0c2c197737f46d686989","first_computed_at":"2026-06-12T01:09:20.464311Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-12T01:09:20.464311Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"LkkrNumAY2HpwxHMe1cRW9AXnmPQDFtIVGF07NrajaqA47ve4gOrMzp3YMs0Fno00tHOqBpW8VOraQym1drNBQ==","signature_status":"signed_v1","signed_at":"2026-06-12T01:09:20.465095Z","signed_message":"canonical_sha256_bytes"},"source_id":"2601.13823","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0c122cc661e86dd31e4c7ab444961dc74f5885b3969c88b7d6db63c4087610ec","sha256:5f9e78d454db7377e6b93f2ee1ad0e744f09ec8edcfc1fd40f5ac4ac98bbbd2a"],"state_sha256":"b225602c8f8d3435e6be7c28572a1b816f48f034e0bade2831086cb2a69e8a1b"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"vxaNJ1Zxw6bf/2wW4T1GdOF0GiOXVwVEPiQxHMV1j9WDDporToIa84QA7bYurf7UZmu/kOfanQNv/UFTSzYpCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-20T19:11:00.018551Z","bundle_sha256":"7a6bf3fb02dc695c6e730c6e6711d1645bf1eb78d2d64c1b351f2577b2b211a8"}}