{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:GDTQQ6SWUKCVOFYJORATB2A7RL","short_pith_number":"pith:GDTQQ6SW","canonical_record":{"source":{"id":"1505.07157","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2015-05-26T23:15:11Z","cross_cats_sorted":[],"title_canon_sha256":"2e1746fed44c03d2a398228a727346de7898adeca85f9a6dbbad1988ea5a91aa","abstract_canon_sha256":"ec407b3dda4c735d161929ca219185233c459c0e23a25126b711f8fa30340794"},"schema_version":"1.0"},"canonical_sha256":"30e7087a56a285571709744130e81f8ac7b374fd1cdd45bd1447c26cc6742e83","source":{"kind":"arxiv","id":"1505.07157","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1505.07157","created_at":"2026-05-18T02:02:07Z"},{"alias_kind":"arxiv_version","alias_value":"1505.07157v1","created_at":"2026-05-18T02:02:07Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1505.07157","created_at":"2026-05-18T02:02:07Z"},{"alias_kind":"pith_short_12","alias_value":"GDTQQ6SWUKCV","created_at":"2026-05-18T12:29:22Z"},{"alias_kind":"pith_short_16","alias_value":"GDTQQ6SWUKCVOFYJ","created_at":"2026-05-18T12:29:22Z"},{"alias_kind":"pith_short_8","alias_value":"GDTQQ6SW","created_at":"2026-05-18T12:29:22Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:GDTQQ6SWUKCVOFYJORATB2A7RL","target":"record","payload":{"canonical_record":{"source":{"id":"1505.07157","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2015-05-26T23:15:11Z","cross_cats_sorted":[],"title_canon_sha256":"2e1746fed44c03d2a398228a727346de7898adeca85f9a6dbbad1988ea5a91aa","abstract_canon_sha256":"ec407b3dda4c735d161929ca219185233c459c0e23a25126b711f8fa30340794"},"schema_version":"1.0"},"canonical_sha256":"30e7087a56a285571709744130e81f8ac7b374fd1cdd45bd1447c26cc6742e83","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:02:07.344913Z","signature_b64":"EsQyKI/IpDmXaDOO8DxPjbcCSZbsg70cJ0SIwYxYYN7N+SMiSLsIN+0ny2Ratfs9+P9xc+46RTMJrI6KqM5XBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"30e7087a56a285571709744130e81f8ac7b374fd1cdd45bd1447c26cc6742e83","last_reissued_at":"2026-05-18T02:02:07.344322Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:02:07.344322Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1505.07157","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":"2026-05-18T02:02:07Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"tJ9mTz4JNzJWu7iYqdnbMDZgRILw34yRpwJm9u/2/zf/ev03RKCmY8ZDMFPquPfn3BSxVqslSwc0w8BSQBVSDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-06T09:31:48.178366Z"},"content_sha256":"38a1e8b9e75d31c240a8bdd2bb560dc76d282fab9ca69638f8c7fd007a653844","schema_version":"1.0","event_id":"sha256:38a1e8b9e75d31c240a8bdd2bb560dc76d282fab9ca69638f8c7fd007a653844"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:GDTQQ6SWUKCVOFYJORATB2A7RL","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Fast, adaptive, high order accurate discretization of the Lippmann-Schwinger equation in two dimension","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Carlos Borges, Leslie Greengard, Lise-Marie Imbert-Gerard, Sivaram Ambikasaran","submitted_at":"2015-05-26T23:15:11Z","abstract_excerpt":"We present a fast direct solver for two dimensional scattering problems, where an incident wave impinges on a penetrable medium with compact support. We represent the scattered field using a volume potential whose kernel is the outgoing Green's function for the exterior domain. Inserting this representation into the governing partial differential equation, we obtain an integral equation of the Lippmann-Schwinger type. The principal contribution here is the development of an automatically adaptive, high-order accurate discretization based on a quad tree data structure which provides rapid acces"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1505.07157","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":"2026-05-18T02:02:07Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"wf2NqKnN0fdE3XJXrc7UMRNz+NKzSiaeg5ItHpHeR5gQNrHsJl6Z8OZglm9V+D4QidCFvsaPuFbSHlBtl6NPBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-06T09:31:48.179059Z"},"content_sha256":"291bdf8c9c3d8c33d73ac803ef32160b4c71e548a9763e6a459671939b58667f","schema_version":"1.0","event_id":"sha256:291bdf8c9c3d8c33d73ac803ef32160b4c71e548a9763e6a459671939b58667f"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/GDTQQ6SWUKCVOFYJORATB2A7RL/bundle.json","state_url":"https://pith.science/pith/GDTQQ6SWUKCVOFYJORATB2A7RL/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/GDTQQ6SWUKCVOFYJORATB2A7RL/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":"2026-06-06T09:31:48Z","links":{"resolver":"https://pith.science/pith/GDTQQ6SWUKCVOFYJORATB2A7RL","bundle":"https://pith.science/pith/GDTQQ6SWUKCVOFYJORATB2A7RL/bundle.json","state":"https://pith.science/pith/GDTQQ6SWUKCVOFYJORATB2A7RL/state.json","well_known_bundle":"https://pith.science/.well-known/pith/GDTQQ6SWUKCVOFYJORATB2A7RL/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:GDTQQ6SWUKCVOFYJORATB2A7RL","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":"ec407b3dda4c735d161929ca219185233c459c0e23a25126b711f8fa30340794","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2015-05-26T23:15:11Z","title_canon_sha256":"2e1746fed44c03d2a398228a727346de7898adeca85f9a6dbbad1988ea5a91aa"},"schema_version":"1.0","source":{"id":"1505.07157","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1505.07157","created_at":"2026-05-18T02:02:07Z"},{"alias_kind":"arxiv_version","alias_value":"1505.07157v1","created_at":"2026-05-18T02:02:07Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1505.07157","created_at":"2026-05-18T02:02:07Z"},{"alias_kind":"pith_short_12","alias_value":"GDTQQ6SWUKCV","created_at":"2026-05-18T12:29:22Z"},{"alias_kind":"pith_short_16","alias_value":"GDTQQ6SWUKCVOFYJ","created_at":"2026-05-18T12:29:22Z"},{"alias_kind":"pith_short_8","alias_value":"GDTQQ6SW","created_at":"2026-05-18T12:29:22Z"}],"graph_snapshots":[{"event_id":"sha256:291bdf8c9c3d8c33d73ac803ef32160b4c71e548a9763e6a459671939b58667f","target":"graph","created_at":"2026-05-18T02:02:07Z","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 present a fast direct solver for two dimensional scattering problems, where an incident wave impinges on a penetrable medium with compact support. We represent the scattered field using a volume potential whose kernel is the outgoing Green's function for the exterior domain. Inserting this representation into the governing partial differential equation, we obtain an integral equation of the Lippmann-Schwinger type. The principal contribution here is the development of an automatically adaptive, high-order accurate discretization based on a quad tree data structure which provides rapid acces","authors_text":"Carlos Borges, Leslie Greengard, Lise-Marie Imbert-Gerard, Sivaram Ambikasaran","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2015-05-26T23:15:11Z","title":"Fast, adaptive, high order accurate discretization of the Lippmann-Schwinger equation in two dimension"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1505.07157","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":"sha256:38a1e8b9e75d31c240a8bdd2bb560dc76d282fab9ca69638f8c7fd007a653844","target":"record","created_at":"2026-05-18T02:02:07Z","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":"ec407b3dda4c735d161929ca219185233c459c0e23a25126b711f8fa30340794","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2015-05-26T23:15:11Z","title_canon_sha256":"2e1746fed44c03d2a398228a727346de7898adeca85f9a6dbbad1988ea5a91aa"},"schema_version":"1.0","source":{"id":"1505.07157","kind":"arxiv","version":1}},"canonical_sha256":"30e7087a56a285571709744130e81f8ac7b374fd1cdd45bd1447c26cc6742e83","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"30e7087a56a285571709744130e81f8ac7b374fd1cdd45bd1447c26cc6742e83","first_computed_at":"2026-05-18T02:02:07.344322Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:02:07.344322Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"EsQyKI/IpDmXaDOO8DxPjbcCSZbsg70cJ0SIwYxYYN7N+SMiSLsIN+0ny2Ratfs9+P9xc+46RTMJrI6KqM5XBw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:02:07.344913Z","signed_message":"canonical_sha256_bytes"},"source_id":"1505.07157","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:38a1e8b9e75d31c240a8bdd2bb560dc76d282fab9ca69638f8c7fd007a653844","sha256:291bdf8c9c3d8c33d73ac803ef32160b4c71e548a9763e6a459671939b58667f"],"state_sha256":"18299c8f419b76557fd965f038980fd27b9b6661538fa1c4b4c01d4a925721f8"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"nunQcuJNpyypKGsT+91s8yQLMhG7ricYmGKu2zhy9kVD1/tx4Ovg1D1WikSlyYyHU6cQ5a/qI2KVWzTBpYy/CA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-06T09:31:48.183621Z","bundle_sha256":"636eda731ba60839ab415b8bb3855d5c6d1af965a376a585e1e3d850d6e86d0a"}}