{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:SFU6OL5J2EH7QQYPML2H5EP5S2","short_pith_number":"pith:SFU6OL5J","canonical_record":{"source":{"id":"1801.00900","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2018-01-03T05:21:47Z","cross_cats_sorted":[],"title_canon_sha256":"e73701b3b6adb448517c6f0d9ece1c540ed67cda6cd3eac2f7ea2e586f774556","abstract_canon_sha256":"dfbb5ccfc6fa7cc9403dd5fd308f887817a99f31d1fed394a5f6fe5c5d06fd41"},"schema_version":"1.0"},"canonical_sha256":"9169e72fa9d10ff8430f62f47e91fd96ba42d633bef87b4292002f8fde2dc17f","source":{"kind":"arxiv","id":"1801.00900","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1801.00900","created_at":"2026-05-18T00:26:48Z"},{"alias_kind":"arxiv_version","alias_value":"1801.00900v1","created_at":"2026-05-18T00:26:48Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1801.00900","created_at":"2026-05-18T00:26:48Z"},{"alias_kind":"pith_short_12","alias_value":"SFU6OL5J2EH7","created_at":"2026-05-18T12:32:53Z"},{"alias_kind":"pith_short_16","alias_value":"SFU6OL5J2EH7QQYP","created_at":"2026-05-18T12:32:53Z"},{"alias_kind":"pith_short_8","alias_value":"SFU6OL5J","created_at":"2026-05-18T12:32:53Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:SFU6OL5J2EH7QQYPML2H5EP5S2","target":"record","payload":{"canonical_record":{"source":{"id":"1801.00900","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2018-01-03T05:21:47Z","cross_cats_sorted":[],"title_canon_sha256":"e73701b3b6adb448517c6f0d9ece1c540ed67cda6cd3eac2f7ea2e586f774556","abstract_canon_sha256":"dfbb5ccfc6fa7cc9403dd5fd308f887817a99f31d1fed394a5f6fe5c5d06fd41"},"schema_version":"1.0"},"canonical_sha256":"9169e72fa9d10ff8430f62f47e91fd96ba42d633bef87b4292002f8fde2dc17f","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:26:48.453069Z","signature_b64":"LWeqRAXfnHQuK1LHXpKinn1/f7Ziw0Kw6I/KlW5fmO8bHP1+YAb1ijVCTx+Q4Azkxu+6dxt7Sbcrb6vWNLRkCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9169e72fa9d10ff8430f62f47e91fd96ba42d633bef87b4292002f8fde2dc17f","last_reissued_at":"2026-05-18T00:26:48.452528Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:26:48.452528Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1801.00900","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":"2026-05-18T00:26:48Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"RGGKjiKiGOYoqRJTVhgwhP9r9NsxkImg/GfH+F/t8/4XX20c5az9cXpWiVgzJX9O8zVLPeCNd9e78psp2ig1CQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T21:16:05.415400Z"},"content_sha256":"148988d3bc937785cbbd39758ef57f78c2ddd1d82818cc80adcb6d7b5a74e592","schema_version":"1.0","event_id":"sha256:148988d3bc937785cbbd39758ef57f78c2ddd1d82818cc80adcb6d7b5a74e592"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:SFU6OL5J2EH7QQYPML2H5EP5S2","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Doubling algorithm for the discretized Bethe-Salpeter eigenvalue problem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Eric King-wah Chu, Wen-Wei Lin, Zhen-Chen Guo","submitted_at":"2018-01-03T05:21:47Z","abstract_excerpt":"The discretized Bethe-Salpeter eigenvalue problem arises in the Green's function evaluation in many body physics and quantum chemistry. Discretization leads to a matrix eigenvalue problem for $H \\in \\mathbb{C}^{2n\\times 2n}$ with a Hamiltonian-like structure. After an appropriate transformation of $H$ to a standard symplectic form, the structure-preserving doubling algorithm, originally for algebraic Riccati equations, is extended for the discretized Bethe-Salpeter eigenvalue problem. Potential breakdowns of the algorithm, due to the ill condition or singularity of certain matrices, can be avo"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1801.00900","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":"2026-05-18T00:26:48Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"AZZQ8uEHv4AzwPzK/KZ85agpomRvXXcEXhu1sL2rfFlMsp5K3d+2kIV+a7XwBed7FVh+5hasxNjDOjtWiaE4AA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T21:16:05.415764Z"},"content_sha256":"77fcfdcdf6c45a9b46b7945827caf4f79fac21d27943b7114b7e633b375eed6d","schema_version":"1.0","event_id":"sha256:77fcfdcdf6c45a9b46b7945827caf4f79fac21d27943b7114b7e633b375eed6d"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/SFU6OL5J2EH7QQYPML2H5EP5S2/bundle.json","state_url":"https://pith.science/pith/SFU6OL5J2EH7QQYPML2H5EP5S2/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/SFU6OL5J2EH7QQYPML2H5EP5S2/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":"2026-05-27T21:16:05Z","links":{"resolver":"https://pith.science/pith/SFU6OL5J2EH7QQYPML2H5EP5S2","bundle":"https://pith.science/pith/SFU6OL5J2EH7QQYPML2H5EP5S2/bundle.json","state":"https://pith.science/pith/SFU6OL5J2EH7QQYPML2H5EP5S2/state.json","well_known_bundle":"https://pith.science/.well-known/pith/SFU6OL5J2EH7QQYPML2H5EP5S2/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:SFU6OL5J2EH7QQYPML2H5EP5S2","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":"dfbb5ccfc6fa7cc9403dd5fd308f887817a99f31d1fed394a5f6fe5c5d06fd41","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2018-01-03T05:21:47Z","title_canon_sha256":"e73701b3b6adb448517c6f0d9ece1c540ed67cda6cd3eac2f7ea2e586f774556"},"schema_version":"1.0","source":{"id":"1801.00900","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1801.00900","created_at":"2026-05-18T00:26:48Z"},{"alias_kind":"arxiv_version","alias_value":"1801.00900v1","created_at":"2026-05-18T00:26:48Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1801.00900","created_at":"2026-05-18T00:26:48Z"},{"alias_kind":"pith_short_12","alias_value":"SFU6OL5J2EH7","created_at":"2026-05-18T12:32:53Z"},{"alias_kind":"pith_short_16","alias_value":"SFU6OL5J2EH7QQYP","created_at":"2026-05-18T12:32:53Z"},{"alias_kind":"pith_short_8","alias_value":"SFU6OL5J","created_at":"2026-05-18T12:32:53Z"}],"graph_snapshots":[{"event_id":"sha256:77fcfdcdf6c45a9b46b7945827caf4f79fac21d27943b7114b7e633b375eed6d","target":"graph","created_at":"2026-05-18T00:26:48Z","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":"The discretized Bethe-Salpeter eigenvalue problem arises in the Green's function evaluation in many body physics and quantum chemistry. Discretization leads to a matrix eigenvalue problem for $H \\in \\mathbb{C}^{2n\\times 2n}$ with a Hamiltonian-like structure. After an appropriate transformation of $H$ to a standard symplectic form, the structure-preserving doubling algorithm, originally for algebraic Riccati equations, is extended for the discretized Bethe-Salpeter eigenvalue problem. Potential breakdowns of the algorithm, due to the ill condition or singularity of certain matrices, can be avo","authors_text":"Eric King-wah Chu, Wen-Wei Lin, Zhen-Chen Guo","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2018-01-03T05:21:47Z","title":"Doubling algorithm for the discretized Bethe-Salpeter eigenvalue problem"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1801.00900","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":"sha256:148988d3bc937785cbbd39758ef57f78c2ddd1d82818cc80adcb6d7b5a74e592","target":"record","created_at":"2026-05-18T00:26:48Z","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":"dfbb5ccfc6fa7cc9403dd5fd308f887817a99f31d1fed394a5f6fe5c5d06fd41","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2018-01-03T05:21:47Z","title_canon_sha256":"e73701b3b6adb448517c6f0d9ece1c540ed67cda6cd3eac2f7ea2e586f774556"},"schema_version":"1.0","source":{"id":"1801.00900","kind":"arxiv","version":1}},"canonical_sha256":"9169e72fa9d10ff8430f62f47e91fd96ba42d633bef87b4292002f8fde2dc17f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9169e72fa9d10ff8430f62f47e91fd96ba42d633bef87b4292002f8fde2dc17f","first_computed_at":"2026-05-18T00:26:48.452528Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:26:48.452528Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"LWeqRAXfnHQuK1LHXpKinn1/f7Ziw0Kw6I/KlW5fmO8bHP1+YAb1ijVCTx+Q4Azkxu+6dxt7Sbcrb6vWNLRkCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:26:48.453069Z","signed_message":"canonical_sha256_bytes"},"source_id":"1801.00900","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:148988d3bc937785cbbd39758ef57f78c2ddd1d82818cc80adcb6d7b5a74e592","sha256:77fcfdcdf6c45a9b46b7945827caf4f79fac21d27943b7114b7e633b375eed6d"],"state_sha256":"c5dc416a82a20cdf3abbe5886bb58cb9dc1da8c71725e07c2b08da04a8f3d396"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"CZSm8DTnLu4pMNCkD8Kk+x1i3XsHugXaRarQJRekjAa03f/ZNDnaM/6bvSjzhpSNy3VylFaMZc0j+jW5cX3BAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-27T21:16:05.417935Z","bundle_sha256":"f9f5aa0fd2afcdfa1d3c9ac104cc5c9c4bebb038ebd6e88aee451c96e4793f7a"}}