{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:SCEAHHYZYSWHYLH5GBNXRTRLEV","short_pith_number":"pith:SCEAHHYZ","canonical_record":{"source":{"id":"1111.5105","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2011-11-22T05:48:44Z","cross_cats_sorted":["math.AP"],"title_canon_sha256":"0fdcd661c8c6e1bba8588a3ba4253fb31539f60e83a22612609f5dc8ba9dfdaf","abstract_canon_sha256":"5e75779d85b8a447346e7b1c2e771fd74e3e450e4cd0582749409f8db7e5ef44"},"schema_version":"1.0"},"canonical_sha256":"9088039f19c4ac7c2cfd305b78ce2b254b9d64d1f037963f030cca3c53d76e53","source":{"kind":"arxiv","id":"1111.5105","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1111.5105","created_at":"2026-05-18T01:21:39Z"},{"alias_kind":"arxiv_version","alias_value":"1111.5105v1","created_at":"2026-05-18T01:21:39Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1111.5105","created_at":"2026-05-18T01:21:39Z"},{"alias_kind":"pith_short_12","alias_value":"SCEAHHYZYSWH","created_at":"2026-05-18T12:26:41Z"},{"alias_kind":"pith_short_16","alias_value":"SCEAHHYZYSWHYLH5","created_at":"2026-05-18T12:26:41Z"},{"alias_kind":"pith_short_8","alias_value":"SCEAHHYZ","created_at":"2026-05-18T12:26:41Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:SCEAHHYZYSWHYLH5GBNXRTRLEV","target":"record","payload":{"canonical_record":{"source":{"id":"1111.5105","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2011-11-22T05:48:44Z","cross_cats_sorted":["math.AP"],"title_canon_sha256":"0fdcd661c8c6e1bba8588a3ba4253fb31539f60e83a22612609f5dc8ba9dfdaf","abstract_canon_sha256":"5e75779d85b8a447346e7b1c2e771fd74e3e450e4cd0582749409f8db7e5ef44"},"schema_version":"1.0"},"canonical_sha256":"9088039f19c4ac7c2cfd305b78ce2b254b9d64d1f037963f030cca3c53d76e53","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:21:39.864557Z","signature_b64":"q9eLs8Pe6T9dY2AVDwuBUx2KVeX1AtHixlU2O6wJwbqVdZ7t/0lp2HiVrlkqV0bekvdcj+fZsWQDM+acr0vKAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9088039f19c4ac7c2cfd305b78ce2b254b9d64d1f037963f030cca3c53d76e53","last_reissued_at":"2026-05-18T01:21:39.864027Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:21:39.864027Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1111.5105","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":"2026-05-18T01:21:39Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"xqEmModVEDHqfuPcmgsZq0wenLF93t4lsAHvL5gT2/2rc2l3TNY4PxdQTmsnG7do/fu7kvk9Z22Q73AoOKWLBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T09:47:24.198729Z"},"content_sha256":"2a3a7b95022ca1b7d45b2179af1d197a7346f8d26fff8f7bb4ecea43279ad98e","schema_version":"1.0","event_id":"sha256:2a3a7b95022ca1b7d45b2179af1d197a7346f8d26fff8f7bb4ecea43279ad98e"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:SCEAHHYZYSWHYLH5GBNXRTRLEV","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Iterative methods for shifted positive definite linear systems and time discretization of the heat equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP"],"primary_cat":"math.NA","authors_text":"Vidar Thom\\'ee, William McLean","submitted_at":"2011-11-22T05:48:44Z","abstract_excerpt":"In earlier work we have studied a method for discretization in time of a parabolic problem which consists in representing the exact solution as an integral in the complex plane and then applying a quadrature formula to this integral. In application to a spatially semidiscrete finite element version of the parabolic problem, at each quadrature point one then needs to solve a linear algebraic system having a positive definite matrix with a complex shift, and in this paper we study iterative methods for such systems. We first consider the basic and a preconditioned version of the Richardson algor"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1111.5105","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":"2026-05-18T01:21:39Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"9H1j58wvwCJ6+90utQ6N52VLZG3pN75392RrPHR0R0UOpyQVjRJkoavD0ou2gaT21bYeyWvJ2W951YKSJF8rAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T09:47:24.199082Z"},"content_sha256":"d8790c24e112bbb244d484c24cdee8390887c75627f699afba809745d1b877a3","schema_version":"1.0","event_id":"sha256:d8790c24e112bbb244d484c24cdee8390887c75627f699afba809745d1b877a3"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/SCEAHHYZYSWHYLH5GBNXRTRLEV/bundle.json","state_url":"https://pith.science/pith/SCEAHHYZYSWHYLH5GBNXRTRLEV/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/SCEAHHYZYSWHYLH5GBNXRTRLEV/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":"2026-06-02T09:47:24Z","links":{"resolver":"https://pith.science/pith/SCEAHHYZYSWHYLH5GBNXRTRLEV","bundle":"https://pith.science/pith/SCEAHHYZYSWHYLH5GBNXRTRLEV/bundle.json","state":"https://pith.science/pith/SCEAHHYZYSWHYLH5GBNXRTRLEV/state.json","well_known_bundle":"https://pith.science/.well-known/pith/SCEAHHYZYSWHYLH5GBNXRTRLEV/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:SCEAHHYZYSWHYLH5GBNXRTRLEV","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":"5e75779d85b8a447346e7b1c2e771fd74e3e450e4cd0582749409f8db7e5ef44","cross_cats_sorted":["math.AP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2011-11-22T05:48:44Z","title_canon_sha256":"0fdcd661c8c6e1bba8588a3ba4253fb31539f60e83a22612609f5dc8ba9dfdaf"},"schema_version":"1.0","source":{"id":"1111.5105","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1111.5105","created_at":"2026-05-18T01:21:39Z"},{"alias_kind":"arxiv_version","alias_value":"1111.5105v1","created_at":"2026-05-18T01:21:39Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1111.5105","created_at":"2026-05-18T01:21:39Z"},{"alias_kind":"pith_short_12","alias_value":"SCEAHHYZYSWH","created_at":"2026-05-18T12:26:41Z"},{"alias_kind":"pith_short_16","alias_value":"SCEAHHYZYSWHYLH5","created_at":"2026-05-18T12:26:41Z"},{"alias_kind":"pith_short_8","alias_value":"SCEAHHYZ","created_at":"2026-05-18T12:26:41Z"}],"graph_snapshots":[{"event_id":"sha256:d8790c24e112bbb244d484c24cdee8390887c75627f699afba809745d1b877a3","target":"graph","created_at":"2026-05-18T01:21:39Z","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":"In earlier work we have studied a method for discretization in time of a parabolic problem which consists in representing the exact solution as an integral in the complex plane and then applying a quadrature formula to this integral. In application to a spatially semidiscrete finite element version of the parabolic problem, at each quadrature point one then needs to solve a linear algebraic system having a positive definite matrix with a complex shift, and in this paper we study iterative methods for such systems. We first consider the basic and a preconditioned version of the Richardson algor","authors_text":"Vidar Thom\\'ee, William McLean","cross_cats":["math.AP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2011-11-22T05:48:44Z","title":"Iterative methods for shifted positive definite linear systems and time discretization of the heat equation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1111.5105","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":"sha256:2a3a7b95022ca1b7d45b2179af1d197a7346f8d26fff8f7bb4ecea43279ad98e","target":"record","created_at":"2026-05-18T01:21:39Z","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":"5e75779d85b8a447346e7b1c2e771fd74e3e450e4cd0582749409f8db7e5ef44","cross_cats_sorted":["math.AP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2011-11-22T05:48:44Z","title_canon_sha256":"0fdcd661c8c6e1bba8588a3ba4253fb31539f60e83a22612609f5dc8ba9dfdaf"},"schema_version":"1.0","source":{"id":"1111.5105","kind":"arxiv","version":1}},"canonical_sha256":"9088039f19c4ac7c2cfd305b78ce2b254b9d64d1f037963f030cca3c53d76e53","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9088039f19c4ac7c2cfd305b78ce2b254b9d64d1f037963f030cca3c53d76e53","first_computed_at":"2026-05-18T01:21:39.864027Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:21:39.864027Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"q9eLs8Pe6T9dY2AVDwuBUx2KVeX1AtHixlU2O6wJwbqVdZ7t/0lp2HiVrlkqV0bekvdcj+fZsWQDM+acr0vKAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:21:39.864557Z","signed_message":"canonical_sha256_bytes"},"source_id":"1111.5105","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2a3a7b95022ca1b7d45b2179af1d197a7346f8d26fff8f7bb4ecea43279ad98e","sha256:d8790c24e112bbb244d484c24cdee8390887c75627f699afba809745d1b877a3"],"state_sha256":"93c0c3251328fdefe5fa97bd681f3fe6de811fed388ff4acc332ecff9ee9e465"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"E5+7F93R6XvgLlFgjdlxpC/d4IcyW86/WenyiX4t3IULLqhbNEsPTBfAd2TevCluMD5BQP4UV+eE1yOdhAr9Bw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-02T09:47:24.201117Z","bundle_sha256":"7ff07f09c5d0e21c03c19ba5159be09270050e999509d47bd76ca811e3007793"}}