{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2008:CEDJ24ER7QROBIME3JCTBPBRCS","short_pith_number":"pith:CEDJ24ER","canonical_record":{"source":{"id":"0810.0330","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2008-10-02T03:20:03Z","cross_cats_sorted":["hep-lat","math.MP"],"title_canon_sha256":"45b505170f329d2d59550053564656983d7318f187dc8dac189ba1d6121f7547","abstract_canon_sha256":"45581fc4334c9d3841fd9d754904231d0d69a7b2ff3c866a8a8aa9bd7675aad1"},"schema_version":"1.0"},"canonical_sha256":"11069d7091fc22e0a184da4530bc3114881a72e1bd3dc0c7073d15c3ff7bb12e","source":{"kind":"arxiv","id":"0810.0330","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0810.0330","created_at":"2026-05-18T02:44:23Z"},{"alias_kind":"arxiv_version","alias_value":"0810.0330v1","created_at":"2026-05-18T02:44:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0810.0330","created_at":"2026-05-18T02:44:23Z"},{"alias_kind":"pith_short_12","alias_value":"CEDJ24ER7QRO","created_at":"2026-05-18T12:25:57Z"},{"alias_kind":"pith_short_16","alias_value":"CEDJ24ER7QROBIME","created_at":"2026-05-18T12:25:57Z"},{"alias_kind":"pith_short_8","alias_value":"CEDJ24ER","created_at":"2026-05-18T12:25:57Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2008:CEDJ24ER7QROBIME3JCTBPBRCS","target":"record","payload":{"canonical_record":{"source":{"id":"0810.0330","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2008-10-02T03:20:03Z","cross_cats_sorted":["hep-lat","math.MP"],"title_canon_sha256":"45b505170f329d2d59550053564656983d7318f187dc8dac189ba1d6121f7547","abstract_canon_sha256":"45581fc4334c9d3841fd9d754904231d0d69a7b2ff3c866a8a8aa9bd7675aad1"},"schema_version":"1.0"},"canonical_sha256":"11069d7091fc22e0a184da4530bc3114881a72e1bd3dc0c7073d15c3ff7bb12e","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:44:23.837216Z","signature_b64":"LI0qJZ55+kL4OONbrQTpRhmC/rmditeGotUKAaaUD4qenP8U92dhfEIGvZq7FGxvuQnZ7FVWd6abwseXxiMpAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"11069d7091fc22e0a184da4530bc3114881a72e1bd3dc0c7073d15c3ff7bb12e","last_reissued_at":"2026-05-18T02:44:23.836820Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:44:23.836820Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"0810.0330","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":"2026-05-18T02:44:23Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"8xsVHs8O0YQPOHS9g54I+YQBzvl9JIRSdK9u+xunCoL+TdOBeBD8uW5sJJtcNmBFTgn/sCwYJnwI1M8netuhAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T17:39:15.692443Z"},"content_sha256":"36f5b3debf65dea1ac57be370aeb07f3d8800353a2d54969b46eed1a97aa3008","schema_version":"1.0","event_id":"sha256:36f5b3debf65dea1ac57be370aeb07f3d8800353a2d54969b46eed1a97aa3008"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2008:CEDJ24ER7QROBIME3JCTBPBRCS","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Improved Seed Methods for Symmetric Positive Definite Linear Equations with Multiple Right-hand Sides","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["hep-lat","math.MP"],"primary_cat":"math-ph","authors_text":"Abdou M. Abdel-Rehim, Ronald B. Morgan, Walter Wilcox","submitted_at":"2008-10-02T03:20:03Z","abstract_excerpt":"We consider symmetric positive definite systems of linear equations with multiple right-hand sides. The seed conjugate gradient method solves one right-hand side with the conjugate gradient method and simultaneously projects over the Krylov subspace thus developed for the other right-hand sides. Then the next system is solved and used to seed the remaining ones. Rounding error in the conjugate gradient method limits how much the seeding can improve convergence. We propose three changes to the seed conjugate gradient method: only the first right-hand side is used for seeding, this system is sol"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0810.0330","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":"2026-05-18T02:44:23Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"I2MKV+G7yG8ZmZjIe4HgcKWP4zCaAsMF1QKKyBxMpJBW8fwMm4/AfP7odESMZeTHYmCfhSU90n7eZpL2wMfVDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T17:39:15.692913Z"},"content_sha256":"652889e60b2b2907327105d3ff8f60b340a23ca9acd55d1ffac9d8c0012615fa","schema_version":"1.0","event_id":"sha256:652889e60b2b2907327105d3ff8f60b340a23ca9acd55d1ffac9d8c0012615fa"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/CEDJ24ER7QROBIME3JCTBPBRCS/bundle.json","state_url":"https://pith.science/pith/CEDJ24ER7QROBIME3JCTBPBRCS/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/CEDJ24ER7QROBIME3JCTBPBRCS/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":"2026-06-23T17:39:15Z","links":{"resolver":"https://pith.science/pith/CEDJ24ER7QROBIME3JCTBPBRCS","bundle":"https://pith.science/pith/CEDJ24ER7QROBIME3JCTBPBRCS/bundle.json","state":"https://pith.science/pith/CEDJ24ER7QROBIME3JCTBPBRCS/state.json","well_known_bundle":"https://pith.science/.well-known/pith/CEDJ24ER7QROBIME3JCTBPBRCS/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2008:CEDJ24ER7QROBIME3JCTBPBRCS","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":"45581fc4334c9d3841fd9d754904231d0d69a7b2ff3c866a8a8aa9bd7675aad1","cross_cats_sorted":["hep-lat","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2008-10-02T03:20:03Z","title_canon_sha256":"45b505170f329d2d59550053564656983d7318f187dc8dac189ba1d6121f7547"},"schema_version":"1.0","source":{"id":"0810.0330","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0810.0330","created_at":"2026-05-18T02:44:23Z"},{"alias_kind":"arxiv_version","alias_value":"0810.0330v1","created_at":"2026-05-18T02:44:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0810.0330","created_at":"2026-05-18T02:44:23Z"},{"alias_kind":"pith_short_12","alias_value":"CEDJ24ER7QRO","created_at":"2026-05-18T12:25:57Z"},{"alias_kind":"pith_short_16","alias_value":"CEDJ24ER7QROBIME","created_at":"2026-05-18T12:25:57Z"},{"alias_kind":"pith_short_8","alias_value":"CEDJ24ER","created_at":"2026-05-18T12:25:57Z"}],"graph_snapshots":[{"event_id":"sha256:652889e60b2b2907327105d3ff8f60b340a23ca9acd55d1ffac9d8c0012615fa","target":"graph","created_at":"2026-05-18T02:44:23Z","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 consider symmetric positive definite systems of linear equations with multiple right-hand sides. The seed conjugate gradient method solves one right-hand side with the conjugate gradient method and simultaneously projects over the Krylov subspace thus developed for the other right-hand sides. Then the next system is solved and used to seed the remaining ones. Rounding error in the conjugate gradient method limits how much the seeding can improve convergence. We propose three changes to the seed conjugate gradient method: only the first right-hand side is used for seeding, this system is sol","authors_text":"Abdou M. Abdel-Rehim, Ronald B. Morgan, Walter Wilcox","cross_cats":["hep-lat","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2008-10-02T03:20:03Z","title":"Improved Seed Methods for Symmetric Positive Definite Linear Equations with Multiple Right-hand Sides"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0810.0330","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":"sha256:36f5b3debf65dea1ac57be370aeb07f3d8800353a2d54969b46eed1a97aa3008","target":"record","created_at":"2026-05-18T02:44:23Z","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":"45581fc4334c9d3841fd9d754904231d0d69a7b2ff3c866a8a8aa9bd7675aad1","cross_cats_sorted":["hep-lat","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2008-10-02T03:20:03Z","title_canon_sha256":"45b505170f329d2d59550053564656983d7318f187dc8dac189ba1d6121f7547"},"schema_version":"1.0","source":{"id":"0810.0330","kind":"arxiv","version":1}},"canonical_sha256":"11069d7091fc22e0a184da4530bc3114881a72e1bd3dc0c7073d15c3ff7bb12e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"11069d7091fc22e0a184da4530bc3114881a72e1bd3dc0c7073d15c3ff7bb12e","first_computed_at":"2026-05-18T02:44:23.836820Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:44:23.836820Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"LI0qJZ55+kL4OONbrQTpRhmC/rmditeGotUKAaaUD4qenP8U92dhfEIGvZq7FGxvuQnZ7FVWd6abwseXxiMpAA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:44:23.837216Z","signed_message":"canonical_sha256_bytes"},"source_id":"0810.0330","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:36f5b3debf65dea1ac57be370aeb07f3d8800353a2d54969b46eed1a97aa3008","sha256:652889e60b2b2907327105d3ff8f60b340a23ca9acd55d1ffac9d8c0012615fa"],"state_sha256":"6291af9d4b382877ab421982195a9ee8dea41341fd42490806cbe25025496dc3"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Nn6prD5xGOMZvVlqBcsw5PHkyADnzGv8CdJV9qxbDWCERlsiXK5fzgRPYJf85tkCLyIocELiuZQLbFQ+GicvCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-23T17:39:15.695482Z","bundle_sha256":"12606814e9207685aeb470fdcd55deabc93b91042a94b7c8511141add9ef5f69"}}