{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2024:723ZARWLO5VPH473K6S5CCIBKL","short_pith_number":"pith:723ZARWL","canonical_record":{"source":{"id":"2411.14578","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2024-11-21T20:46:11Z","cross_cats_sorted":["cs.NA","math.FA"],"title_canon_sha256":"3463fe4587dea1404e63c952267b0f0ea5e75677582f97fed1c5f2407b8f3971","abstract_canon_sha256":"f989b22a1a61bf1ed1fd28bbdd56de3035477b5f819990470c80a1a810414abe"},"schema_version":"1.0"},"canonical_sha256":"feb79046cb776af3f3fb57a5d1090152e867cd81362636ba0b321f990f10442c","source":{"kind":"arxiv","id":"2411.14578","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2411.14578","created_at":"2026-07-05T09:49:12Z"},{"alias_kind":"arxiv_version","alias_value":"2411.14578v1","created_at":"2026-07-05T09:49:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2411.14578","created_at":"2026-07-05T09:49:12Z"},{"alias_kind":"pith_short_12","alias_value":"723ZARWLO5VP","created_at":"2026-07-05T09:49:12Z"},{"alias_kind":"pith_short_16","alias_value":"723ZARWLO5VPH473","created_at":"2026-07-05T09:49:12Z"},{"alias_kind":"pith_short_8","alias_value":"723ZARWL","created_at":"2026-07-05T09:49:12Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2024:723ZARWLO5VPH473K6S5CCIBKL","target":"record","payload":{"canonical_record":{"source":{"id":"2411.14578","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2024-11-21T20:46:11Z","cross_cats_sorted":["cs.NA","math.FA"],"title_canon_sha256":"3463fe4587dea1404e63c952267b0f0ea5e75677582f97fed1c5f2407b8f3971","abstract_canon_sha256":"f989b22a1a61bf1ed1fd28bbdd56de3035477b5f819990470c80a1a810414abe"},"schema_version":"1.0"},"canonical_sha256":"feb79046cb776af3f3fb57a5d1090152e867cd81362636ba0b321f990f10442c","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T09:49:12.537601Z","signature_b64":"OE3VqlRhrkSPZfzdzr4HlxtE7B6swbeo/7o2s0uBUpgHcZwztqa9QLD3VP3NipJL312TfGQhSKlBx4TxVQ68Ag==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"feb79046cb776af3f3fb57a5d1090152e867cd81362636ba0b321f990f10442c","last_reissued_at":"2026-07-05T09:49:12.537145Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T09:49:12.537145Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2411.14578","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":"2026-07-05T09:49:12Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"v+Biv71Qqblew93A/KRnY+ZfDy5ewl0cuLOkjJWvn3nmDfd7UjjxnBCqug6ns1V2VDJozVgo/keoS+tuHillDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-13T04:05:37.830555Z"},"content_sha256":"c3038ffb36d837ecc40dcd661d8235f5d174912a6a56d2a8e0a4bb3e14158cb3","schema_version":"1.0","event_id":"sha256:c3038ffb36d837ecc40dcd661d8235f5d174912a6a56d2a8e0a4bb3e14158cb3"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2024:723ZARWLO5VPH473K6S5CCIBKL","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Block subspace expansions for eigenvalues and eigenvectors approximation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.NA","math.FA"],"primary_cat":"math.NA","authors_text":"Demetrio Stojanoff, Francisco Arrieta Zuccalli, Pedro Massey","submitted_at":"2024-11-21T20:46:11Z","abstract_excerpt":"Let $A\\in\\mathbb C^{n\\times n}$ and let $\\mathcal X\\subset \\mathbb C^n$ be an $A$-invariant subspace with $\\dim \\mathcal X=d\\geq 1$, corresponding to exterior eigenvalues of $A$. Given an initial subspace $\\mathcal V\\subset \\mathbb C^n$ with $\\dim \\mathcal V=r\\geq d$, we search for expansions of $\\mathcal V$ of the form $\\mathcal V+A(\\mathcal W_0)$, where $\\mathcal W_0\\subset \\mathcal V$ is such that $\\dim \\mathcal W_0\\leq d$ and such that the expanded subspace is closer to $\\mathcal X$ than the initial $\\mathcal V$. We show that there exist (theoretical) optimal choices of such $\\mathcal W_0$"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2411.14578","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2411.14578/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":"2026-07-05T09:49:12Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"vTsWkGxNLNySOFMXJk7cJRzSBVI1EBERtdk8iptk8KcK3F03dCfkzrmnCx2fsnc4fkY80uWBuLD+k9H7l7k3AQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-13T04:05:37.831536Z"},"content_sha256":"10cf9e7b8905369738e54ebbcb974ef68415a5ae6d157443f1cfeb216560b573","schema_version":"1.0","event_id":"sha256:10cf9e7b8905369738e54ebbcb974ef68415a5ae6d157443f1cfeb216560b573"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/723ZARWLO5VPH473K6S5CCIBKL/bundle.json","state_url":"https://pith.science/pith/723ZARWLO5VPH473K6S5CCIBKL/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/723ZARWLO5VPH473K6S5CCIBKL/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":"2026-08-13T04:05:37Z","links":{"resolver":"https://pith.science/pith/723ZARWLO5VPH473K6S5CCIBKL","bundle":"https://pith.science/pith/723ZARWLO5VPH473K6S5CCIBKL/bundle.json","state":"https://pith.science/pith/723ZARWLO5VPH473K6S5CCIBKL/state.json","well_known_bundle":"https://pith.science/.well-known/pith/723ZARWLO5VPH473K6S5CCIBKL/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:723ZARWLO5VPH473K6S5CCIBKL","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":"f989b22a1a61bf1ed1fd28bbdd56de3035477b5f819990470c80a1a810414abe","cross_cats_sorted":["cs.NA","math.FA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2024-11-21T20:46:11Z","title_canon_sha256":"3463fe4587dea1404e63c952267b0f0ea5e75677582f97fed1c5f2407b8f3971"},"schema_version":"1.0","source":{"id":"2411.14578","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2411.14578","created_at":"2026-07-05T09:49:12Z"},{"alias_kind":"arxiv_version","alias_value":"2411.14578v1","created_at":"2026-07-05T09:49:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2411.14578","created_at":"2026-07-05T09:49:12Z"},{"alias_kind":"pith_short_12","alias_value":"723ZARWLO5VP","created_at":"2026-07-05T09:49:12Z"},{"alias_kind":"pith_short_16","alias_value":"723ZARWLO5VPH473","created_at":"2026-07-05T09:49:12Z"},{"alias_kind":"pith_short_8","alias_value":"723ZARWL","created_at":"2026-07-05T09:49:12Z"}],"graph_snapshots":[{"event_id":"sha256:10cf9e7b8905369738e54ebbcb974ef68415a5ae6d157443f1cfeb216560b573","target":"graph","created_at":"2026-07-05T09:49:12Z","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/2411.14578/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Let $A\\in\\mathbb C^{n\\times n}$ and let $\\mathcal X\\subset \\mathbb C^n$ be an $A$-invariant subspace with $\\dim \\mathcal X=d\\geq 1$, corresponding to exterior eigenvalues of $A$. Given an initial subspace $\\mathcal V\\subset \\mathbb C^n$ with $\\dim \\mathcal V=r\\geq d$, we search for expansions of $\\mathcal V$ of the form $\\mathcal V+A(\\mathcal W_0)$, where $\\mathcal W_0\\subset \\mathcal V$ is such that $\\dim \\mathcal W_0\\leq d$ and such that the expanded subspace is closer to $\\mathcal X$ than the initial $\\mathcal V$. We show that there exist (theoretical) optimal choices of such $\\mathcal W_0$","authors_text":"Demetrio Stojanoff, Francisco Arrieta Zuccalli, Pedro Massey","cross_cats":["cs.NA","math.FA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2024-11-21T20:46:11Z","title":"Block subspace expansions for eigenvalues and eigenvectors approximation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2411.14578","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:c3038ffb36d837ecc40dcd661d8235f5d174912a6a56d2a8e0a4bb3e14158cb3","target":"record","created_at":"2026-07-05T09:49:12Z","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":"f989b22a1a61bf1ed1fd28bbdd56de3035477b5f819990470c80a1a810414abe","cross_cats_sorted":["cs.NA","math.FA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2024-11-21T20:46:11Z","title_canon_sha256":"3463fe4587dea1404e63c952267b0f0ea5e75677582f97fed1c5f2407b8f3971"},"schema_version":"1.0","source":{"id":"2411.14578","kind":"arxiv","version":1}},"canonical_sha256":"feb79046cb776af3f3fb57a5d1090152e867cd81362636ba0b321f990f10442c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"feb79046cb776af3f3fb57a5d1090152e867cd81362636ba0b321f990f10442c","first_computed_at":"2026-07-05T09:49:12.537145Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T09:49:12.537145Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"OE3VqlRhrkSPZfzdzr4HlxtE7B6swbeo/7o2s0uBUpgHcZwztqa9QLD3VP3NipJL312TfGQhSKlBx4TxVQ68Ag==","signature_status":"signed_v1","signed_at":"2026-07-05T09:49:12.537601Z","signed_message":"canonical_sha256_bytes"},"source_id":"2411.14578","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c3038ffb36d837ecc40dcd661d8235f5d174912a6a56d2a8e0a4bb3e14158cb3","sha256:10cf9e7b8905369738e54ebbcb974ef68415a5ae6d157443f1cfeb216560b573"],"state_sha256":"62695390e1a33470c9a712a1c55d5fe69bebc3de22af699173e3d5098e97b2bb"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ixBlDeEhrZ8ST5mxGQlwyTshnr6tddG29GuTKQmoq0LzodDf6QBQE9v9sQg+RDIiDdOg/Cgh4bnxpZsl7CbaAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-13T04:05:37.838080Z","bundle_sha256":"bf93a825a408bdba1fb8326ae3c79d6b106589c7b6337717b151f970d627c70d"}}