{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2019:ZXTXZULHVPTH44IUGV5MNW2UZB","short_pith_number":"pith:ZXTXZULH","canonical_record":{"source":{"id":"1901.00904","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.SC","submitted_at":"2019-01-03T20:20:13Z","cross_cats_sorted":[],"title_canon_sha256":"a80b2ebf1418ed491746507d1ddfa20d2723d265e1dd93626e2c46efe6ca340c","abstract_canon_sha256":"345e53d6939486f814c38c67338428130fd882fed7d9888a1fbbdc5809109938"},"schema_version":"1.0"},"canonical_sha256":"cde77cd167abe67e7114357ac6db54c84a53aaf58aa3ffca58df38edfc781617","source":{"kind":"arxiv","id":"1901.00904","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1901.00904","created_at":"2026-05-17T23:56:57Z"},{"alias_kind":"arxiv_version","alias_value":"1901.00904v1","created_at":"2026-05-17T23:56:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1901.00904","created_at":"2026-05-17T23:56:57Z"},{"alias_kind":"pith_short_12","alias_value":"ZXTXZULHVPTH","created_at":"2026-05-18T12:33:33Z"},{"alias_kind":"pith_short_16","alias_value":"ZXTXZULHVPTH44IU","created_at":"2026-05-18T12:33:33Z"},{"alias_kind":"pith_short_8","alias_value":"ZXTXZULH","created_at":"2026-05-18T12:33:33Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2019:ZXTXZULHVPTH44IUGV5MNW2UZB","target":"record","payload":{"canonical_record":{"source":{"id":"1901.00904","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.SC","submitted_at":"2019-01-03T20:20:13Z","cross_cats_sorted":[],"title_canon_sha256":"a80b2ebf1418ed491746507d1ddfa20d2723d265e1dd93626e2c46efe6ca340c","abstract_canon_sha256":"345e53d6939486f814c38c67338428130fd882fed7d9888a1fbbdc5809109938"},"schema_version":"1.0"},"canonical_sha256":"cde77cd167abe67e7114357ac6db54c84a53aaf58aa3ffca58df38edfc781617","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:56:57.724093Z","signature_b64":"V41V/RB3kVqUyIR60xwDZLpOS5dn2+PacGRJqu/s5LA2I4l7B0s0tCwf+PJYC9TwVDaDQoDjMgD8NFqbq9psAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"cde77cd167abe67e7114357ac6db54c84a53aaf58aa3ffca58df38edfc781617","last_reissued_at":"2026-05-17T23:56:57.723444Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:56:57.723444Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1901.00904","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":"2026-05-17T23:56:57Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"LPMZVxqOnOTnmRE8MOpjeBTv5RVz/ybYMIua2BNVeWK6BJRvaHmVRc1G1hO23enIF6yYdv51FGfhgseBrMWzAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T01:33:36.864769Z"},"content_sha256":"03f238c6db207983093b0a9864ea87bbca51ff25d7737910a4ce3ef052692bcd","schema_version":"1.0","event_id":"sha256:03f238c6db207983093b0a9864ea87bbca51ff25d7737910a4ce3ef052692bcd"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2019:ZXTXZULHVPTH44IUGV5MNW2UZB","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On Fast Matrix Inversion via Fast Matrix Multiplication","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.SC","authors_text":"Zak Tonks","submitted_at":"2019-01-03T20:20:13Z","abstract_excerpt":"Volker Strassen first suggested an algorithm to multiply matrices with worst case running time less than the conventional $\\mathcal{O}(n^3)$ operations in 1969. He also presented a recursive algorithm with which to invert matrices, and calculate determinants using matrix multiplication. James R. Bunch & John E. Hopcroft improved upon this in 1974 by providing modifications to the inversion algorithm in the case where principal submatrices were singular, amongst other improvements. We cover the case of multivariate polynomial matrix inversion, where it is noted that conventional methods that as"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1901.00904","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":"2026-05-17T23:56:57Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"aiiFVygF9RZkVsVjuyiarzLmfwYy61DOlpEzm8wJrIIbBYZr+YpQaFSDZ792UwZl9jJkmMp4BRz8nuGzOYqWAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T01:33:36.865129Z"},"content_sha256":"df6b9b0860b10414de078451d348d070e4f2817026fa89f6b9dcabfad81e0fd8","schema_version":"1.0","event_id":"sha256:df6b9b0860b10414de078451d348d070e4f2817026fa89f6b9dcabfad81e0fd8"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/ZXTXZULHVPTH44IUGV5MNW2UZB/bundle.json","state_url":"https://pith.science/pith/ZXTXZULHVPTH44IUGV5MNW2UZB/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/ZXTXZULHVPTH44IUGV5MNW2UZB/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":"2026-06-03T01:33:36Z","links":{"resolver":"https://pith.science/pith/ZXTXZULHVPTH44IUGV5MNW2UZB","bundle":"https://pith.science/pith/ZXTXZULHVPTH44IUGV5MNW2UZB/bundle.json","state":"https://pith.science/pith/ZXTXZULHVPTH44IUGV5MNW2UZB/state.json","well_known_bundle":"https://pith.science/.well-known/pith/ZXTXZULHVPTH44IUGV5MNW2UZB/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:ZXTXZULHVPTH44IUGV5MNW2UZB","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":"345e53d6939486f814c38c67338428130fd882fed7d9888a1fbbdc5809109938","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.SC","submitted_at":"2019-01-03T20:20:13Z","title_canon_sha256":"a80b2ebf1418ed491746507d1ddfa20d2723d265e1dd93626e2c46efe6ca340c"},"schema_version":"1.0","source":{"id":"1901.00904","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1901.00904","created_at":"2026-05-17T23:56:57Z"},{"alias_kind":"arxiv_version","alias_value":"1901.00904v1","created_at":"2026-05-17T23:56:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1901.00904","created_at":"2026-05-17T23:56:57Z"},{"alias_kind":"pith_short_12","alias_value":"ZXTXZULHVPTH","created_at":"2026-05-18T12:33:33Z"},{"alias_kind":"pith_short_16","alias_value":"ZXTXZULHVPTH44IU","created_at":"2026-05-18T12:33:33Z"},{"alias_kind":"pith_short_8","alias_value":"ZXTXZULH","created_at":"2026-05-18T12:33:33Z"}],"graph_snapshots":[{"event_id":"sha256:df6b9b0860b10414de078451d348d070e4f2817026fa89f6b9dcabfad81e0fd8","target":"graph","created_at":"2026-05-17T23:56:57Z","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":"Volker Strassen first suggested an algorithm to multiply matrices with worst case running time less than the conventional $\\mathcal{O}(n^3)$ operations in 1969. He also presented a recursive algorithm with which to invert matrices, and calculate determinants using matrix multiplication. James R. Bunch & John E. Hopcroft improved upon this in 1974 by providing modifications to the inversion algorithm in the case where principal submatrices were singular, amongst other improvements. We cover the case of multivariate polynomial matrix inversion, where it is noted that conventional methods that as","authors_text":"Zak Tonks","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.SC","submitted_at":"2019-01-03T20:20:13Z","title":"On Fast Matrix Inversion via Fast Matrix Multiplication"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1901.00904","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":"sha256:03f238c6db207983093b0a9864ea87bbca51ff25d7737910a4ce3ef052692bcd","target":"record","created_at":"2026-05-17T23:56:57Z","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":"345e53d6939486f814c38c67338428130fd882fed7d9888a1fbbdc5809109938","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.SC","submitted_at":"2019-01-03T20:20:13Z","title_canon_sha256":"a80b2ebf1418ed491746507d1ddfa20d2723d265e1dd93626e2c46efe6ca340c"},"schema_version":"1.0","source":{"id":"1901.00904","kind":"arxiv","version":1}},"canonical_sha256":"cde77cd167abe67e7114357ac6db54c84a53aaf58aa3ffca58df38edfc781617","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"cde77cd167abe67e7114357ac6db54c84a53aaf58aa3ffca58df38edfc781617","first_computed_at":"2026-05-17T23:56:57.723444Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:56:57.723444Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"V41V/RB3kVqUyIR60xwDZLpOS5dn2+PacGRJqu/s5LA2I4l7B0s0tCwf+PJYC9TwVDaDQoDjMgD8NFqbq9psAQ==","signature_status":"signed_v1","signed_at":"2026-05-17T23:56:57.724093Z","signed_message":"canonical_sha256_bytes"},"source_id":"1901.00904","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:03f238c6db207983093b0a9864ea87bbca51ff25d7737910a4ce3ef052692bcd","sha256:df6b9b0860b10414de078451d348d070e4f2817026fa89f6b9dcabfad81e0fd8"],"state_sha256":"51eb191602a8190f7b6e3a9cdb7d0192bd883b3f0c115c18c6fdadb36b830f68"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Dxsel1+JQaJ+1vWmAeOVX+3HCjS2We0jl/ZLpNf/qZaRZcl8yajgMb/kthUAPNYQslm6r93/yZq7diI2TpT1Aw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-03T01:33:36.867029Z","bundle_sha256":"3c9fca9e974e102d49ff811c72be01898883739cf3f7d1e47f0b756edc3a4343"}}