{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2009:J5EYO2SSNCB6RXJK24LG4RDFWM","short_pith_number":"pith:J5EYO2SS","canonical_record":{"source":{"id":"0902.1155","kind":"arxiv","version":5},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2009-02-06T18:20:42Z","cross_cats_sorted":[],"title_canon_sha256":"5a272b84a237c58b0e0a29979097df4bacaeb401462e24ac36f93217893bba89","abstract_canon_sha256":"8a50da92936505b27a7b1466834cc680f1e3df91ac14996b4c199b73013e6626"},"schema_version":"1.0"},"canonical_sha256":"4f49876a526883e8dd2ad7166e4465b315fc7fe4fc50597e30dc3117f0c7a119","source":{"kind":"arxiv","id":"0902.1155","version":5},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0902.1155","created_at":"2026-05-18T02:56:58Z"},{"alias_kind":"arxiv_version","alias_value":"0902.1155v5","created_at":"2026-05-18T02:56:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0902.1155","created_at":"2026-05-18T02:56:58Z"},{"alias_kind":"pith_short_12","alias_value":"J5EYO2SSNCB6","created_at":"2026-05-18T12:26:00Z"},{"alias_kind":"pith_short_16","alias_value":"J5EYO2SSNCB6RXJK","created_at":"2026-05-18T12:26:00Z"},{"alias_kind":"pith_short_8","alias_value":"J5EYO2SS","created_at":"2026-05-18T12:26:00Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2009:J5EYO2SSNCB6RXJK24LG4RDFWM","target":"record","payload":{"canonical_record":{"source":{"id":"0902.1155","kind":"arxiv","version":5},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2009-02-06T18:20:42Z","cross_cats_sorted":[],"title_canon_sha256":"5a272b84a237c58b0e0a29979097df4bacaeb401462e24ac36f93217893bba89","abstract_canon_sha256":"8a50da92936505b27a7b1466834cc680f1e3df91ac14996b4c199b73013e6626"},"schema_version":"1.0"},"canonical_sha256":"4f49876a526883e8dd2ad7166e4465b315fc7fe4fc50597e30dc3117f0c7a119","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:56:58.720902Z","signature_b64":"nQlGpIrdzMKGv8PCEg9TZdXlpBYzuKZcj1pCuZYA4R/UNNtCCGJtKvcL9OCabCYPBsiVkP5EfEiWb5sp2mnbBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4f49876a526883e8dd2ad7166e4465b315fc7fe4fc50597e30dc3117f0c7a119","last_reissued_at":"2026-05-18T02:56:58.720437Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:56:58.720437Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"0902.1155","source_version":5,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:56:58Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Crnh15OxSSoj4zrA0Jox42y8GPnK5lWYCHEhB/Txc8CZCotWiFut18Q3j1qee5cyH0q2C7MBsxuQZigeu+VACQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T05:08:24.139574Z"},"content_sha256":"33b43dbec89b3a5566c951212b151cf2a86ddc9aef49ab9d643f1683cdafcf7a","schema_version":"1.0","event_id":"sha256:33b43dbec89b3a5566c951212b151cf2a86ddc9aef49ab9d643f1683cdafcf7a"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2009:J5EYO2SSNCB6RXJK24LG4RDFWM","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Matrix identities involving multiplication and transposition","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"Igor Dolinka, Karl Auinger, Mikhail Volkov","submitted_at":"2009-02-06T18:20:42Z","abstract_excerpt":"We study matrix identities involving multiplication and unary operations such as transposition or Moore-Penrose inversion. We prove that in many cases such identities admit no finite basis."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0902.1155","kind":"arxiv","version":5},"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":"2026-05-18T02:56:58Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"S7Z/IGcD+8tYemCV7wu4Dnp9pSGyB3xiCd+eolrQKCzpgGMxAqpVM1nhPKqRowPKILsnBBeFlTLQH6TSeZ8GCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T05:08:24.140159Z"},"content_sha256":"2dc6e64c73bce4f45b2909bf6a9d07a398a65dc80cd3d84d980e7709229fd9bc","schema_version":"1.0","event_id":"sha256:2dc6e64c73bce4f45b2909bf6a9d07a398a65dc80cd3d84d980e7709229fd9bc"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/J5EYO2SSNCB6RXJK24LG4RDFWM/bundle.json","state_url":"https://pith.science/pith/J5EYO2SSNCB6RXJK24LG4RDFWM/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/J5EYO2SSNCB6RXJK24LG4RDFWM/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":"2026-06-24T05:08:24Z","links":{"resolver":"https://pith.science/pith/J5EYO2SSNCB6RXJK24LG4RDFWM","bundle":"https://pith.science/pith/J5EYO2SSNCB6RXJK24LG4RDFWM/bundle.json","state":"https://pith.science/pith/J5EYO2SSNCB6RXJK24LG4RDFWM/state.json","well_known_bundle":"https://pith.science/.well-known/pith/J5EYO2SSNCB6RXJK24LG4RDFWM/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2009:J5EYO2SSNCB6RXJK24LG4RDFWM","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":"8a50da92936505b27a7b1466834cc680f1e3df91ac14996b4c199b73013e6626","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2009-02-06T18:20:42Z","title_canon_sha256":"5a272b84a237c58b0e0a29979097df4bacaeb401462e24ac36f93217893bba89"},"schema_version":"1.0","source":{"id":"0902.1155","kind":"arxiv","version":5}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0902.1155","created_at":"2026-05-18T02:56:58Z"},{"alias_kind":"arxiv_version","alias_value":"0902.1155v5","created_at":"2026-05-18T02:56:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0902.1155","created_at":"2026-05-18T02:56:58Z"},{"alias_kind":"pith_short_12","alias_value":"J5EYO2SSNCB6","created_at":"2026-05-18T12:26:00Z"},{"alias_kind":"pith_short_16","alias_value":"J5EYO2SSNCB6RXJK","created_at":"2026-05-18T12:26:00Z"},{"alias_kind":"pith_short_8","alias_value":"J5EYO2SS","created_at":"2026-05-18T12:26:00Z"}],"graph_snapshots":[{"event_id":"sha256:2dc6e64c73bce4f45b2909bf6a9d07a398a65dc80cd3d84d980e7709229fd9bc","target":"graph","created_at":"2026-05-18T02:56:58Z","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 study matrix identities involving multiplication and unary operations such as transposition or Moore-Penrose inversion. We prove that in many cases such identities admit no finite basis.","authors_text":"Igor Dolinka, Karl Auinger, Mikhail Volkov","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2009-02-06T18:20:42Z","title":"Matrix identities involving multiplication and transposition"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0902.1155","kind":"arxiv","version":5},"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":"sha256:33b43dbec89b3a5566c951212b151cf2a86ddc9aef49ab9d643f1683cdafcf7a","target":"record","created_at":"2026-05-18T02:56:58Z","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":"8a50da92936505b27a7b1466834cc680f1e3df91ac14996b4c199b73013e6626","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2009-02-06T18:20:42Z","title_canon_sha256":"5a272b84a237c58b0e0a29979097df4bacaeb401462e24ac36f93217893bba89"},"schema_version":"1.0","source":{"id":"0902.1155","kind":"arxiv","version":5}},"canonical_sha256":"4f49876a526883e8dd2ad7166e4465b315fc7fe4fc50597e30dc3117f0c7a119","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4f49876a526883e8dd2ad7166e4465b315fc7fe4fc50597e30dc3117f0c7a119","first_computed_at":"2026-05-18T02:56:58.720437Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:56:58.720437Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"nQlGpIrdzMKGv8PCEg9TZdXlpBYzuKZcj1pCuZYA4R/UNNtCCGJtKvcL9OCabCYPBsiVkP5EfEiWb5sp2mnbBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:56:58.720902Z","signed_message":"canonical_sha256_bytes"},"source_id":"0902.1155","source_kind":"arxiv","source_version":5}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:33b43dbec89b3a5566c951212b151cf2a86ddc9aef49ab9d643f1683cdafcf7a","sha256:2dc6e64c73bce4f45b2909bf6a9d07a398a65dc80cd3d84d980e7709229fd9bc"],"state_sha256":"4f1490e5fb2016caa1a23454022db8a0e0a56e5525f9b55d97f2b107d33842f5"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"8HqTUGqg9BwSpiq1vC1A670aokDz7fmzCrUExm4GVIm2T9IXPLgRW4NdjuDIfM7bReyD/vPzmQZeclJ0ClWJDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-24T05:08:24.142849Z","bundle_sha256":"c3602b8f3e4afc60bec0a37ca6500defb208a4420e8898b74c9c77280a859b9f"}}