{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:D4SEG3RUVXLH5N3LSFNFV2WRZW","short_pith_number":"pith:D4SEG3RU","canonical_record":{"source":{"id":"1508.00209","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2015-08-02T08:38:08Z","cross_cats_sorted":[],"title_canon_sha256":"9b7c3dcae3f174055e9b15714f3254089368364278720ba72486a2a1e5d70863","abstract_canon_sha256":"604861be6f30f8712cd0f9df884572dc6590984ccc438fd7e551f21571463e9b"},"schema_version":"1.0"},"canonical_sha256":"1f24436e34add67eb76b915a5aead1cdb3e46a5ee31287eb253d192fba90c9c5","source":{"kind":"arxiv","id":"1508.00209","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1508.00209","created_at":"2026-05-18T01:35:58Z"},{"alias_kind":"arxiv_version","alias_value":"1508.00209v1","created_at":"2026-05-18T01:35:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1508.00209","created_at":"2026-05-18T01:35:58Z"},{"alias_kind":"pith_short_12","alias_value":"D4SEG3RUVXLH","created_at":"2026-05-18T12:29:17Z"},{"alias_kind":"pith_short_16","alias_value":"D4SEG3RUVXLH5N3L","created_at":"2026-05-18T12:29:17Z"},{"alias_kind":"pith_short_8","alias_value":"D4SEG3RU","created_at":"2026-05-18T12:29:17Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:D4SEG3RUVXLH5N3LSFNFV2WRZW","target":"record","payload":{"canonical_record":{"source":{"id":"1508.00209","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2015-08-02T08:38:08Z","cross_cats_sorted":[],"title_canon_sha256":"9b7c3dcae3f174055e9b15714f3254089368364278720ba72486a2a1e5d70863","abstract_canon_sha256":"604861be6f30f8712cd0f9df884572dc6590984ccc438fd7e551f21571463e9b"},"schema_version":"1.0"},"canonical_sha256":"1f24436e34add67eb76b915a5aead1cdb3e46a5ee31287eb253d192fba90c9c5","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:35:58.707862Z","signature_b64":"BuKFwoXiAmCHDu6bnojhO85WBbTVXCi6f7j54ncG+AnuZLQbnoTnOjSOM/QqUBVfx1XftTx4jfOwxOkqOG/xBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1f24436e34add67eb76b915a5aead1cdb3e46a5ee31287eb253d192fba90c9c5","last_reissued_at":"2026-05-18T01:35:58.707177Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:35:58.707177Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1508.00209","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":"2026-05-18T01:35:58Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"DRyNs1Mokujsq+YtAFYcLrPqLmo3YE28jdNmi6Zo7R1m/hbAOYE4GofQc8bZqG4e7A4ZMowJCvm3qWwwgudsDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-21T03:31:08.637642Z"},"content_sha256":"212bc9887713a6b8a6d70db54776c70bd52dcd1d65b269c87516deea42d45f63","schema_version":"1.0","event_id":"sha256:212bc9887713a6b8a6d70db54776c70bd52dcd1d65b269c87516deea42d45f63"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:D4SEG3RUVXLH5N3LSFNFV2WRZW","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Spaces of matrices of constant rank and uniform vector bundles","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Paolo Menegatti, Philippe Ellia","submitted_at":"2015-08-02T08:38:08Z","abstract_excerpt":"Let A be a k-vector space of dimension a. A subvector space M of End(A) is said to be of rank r if every non-zero f in M has rank r. The problem considered in this paper is to determine l(r;a) the maximal dimension of a rank r subspace of End(A). Known results are reviewed in the language of vector bundles. Some new results are proved and a conjecture is made."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1508.00209","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":"2026-05-18T01:35:58Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"gvip48I0J9LdNM1PVYwsoo3uxiYbTN2ZdAJlO+n3KUzf8sfHNpV00zTfq+sUxhhlAsYe693bsWmbq2C8QZ7fDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-21T03:31:08.638013Z"},"content_sha256":"47216a02480840354c7b5232a65e1c9d2d09d29da9f4f33105c2bc0d57e9505e","schema_version":"1.0","event_id":"sha256:47216a02480840354c7b5232a65e1c9d2d09d29da9f4f33105c2bc0d57e9505e"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/D4SEG3RUVXLH5N3LSFNFV2WRZW/bundle.json","state_url":"https://pith.science/pith/D4SEG3RUVXLH5N3LSFNFV2WRZW/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/D4SEG3RUVXLH5N3LSFNFV2WRZW/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":"2026-06-21T03:31:08Z","links":{"resolver":"https://pith.science/pith/D4SEG3RUVXLH5N3LSFNFV2WRZW","bundle":"https://pith.science/pith/D4SEG3RUVXLH5N3LSFNFV2WRZW/bundle.json","state":"https://pith.science/pith/D4SEG3RUVXLH5N3LSFNFV2WRZW/state.json","well_known_bundle":"https://pith.science/.well-known/pith/D4SEG3RUVXLH5N3LSFNFV2WRZW/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:D4SEG3RUVXLH5N3LSFNFV2WRZW","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":"604861be6f30f8712cd0f9df884572dc6590984ccc438fd7e551f21571463e9b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2015-08-02T08:38:08Z","title_canon_sha256":"9b7c3dcae3f174055e9b15714f3254089368364278720ba72486a2a1e5d70863"},"schema_version":"1.0","source":{"id":"1508.00209","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1508.00209","created_at":"2026-05-18T01:35:58Z"},{"alias_kind":"arxiv_version","alias_value":"1508.00209v1","created_at":"2026-05-18T01:35:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1508.00209","created_at":"2026-05-18T01:35:58Z"},{"alias_kind":"pith_short_12","alias_value":"D4SEG3RUVXLH","created_at":"2026-05-18T12:29:17Z"},{"alias_kind":"pith_short_16","alias_value":"D4SEG3RUVXLH5N3L","created_at":"2026-05-18T12:29:17Z"},{"alias_kind":"pith_short_8","alias_value":"D4SEG3RU","created_at":"2026-05-18T12:29:17Z"}],"graph_snapshots":[{"event_id":"sha256:47216a02480840354c7b5232a65e1c9d2d09d29da9f4f33105c2bc0d57e9505e","target":"graph","created_at":"2026-05-18T01:35:58Z","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":"Let A be a k-vector space of dimension a. A subvector space M of End(A) is said to be of rank r if every non-zero f in M has rank r. The problem considered in this paper is to determine l(r;a) the maximal dimension of a rank r subspace of End(A). Known results are reviewed in the language of vector bundles. Some new results are proved and a conjecture is made.","authors_text":"Paolo Menegatti, Philippe Ellia","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2015-08-02T08:38:08Z","title":"Spaces of matrices of constant rank and uniform vector bundles"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1508.00209","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":"sha256:212bc9887713a6b8a6d70db54776c70bd52dcd1d65b269c87516deea42d45f63","target":"record","created_at":"2026-05-18T01:35:58Z","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":"604861be6f30f8712cd0f9df884572dc6590984ccc438fd7e551f21571463e9b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2015-08-02T08:38:08Z","title_canon_sha256":"9b7c3dcae3f174055e9b15714f3254089368364278720ba72486a2a1e5d70863"},"schema_version":"1.0","source":{"id":"1508.00209","kind":"arxiv","version":1}},"canonical_sha256":"1f24436e34add67eb76b915a5aead1cdb3e46a5ee31287eb253d192fba90c9c5","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1f24436e34add67eb76b915a5aead1cdb3e46a5ee31287eb253d192fba90c9c5","first_computed_at":"2026-05-18T01:35:58.707177Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:35:58.707177Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"BuKFwoXiAmCHDu6bnojhO85WBbTVXCi6f7j54ncG+AnuZLQbnoTnOjSOM/QqUBVfx1XftTx4jfOwxOkqOG/xBw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:35:58.707862Z","signed_message":"canonical_sha256_bytes"},"source_id":"1508.00209","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:212bc9887713a6b8a6d70db54776c70bd52dcd1d65b269c87516deea42d45f63","sha256:47216a02480840354c7b5232a65e1c9d2d09d29da9f4f33105c2bc0d57e9505e"],"state_sha256":"a38d6eebc1ccf2ab3b996d767d26123818d57f5f5418aa020faa763631dda330"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"4yrkbQG8pM8QjrttjBDGbEuomgl53o6MJl6cnagrtUOuHsCdSuarM6WcVzcjL+Yj6SqDWEDo+gDAoCaAmFnKDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-21T03:31:08.639949Z","bundle_sha256":"e62b67fbbd7359226f8d7ee7c944df4a94a584b54bea8461f56199189870cb10"}}