{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:1999:D7J5NFRYR3GK7YP5R6B4JTJPUT","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":"0b13fe4a75a719cbc34483e3b2c1913925fab02fa01a61acc30cf031bb9c7847","cross_cats_sorted":["math.AT","math.CO"],"license":"","primary_cat":"math.GT","submitted_at":"1999-11-21T00:32:48Z","title_canon_sha256":"770b878b76a9a48c5c5207b1e56523d0a95656dbd8319d01cdbcee99f5000bc7"},"schema_version":"1.0","source":{"id":"math/9911158","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/9911158","created_at":"2026-05-18T01:25:40Z"},{"alias_kind":"arxiv_version","alias_value":"math/9911158v1","created_at":"2026-05-18T01:25:40Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/9911158","created_at":"2026-05-18T01:25:40Z"},{"alias_kind":"pith_short_12","alias_value":"D7J5NFRYR3GK","created_at":"2026-05-18T12:25:49Z"},{"alias_kind":"pith_short_16","alias_value":"D7J5NFRYR3GK7YP5","created_at":"2026-05-18T12:25:49Z"},{"alias_kind":"pith_short_8","alias_value":"D7J5NFRY","created_at":"2026-05-18T12:25:49Z"}],"graph_snapshots":[{"event_id":"sha256:f5b856d2a2ff2c2c09ac53b39d54be85cfa146a82cda275d04c50c263b470efd","target":"graph","created_at":"2026-05-18T01:25:40Z","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":"Matroid bundles, introduced by MacPherson, are combinatorial analogues of real vector bundles. This paper sets up the foundations of matroid bundles, and defines a natural transformation from isomorphism classes of real vector bundles to isomorphism classes of matroid bundles, as well as a transformation from matroid bundles to spherical quasifibrations. The poset of oriented matroids of a fixed rank classifies matroid bundles, and the above transformations give a splitting from topology to combinatorics back to topology. This shows the mod 2 cohomology of the poset of rank k oriented matroids","authors_text":"James F. Davis, Laura Anderson","cross_cats":["math.AT","math.CO"],"headline":"","license":"","primary_cat":"math.GT","submitted_at":"1999-11-21T00:32:48Z","title":"Mod 2 cohomology of combinatorial Grassmannians"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/9911158","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:f932aef625b36781efa264407cc5d18c4db34f6ea710ea460c95c4119fa3aebd","target":"record","created_at":"2026-05-18T01:25:40Z","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":"0b13fe4a75a719cbc34483e3b2c1913925fab02fa01a61acc30cf031bb9c7847","cross_cats_sorted":["math.AT","math.CO"],"license":"","primary_cat":"math.GT","submitted_at":"1999-11-21T00:32:48Z","title_canon_sha256":"770b878b76a9a48c5c5207b1e56523d0a95656dbd8319d01cdbcee99f5000bc7"},"schema_version":"1.0","source":{"id":"math/9911158","kind":"arxiv","version":1}},"canonical_sha256":"1fd3d696388eccafe1fd8f83c4cd2fa4e738b479b4185f3476d2d730f95a586b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1fd3d696388eccafe1fd8f83c4cd2fa4e738b479b4185f3476d2d730f95a586b","first_computed_at":"2026-05-18T01:25:40.166346Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:25:40.166346Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"bSI8bdfBX0m5fBVjbDLZDvwTGFdmcTUS1LaswPoRwyQIdhVo0pn6Q/SHGvFCPu7m0JHd5wrRMAZVTP8iyA5kDg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:25:40.167027Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/9911158","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f932aef625b36781efa264407cc5d18c4db34f6ea710ea460c95c4119fa3aebd","sha256:f5b856d2a2ff2c2c09ac53b39d54be85cfa146a82cda275d04c50c263b470efd"],"state_sha256":"89c191b0c6722ef8bc1b5891b59a9012de296a8f16075958e97be3e5849cafe7"}