{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2020:LJHXCU3X6CFVPU7F6LFEAH6Z7I","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":"7e732a094b915ef016b2064fb81b715ad0104f0e486778d9b12efa37973265ff","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2020-10-10T15:23:58Z","title_canon_sha256":"afc0bf686372156fa79b7d75b33c503a23d71738606ac298a6930efe90f1021e"},"schema_version":"1.0","source":{"id":"2010.05030","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2010.05030","created_at":"2026-07-05T01:42:02Z"},{"alias_kind":"arxiv_version","alias_value":"2010.05030v1","created_at":"2026-07-05T01:42:02Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2010.05030","created_at":"2026-07-05T01:42:02Z"},{"alias_kind":"pith_short_12","alias_value":"LJHXCU3X6CFV","created_at":"2026-07-05T01:42:02Z"},{"alias_kind":"pith_short_16","alias_value":"LJHXCU3X6CFVPU7F","created_at":"2026-07-05T01:42:02Z"},{"alias_kind":"pith_short_8","alias_value":"LJHXCU3X","created_at":"2026-07-05T01:42:02Z"}],"graph_snapshots":[{"event_id":"sha256:e0cfddcb1d2c874f2944f1b19ec2e88dbc177abd82371b390c8bdd68e6e8bd27","target":"graph","created_at":"2026-07-05T01:42:02Z","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/2010.05030/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Let $\\mathscr{P}$ be a symplectic polar space over a finite field $\\mathbb{F}_q$, and $\\mathscr{P}_m$ denote the set of all $m$-dimensional subspaces in $\\mathscr{P}$. We say a $t$-intersecting subfamily of $\\mathscr{P}_m$ is trivial if there exists a $t$-dimensional subspace contained in each member of this family. In this paper, we determine the structure of maximum sized non-trivial $t$-intersecting subfamilies of $\\mathscr{P}_m$.","authors_text":"Benjian Lv, Kaishun Wang, Tian Yao","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2020-10-10T15:23:58Z","title":"Non-trivial $t$-intersecting families for symplectic polar spaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2010.05030","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:e98759514a11bc2d33c58ccdf7272a094818416ddbbb63a2b2f617e0336a60fc","target":"record","created_at":"2026-07-05T01:42:02Z","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":"7e732a094b915ef016b2064fb81b715ad0104f0e486778d9b12efa37973265ff","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2020-10-10T15:23:58Z","title_canon_sha256":"afc0bf686372156fa79b7d75b33c503a23d71738606ac298a6930efe90f1021e"},"schema_version":"1.0","source":{"id":"2010.05030","kind":"arxiv","version":1}},"canonical_sha256":"5a4f715377f08b57d3e5f2ca401fd9fa127fe29bac147a1a2b92ab695d191830","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5a4f715377f08b57d3e5f2ca401fd9fa127fe29bac147a1a2b92ab695d191830","first_computed_at":"2026-07-05T01:42:02.132646Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T01:42:02.132646Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"MKRwKqDX1UEImi+0u07MSbTuz3XhqPfIEVSN21JxftABmuO/h8PMBcWrCqxfQR62CEpin9XoxgqxtI7WYtjnDw==","signature_status":"signed_v1","signed_at":"2026-07-05T01:42:02.133031Z","signed_message":"canonical_sha256_bytes"},"source_id":"2010.05030","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e98759514a11bc2d33c58ccdf7272a094818416ddbbb63a2b2f617e0336a60fc","sha256:e0cfddcb1d2c874f2944f1b19ec2e88dbc177abd82371b390c8bdd68e6e8bd27"],"state_sha256":"d3b971c6ca4fe4f94880e7c3a321fb6886fca7d43a4e9e4775614ce6953465d3"}