{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:OJAHS3QAWY3YU7Z7V4CEHFIIXR","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":"23f113778b47c35481b210ccda68c656875eda1f6e33dd8f070f9de7ceb9e295","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-12-03T09:33:33Z","title_canon_sha256":"3932004948314354458d21b4ed5c2283ce0998e77d2f30c7c84d37991f231daf"},"schema_version":"1.0","source":{"id":"1512.01009","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1512.01009","created_at":"2026-05-18T01:25:23Z"},{"alias_kind":"arxiv_version","alias_value":"1512.01009v1","created_at":"2026-05-18T01:25:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1512.01009","created_at":"2026-05-18T01:25:23Z"},{"alias_kind":"pith_short_12","alias_value":"OJAHS3QAWY3Y","created_at":"2026-05-18T12:29:34Z"},{"alias_kind":"pith_short_16","alias_value":"OJAHS3QAWY3YU7Z7","created_at":"2026-05-18T12:29:34Z"},{"alias_kind":"pith_short_8","alias_value":"OJAHS3QA","created_at":"2026-05-18T12:29:34Z"}],"graph_snapshots":[{"event_id":"sha256:9b597c40fc89f2432ec106b0f506157d09e28ce667dab3fbffe88e0ef6a76c15","target":"graph","created_at":"2026-05-18T01:25:23Z","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 $W$ denote the $n$-dimensional affine space over the finite field $\\mathbb F_q$. We prove here a Bollob\\'as-type upper bound in the case of the set of affine subspaces. We give a construction of a pair of families of affine subspaces, which shows that our result is almost sharp.","authors_text":"G\\'abor Heged\\\"us","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-12-03T09:33:33Z","title":"A Bollob\\'as-type theorem for affine subspaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1512.01009","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":"sha256:3e71bd31740e8a0a0453c45edda5673febc0b8666d220deb46c9dad52698acfe","target":"record","created_at":"2026-05-18T01:25:23Z","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":"23f113778b47c35481b210ccda68c656875eda1f6e33dd8f070f9de7ceb9e295","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-12-03T09:33:33Z","title_canon_sha256":"3932004948314354458d21b4ed5c2283ce0998e77d2f30c7c84d37991f231daf"},"schema_version":"1.0","source":{"id":"1512.01009","kind":"arxiv","version":1}},"canonical_sha256":"7240796e00b6378a7f3faf04439508bc41fd46bac14b73e1f44ea2b22d5135d6","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7240796e00b6378a7f3faf04439508bc41fd46bac14b73e1f44ea2b22d5135d6","first_computed_at":"2026-05-18T01:25:23.614872Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:25:23.614872Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"WFlji2fAncdlJ4Yej++rKbwPSS3XAcf0PrqgdhPJx68uIz9LIh0JuVf1DiIqgCkqZXIYjX51PoSTSZq37z8WDA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:25:23.615355Z","signed_message":"canonical_sha256_bytes"},"source_id":"1512.01009","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3e71bd31740e8a0a0453c45edda5673febc0b8666d220deb46c9dad52698acfe","sha256:9b597c40fc89f2432ec106b0f506157d09e28ce667dab3fbffe88e0ef6a76c15"],"state_sha256":"2e6535864fec4267d77f5e405b564b2fd9b743516b2733c8cdba24e19f28385c"}