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Let $\\bar{\\cal L}$ denote the set of points of ${\\rm PG}(r,q^2)$ lying on the extended lines of $\\cal L$.\n  An $m$-cover $\\cal L$ of ${\\rm PG}(r,q)$ is an $(r-2)$-dual $m$-cover if there are two possibilities for the number of lines of $\\cal L$ contained in an $(r-2)$-space of ${\\rm PG}(r,q"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1807.00156","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-06-30T11:39:04Z","cross_cats_sorted":[],"title_canon_sha256":"71b124468163c70616e61c7aa4538c2f38e3f1cbd6ae3a3cab227e89a699a3b2","abstract_canon_sha256":"09fd07ccd570e2dae3013659e1fe0625a637ccd5286325f62c4f911201b739f6"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:11:55.872280Z","signature_b64":"cyifito3J6eY2zhkbdbb6X+Q/SJxxt70FWA5apeMWhF1gH/ylvCRwZcr4mHesQ2evD+2whHrCiEt0ntLRH1UCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7ebdcedf7aca43725c95ef6e4492bc363d2033ab7dd32308ae9c342938a8c022","last_reissued_at":"2026-05-18T00:11:55.871729Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:11:55.871729Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On line covers of finite projective and polar spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"A. 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Let $\\bar{\\cal L}$ denote the set of points of ${\\rm PG}(r,q^2)$ lying on the extended lines of $\\cal L$.\n  An $m$-cover $\\cal L$ of ${\\rm PG}(r,q)$ is an $(r-2)$-dual $m$-cover if there are two possibilities for the number of lines of $\\cal L$ contained in an $(r-2)$-space of ${\\rm PG}(r,q"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1807.00156","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1807.00156","created_at":"2026-05-18T00:11:55.871825+00:00"},{"alias_kind":"arxiv_version","alias_value":"1807.00156v1","created_at":"2026-05-18T00:11:55.871825+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1807.00156","created_at":"2026-05-18T00:11:55.871825+00:00"},{"alias_kind":"pith_short_12","alias_value":"P2645X32ZJBX","created_at":"2026-05-18T12:32:43.782077+00:00"},{"alias_kind":"pith_short_16","alias_value":"P2645X32ZJBXEXEV","created_at":"2026-05-18T12:32:43.782077+00:00"},{"alias_kind":"pith_short_8","alias_value":"P2645X32","created_at":"2026-05-18T12:32:43.782077+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/P2645X32ZJBXEXEV55XEJEV4GY","json":"https://pith.science/pith/P2645X32ZJBXEXEV55XEJEV4GY.json","graph_json":"https://pith.science/api/pith-number/P2645X32ZJBXEXEV55XEJEV4GY/graph.json","events_json":"https://pith.science/api/pith-number/P2645X32ZJBXEXEV55XEJEV4GY/events.json","paper":"https://pith.science/paper/P2645X32"},"agent_actions":{"view_html":"https://pith.science/pith/P2645X32ZJBXEXEV55XEJEV4GY","download_json":"https://pith.science/pith/P2645X32ZJBXEXEV55XEJEV4GY.json","view_paper":"https://pith.science/paper/P2645X32","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1807.00156&json=true","fetch_graph":"https://pith.science/api/pith-number/P2645X32ZJBXEXEV55XEJEV4GY/graph.json","fetch_events":"https://pith.science/api/pith-number/P2645X32ZJBXEXEV55XEJEV4GY/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/P2645X32ZJBXEXEV55XEJEV4GY/action/timestamp_anchor","attest_storage":"https://pith.science/pith/P2645X32ZJBXEXEV55XEJEV4GY/action/storage_attestation","attest_author":"https://pith.science/pith/P2645X32ZJBXEXEV55XEJEV4GY/action/author_attestation","sign_citation":"https://pith.science/pith/P2645X32ZJBXEXEV55XEJEV4GY/action/citation_signature","submit_replication":"https://pith.science/pith/P2645X32ZJBXEXEV55XEJEV4GY/action/replication_record"}},"created_at":"2026-05-18T00:11:55.871825+00:00","updated_at":"2026-05-18T00:11:55.871825+00:00"}