{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:A7YCG4AZGP63YMGL5WZ7B4SMSJ","short_pith_number":"pith:A7YCG4AZ","canonical_record":{"source":{"id":"1810.03485","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-10-08T14:19:11Z","cross_cats_sorted":["math.GR"],"title_canon_sha256":"b8a8bff91c69e726137cc80fb9b2b0e7c62d5f1518877a812d28117dd003afc2","abstract_canon_sha256":"c9ff56dac86e1809a12dbd80941e50e63b9e782a1d13aff129ae63583d62b7e3"},"schema_version":"1.0"},"canonical_sha256":"07f023701933fdbc30cbedb3f0f24c926fd019f9a853e5a8b9939d729f49b2db","source":{"kind":"arxiv","id":"1810.03485","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1810.03485","created_at":"2026-05-17T23:44:48Z"},{"alias_kind":"arxiv_version","alias_value":"1810.03485v3","created_at":"2026-05-17T23:44:48Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1810.03485","created_at":"2026-05-17T23:44:48Z"},{"alias_kind":"pith_short_12","alias_value":"A7YCG4AZGP63","created_at":"2026-05-18T12:32:13Z"},{"alias_kind":"pith_short_16","alias_value":"A7YCG4AZGP63YMGL","created_at":"2026-05-18T12:32:13Z"},{"alias_kind":"pith_short_8","alias_value":"A7YCG4AZ","created_at":"2026-05-18T12:32:13Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:A7YCG4AZGP63YMGL5WZ7B4SMSJ","target":"record","payload":{"canonical_record":{"source":{"id":"1810.03485","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-10-08T14:19:11Z","cross_cats_sorted":["math.GR"],"title_canon_sha256":"b8a8bff91c69e726137cc80fb9b2b0e7c62d5f1518877a812d28117dd003afc2","abstract_canon_sha256":"c9ff56dac86e1809a12dbd80941e50e63b9e782a1d13aff129ae63583d62b7e3"},"schema_version":"1.0"},"canonical_sha256":"07f023701933fdbc30cbedb3f0f24c926fd019f9a853e5a8b9939d729f49b2db","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:44:48.014560Z","signature_b64":"HOuDCVL6/TR1J5SLbhfxBJruZlKqkLqGVMnQpS/PS/dqqhB6Wq210RTT5TXXu9XippQb9Kh+1BC/Yc8tZR9gDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"07f023701933fdbc30cbedb3f0f24c926fd019f9a853e5a8b9939d729f49b2db","last_reissued_at":"2026-05-17T23:44:48.013921Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:44:48.013921Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1810.03485","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-17T23:44:48Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"FBhjHsPTGn9FcVIo5DT4537TGE5m9gcKAFJB9Ni9Je+VBmJR/UfEXOd1THe57qZ57cQuBaKcmvhdopMxHSefCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-08T09:37:50.420094Z"},"content_sha256":"b5424da242dd28ca5005663c1c1ff0107a1b25bbfd0e37205297fc3f5aed595c","schema_version":"1.0","event_id":"sha256:b5424da242dd28ca5005663c1c1ff0107a1b25bbfd0e37205297fc3f5aed595c"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:A7YCG4AZGP63YMGL5WZ7B4SMSJ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Smallest cyclically covering subspaces of $\\mathbb{F}_q^n$, and lower bounds in Isbell's conjecture","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GR"],"primary_cat":"math.CO","authors_text":"David Ellis, Peter Cameron, William Raynaud","submitted_at":"2018-10-08T14:19:11Z","abstract_excerpt":"For a prime power $q$ and a positive integer $n$, we say a subspace $U$ of ${\\mathbb{F}_q^n}$ is {\\em cyclically covering} if the union of the cyclic shifts of $U$ is equal to $\\mathbb{F}_q^n$. We investigate the problem of determining the minimum possible dimension of a cyclically covering subspace of $\\mathbb{F}_q^n$. (This is a natural generalisation of a problem posed in 1991 by the first author.) We prove several upper and lower bounds, and for each fixed $q$, we answer the question completely for infinitely many values of $n$ (which take the form of certain geometric series). Our results"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1810.03485","kind":"arxiv","version":3},"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":"2026-05-17T23:44:48Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"M98iWTmDf/e9BPpXwGLTvGejbZ1zOlxlmLmWR0xI18bYy8pxeqBqzRvq4eq6qaoGDqp4yY51T/6Mo8YPFfsLBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-08T09:37:50.420803Z"},"content_sha256":"0e55112fc31186fa797ecc08857718812e489f9523fa727a06a4cb1c1c5fd296","schema_version":"1.0","event_id":"sha256:0e55112fc31186fa797ecc08857718812e489f9523fa727a06a4cb1c1c5fd296"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/A7YCG4AZGP63YMGL5WZ7B4SMSJ/bundle.json","state_url":"https://pith.science/pith/A7YCG4AZGP63YMGL5WZ7B4SMSJ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/A7YCG4AZGP63YMGL5WZ7B4SMSJ/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":"2026-06-08T09:37:50Z","links":{"resolver":"https://pith.science/pith/A7YCG4AZGP63YMGL5WZ7B4SMSJ","bundle":"https://pith.science/pith/A7YCG4AZGP63YMGL5WZ7B4SMSJ/bundle.json","state":"https://pith.science/pith/A7YCG4AZGP63YMGL5WZ7B4SMSJ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/A7YCG4AZGP63YMGL5WZ7B4SMSJ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:A7YCG4AZGP63YMGL5WZ7B4SMSJ","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":"c9ff56dac86e1809a12dbd80941e50e63b9e782a1d13aff129ae63583d62b7e3","cross_cats_sorted":["math.GR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-10-08T14:19:11Z","title_canon_sha256":"b8a8bff91c69e726137cc80fb9b2b0e7c62d5f1518877a812d28117dd003afc2"},"schema_version":"1.0","source":{"id":"1810.03485","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1810.03485","created_at":"2026-05-17T23:44:48Z"},{"alias_kind":"arxiv_version","alias_value":"1810.03485v3","created_at":"2026-05-17T23:44:48Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1810.03485","created_at":"2026-05-17T23:44:48Z"},{"alias_kind":"pith_short_12","alias_value":"A7YCG4AZGP63","created_at":"2026-05-18T12:32:13Z"},{"alias_kind":"pith_short_16","alias_value":"A7YCG4AZGP63YMGL","created_at":"2026-05-18T12:32:13Z"},{"alias_kind":"pith_short_8","alias_value":"A7YCG4AZ","created_at":"2026-05-18T12:32:13Z"}],"graph_snapshots":[{"event_id":"sha256:0e55112fc31186fa797ecc08857718812e489f9523fa727a06a4cb1c1c5fd296","target":"graph","created_at":"2026-05-17T23:44:48Z","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":"For a prime power $q$ and a positive integer $n$, we say a subspace $U$ of ${\\mathbb{F}_q^n}$ is {\\em cyclically covering} if the union of the cyclic shifts of $U$ is equal to $\\mathbb{F}_q^n$. We investigate the problem of determining the minimum possible dimension of a cyclically covering subspace of $\\mathbb{F}_q^n$. (This is a natural generalisation of a problem posed in 1991 by the first author.) We prove several upper and lower bounds, and for each fixed $q$, we answer the question completely for infinitely many values of $n$ (which take the form of certain geometric series). Our results","authors_text":"David Ellis, Peter Cameron, William Raynaud","cross_cats":["math.GR"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-10-08T14:19:11Z","title":"Smallest cyclically covering subspaces of $\\mathbb{F}_q^n$, and lower bounds in Isbell's conjecture"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1810.03485","kind":"arxiv","version":3},"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:b5424da242dd28ca5005663c1c1ff0107a1b25bbfd0e37205297fc3f5aed595c","target":"record","created_at":"2026-05-17T23:44:48Z","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":"c9ff56dac86e1809a12dbd80941e50e63b9e782a1d13aff129ae63583d62b7e3","cross_cats_sorted":["math.GR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-10-08T14:19:11Z","title_canon_sha256":"b8a8bff91c69e726137cc80fb9b2b0e7c62d5f1518877a812d28117dd003afc2"},"schema_version":"1.0","source":{"id":"1810.03485","kind":"arxiv","version":3}},"canonical_sha256":"07f023701933fdbc30cbedb3f0f24c926fd019f9a853e5a8b9939d729f49b2db","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"07f023701933fdbc30cbedb3f0f24c926fd019f9a853e5a8b9939d729f49b2db","first_computed_at":"2026-05-17T23:44:48.013921Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:44:48.013921Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"HOuDCVL6/TR1J5SLbhfxBJruZlKqkLqGVMnQpS/PS/dqqhB6Wq210RTT5TXXu9XippQb9Kh+1BC/Yc8tZR9gDg==","signature_status":"signed_v1","signed_at":"2026-05-17T23:44:48.014560Z","signed_message":"canonical_sha256_bytes"},"source_id":"1810.03485","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b5424da242dd28ca5005663c1c1ff0107a1b25bbfd0e37205297fc3f5aed595c","sha256:0e55112fc31186fa797ecc08857718812e489f9523fa727a06a4cb1c1c5fd296"],"state_sha256":"b78b058b10e47e9c57d75e2567b7e4c83c0cae9c3cb344de4cd3d6e5e42dfb80"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"mUdOEB9Unbx5+H3rVSVd6RKnyhYSPoE0C4+bZ8K6dDpkEcdpqSW1a6zLnYl7C3ozJXvQA3AkML626wlXKrHyCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-08T09:37:50.424824Z","bundle_sha256":"9e839b1e3aa5e400aa75053a6f254271c0bb434d7a9fd1aa09d712bbc1f32beb"}}