{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:AUDICVDCULNREGECK3PSCLG2RX","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":"3c266875bacf4b48b1a193e884a604d0237027c994cd46c56b23ac5cce2bb8dd","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-03-27T16:54:32Z","title_canon_sha256":"6382912d3db88d7b331278f66e3251b1a560a63e9cff82dfccfc94a9dc414095"},"schema_version":"1.0","source":{"id":"1803.10180","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1803.10180","created_at":"2026-05-17T23:56:15Z"},{"alias_kind":"arxiv_version","alias_value":"1803.10180v2","created_at":"2026-05-17T23:56:15Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1803.10180","created_at":"2026-05-17T23:56:15Z"},{"alias_kind":"pith_short_12","alias_value":"AUDICVDCULNR","created_at":"2026-05-18T12:32:13Z"},{"alias_kind":"pith_short_16","alias_value":"AUDICVDCULNREGEC","created_at":"2026-05-18T12:32:13Z"},{"alias_kind":"pith_short_8","alias_value":"AUDICVDC","created_at":"2026-05-18T12:32:13Z"}],"graph_snapshots":[{"event_id":"sha256:592ba89daed27474a2d77380699fe5996689d7249251c749c902e7653eca9271","target":"graph","created_at":"2026-05-17T23:56:15Z","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":"A vector space partition $\\mathcal{P}$ in $\\mathbb{F}_q^v$ is a set of subspaces such that every $1$-dimensional subspace of $\\mathbb{F}_q^v$ is contained in exactly one element of $\\mathcal{P}$. Replacing \"every point\" by \"every $t$-dimensional subspace\", we generalize this notion to vector space $t$-partitions and study their properties. There is a close connection to subspace codes and some problems are even interesting and unsolved for the set case $q=1$.","authors_text":"Daniel Heinlein, Michael Kiermaier, Sascha Kurz, Thomas Honold","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-03-27T16:54:32Z","title":"Generalized vector space partitions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1803.10180","kind":"arxiv","version":2},"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:a237a259a7c2e93c174c3663cf27e1ed850df93d335b6c8eace04d394f361511","target":"record","created_at":"2026-05-17T23:56:15Z","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":"3c266875bacf4b48b1a193e884a604d0237027c994cd46c56b23ac5cce2bb8dd","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-03-27T16:54:32Z","title_canon_sha256":"6382912d3db88d7b331278f66e3251b1a560a63e9cff82dfccfc94a9dc414095"},"schema_version":"1.0","source":{"id":"1803.10180","kind":"arxiv","version":2}},"canonical_sha256":"0506815462a2db12188256df212cda8dd9a299a1397654fe94b702ce9794f36f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0506815462a2db12188256df212cda8dd9a299a1397654fe94b702ce9794f36f","first_computed_at":"2026-05-17T23:56:15.262113Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:56:15.262113Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"9GtaOnZHoenN2pFWc4MLq1ZSJDzKTD82oQgeaU48Uc9e5e5ZFYcgH20gGLXStfZzbStko8h/ivlCCuBV30wNBw==","signature_status":"signed_v1","signed_at":"2026-05-17T23:56:15.262787Z","signed_message":"canonical_sha256_bytes"},"source_id":"1803.10180","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a237a259a7c2e93c174c3663cf27e1ed850df93d335b6c8eace04d394f361511","sha256:592ba89daed27474a2d77380699fe5996689d7249251c749c902e7653eca9271"],"state_sha256":"61fe9f5d6b871c6055f30bf8617764d19fa8f57a91bc7236aa6031f135a9cfff"}