{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:PAC3J5JE6IL7HYGO7JBFHWWU47","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":"018ec88aaa126fc16c9b3ffd18062997cc72d891328f72871abbf261fa3bd461","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-01-28T14:41:00Z","title_canon_sha256":"65ac39f9c4dbb075d6d1f796efda83ea769aa7f8fd935e45b3e202e0ae707214"},"schema_version":"1.0","source":{"id":"1601.07775","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1601.07775","created_at":"2026-05-18T01:21:42Z"},{"alias_kind":"arxiv_version","alias_value":"1601.07775v1","created_at":"2026-05-18T01:21:42Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1601.07775","created_at":"2026-05-18T01:21:42Z"},{"alias_kind":"pith_short_12","alias_value":"PAC3J5JE6IL7","created_at":"2026-05-18T12:30:39Z"},{"alias_kind":"pith_short_16","alias_value":"PAC3J5JE6IL7HYGO","created_at":"2026-05-18T12:30:39Z"},{"alias_kind":"pith_short_8","alias_value":"PAC3J5JE","created_at":"2026-05-18T12:30:39Z"}],"graph_snapshots":[{"event_id":"sha256:bfb4ca04166eddb599aa290ed45ba77781963784609754b7aa8704dfddaa9953","target":"graph","created_at":"2026-05-18T01:21:42Z","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 $D=(V,A)$ be a digraph and consider an arc subset $A'\\subseteq A$ and an exhaustive mapping $\\phi: A\\to A'$ such that\n  $(i)$ the set of heads of $A'$ is $H(A')=V$; $(ii)$ the map fixes the elements of $A'$, that is, $\\phi|A'=Id$, and for every vertex $j\\in V$, $\\phi(\\omega^-(j))\\subset \\omega^-(j)\\cap A'$.\n  Then, {\\it the partial line digraph} of $D$, denoted by $\\mathcal{L}_{(A',\\phi)}D $ (for short $\\mathcal{L}D$ if the pair $(A', \\phi)$ is clear from the context), is the digraph with vertex set $V (\\mathcal{L}D)=A'$ and set of arcs $A(\\mathcal{L}D) = \\{(ij, \\phi(j,k)) : (j,k)\\in A\\}.$","authors_text":"Camino Balbuena, Hortensia Galeana-S\\'anchez, Mukuy-kak Guevara","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-01-28T14:41:00Z","title":"About $(k,l)$-kernels, semikernels and Grundy functions in partial line digraphs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1601.07775","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":"sha256:93e6e35c518b508413b030bcace72250521ebd5bd02bd02fdfa7f283b297f278","target":"record","created_at":"2026-05-18T01:21:42Z","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":"018ec88aaa126fc16c9b3ffd18062997cc72d891328f72871abbf261fa3bd461","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-01-28T14:41:00Z","title_canon_sha256":"65ac39f9c4dbb075d6d1f796efda83ea769aa7f8fd935e45b3e202e0ae707214"},"schema_version":"1.0","source":{"id":"1601.07775","kind":"arxiv","version":1}},"canonical_sha256":"7805b4f524f217f3e0cefa4253dad4e7e65719faba12edbce993044829f026cc","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7805b4f524f217f3e0cefa4253dad4e7e65719faba12edbce993044829f026cc","first_computed_at":"2026-05-18T01:21:42.244556Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:21:42.244556Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"7Gms3d0q25uDjFPVDoX26XfbbeDVNNalSxa03lzqDmp9257S8rlcnJNhCneIFn8Hh57apPbtVEMiOoAuPAvOCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:21:42.244928Z","signed_message":"canonical_sha256_bytes"},"source_id":"1601.07775","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:93e6e35c518b508413b030bcace72250521ebd5bd02bd02fdfa7f283b297f278","sha256:bfb4ca04166eddb599aa290ed45ba77781963784609754b7aa8704dfddaa9953"],"state_sha256":"6bdb42a58929ba6eb2ff9cf1d2a47a310f4180f5ee6466d0547b404d02220ced"}