{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:6656GN7JJJ6YFNVYNMBBTDKBXJ","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":"9a59c63c77141c0c25c3375398834bbf59f0b4fb6e9d11e6a0bcf658e09131e1","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2012-09-12T11:46:22Z","title_canon_sha256":"d119f87b6a60e7f6bbf49fdcb0a920eba3c3973dbebff584a6c07f742e58e062"},"schema_version":"1.0","source":{"id":"1209.2578","kind":"arxiv","version":5}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1209.2578","created_at":"2026-05-18T01:19:03Z"},{"alias_kind":"arxiv_version","alias_value":"1209.2578v5","created_at":"2026-05-18T01:19:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1209.2578","created_at":"2026-05-18T01:19:03Z"},{"alias_kind":"pith_short_12","alias_value":"6656GN7JJJ6Y","created_at":"2026-05-18T12:26:56Z"},{"alias_kind":"pith_short_16","alias_value":"6656GN7JJJ6YFNVY","created_at":"2026-05-18T12:26:56Z"},{"alias_kind":"pith_short_8","alias_value":"6656GN7J","created_at":"2026-05-18T12:26:56Z"}],"graph_snapshots":[{"event_id":"sha256:22ff9a6f52b95b420d0aa2f13b5d81cde6b1a495593254ff17f523893b884ec4","target":"graph","created_at":"2026-05-18T01:19:03Z","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":"We consider partitioned graphs, by which we mean finite strongly connected directed graphs with a partitioned edge set $ {\\mathcal E} ={\\mathcal E}^- \\cup{\\mathcal E}^+$. With additionally given a relation $\\mathcal R$ between the edges in ${\\mathcal E}^-$ and the edges in $\\mathcal E^+ $, and denoting the vertex set of the graph by ${\\frak P}$, we speak of an an ${\\mathcal R}$-graph ${\\mathcal G}_{\\mathcal R}({\\frak P},{\\mathcal E}^-,{\\mathcal E}^+) $. From ${\\mathcal R}$-graphs ${\\mathcal G}_{\\mathcal R}({\\frak P},{\\mathcal E}^-,{\\mathcal E}^+) $ we construct semigroups (with zero) ${\\mathca","authors_text":"Wolfgang Krieger","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2012-09-12T11:46:22Z","title":"On subshift presentations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1209.2578","kind":"arxiv","version":5},"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:b4b1d5f0f9b2c7612457ff9a1f87cdb076693dcdab6d93e43f2c1e92bf2d1701","target":"record","created_at":"2026-05-18T01:19:03Z","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":"9a59c63c77141c0c25c3375398834bbf59f0b4fb6e9d11e6a0bcf658e09131e1","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2012-09-12T11:46:22Z","title_canon_sha256":"d119f87b6a60e7f6bbf49fdcb0a920eba3c3973dbebff584a6c07f742e58e062"},"schema_version":"1.0","source":{"id":"1209.2578","kind":"arxiv","version":5}},"canonical_sha256":"f7bbe337e94a7d82b6b86b02198d41ba6a5a6f7c281deefe129b75cde6c41d8e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f7bbe337e94a7d82b6b86b02198d41ba6a5a6f7c281deefe129b75cde6c41d8e","first_computed_at":"2026-05-18T01:19:03.852260Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:19:03.852260Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"nq5GsX8l7X281vJQwTSYoqMyzCXKxUNSywAjPI91zY04b+lc0TBRY/ep4KgiN7X4d4c1twN1vd2NO8u399HYDA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:19:03.852777Z","signed_message":"canonical_sha256_bytes"},"source_id":"1209.2578","source_kind":"arxiv","source_version":5}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b4b1d5f0f9b2c7612457ff9a1f87cdb076693dcdab6d93e43f2c1e92bf2d1701","sha256:22ff9a6f52b95b420d0aa2f13b5d81cde6b1a495593254ff17f523893b884ec4"],"state_sha256":"a61b864025419054c2451e5523c525d897fbee4f577218f8646c6e9cf5e37b23"}