{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:3BRRK4PNLNRWBZJ2QCJL74LM7R","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":"1526e0756611d710473caf8399c78c968efd9603fd25d3ba799bf34a1bdc3179","cross_cats_sorted":["math.KT","math.OA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2016-06-13T09:04:20Z","title_canon_sha256":"1c6ae55644b84ef7bf27a8881d7f56c9a0f196bd0ec9197944a9d17d7151ef9a"},"schema_version":"1.0","source":{"id":"1606.03862","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1606.03862","created_at":"2026-05-18T00:49:46Z"},{"alias_kind":"arxiv_version","alias_value":"1606.03862v3","created_at":"2026-05-18T00:49:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1606.03862","created_at":"2026-05-18T00:49:46Z"},{"alias_kind":"pith_short_12","alias_value":"3BRRK4PNLNRW","created_at":"2026-05-18T12:29:55Z"},{"alias_kind":"pith_short_16","alias_value":"3BRRK4PNLNRWBZJ2","created_at":"2026-05-18T12:29:55Z"},{"alias_kind":"pith_short_8","alias_value":"3BRRK4PN","created_at":"2026-05-18T12:29:55Z"}],"graph_snapshots":[{"event_id":"sha256:15ba2f0ebeb5b74c0b6d408ceea7a19639c662876cdfc25c9382b8e8c4617854","target":"graph","created_at":"2026-05-18T00:49:46Z","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":"Graph monoids arise naturally in the study of non-stable K-theory of graph C*-algebras and Leavitt path algebras. They play also an important role in the current approaches to the realization problem for von Neumann regular rings. In this paper, we characterize when a finitely generated conical refinement monoid can be represented as a graph monoid. The characterization is expressed in terms of the behavior of the structural maps of the associated $I$-system at the free primes of the monoid.","authors_text":"E. Pardo, P. Ara","cross_cats":["math.KT","math.OA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2016-06-13T09:04:20Z","title":"Representing finitely generated refinement monoids as graph monoids"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1606.03862","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":"sha256:91e095222623c511b25873c99d3eb3d11676ba3dc50a597ea9172f3468e81811","target":"record","created_at":"2026-05-18T00:49:46Z","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":"1526e0756611d710473caf8399c78c968efd9603fd25d3ba799bf34a1bdc3179","cross_cats_sorted":["math.KT","math.OA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2016-06-13T09:04:20Z","title_canon_sha256":"1c6ae55644b84ef7bf27a8881d7f56c9a0f196bd0ec9197944a9d17d7151ef9a"},"schema_version":"1.0","source":{"id":"1606.03862","kind":"arxiv","version":3}},"canonical_sha256":"d8631571ed5b6360e53a8092bff16cfc6776d8533831f025f98beb600ed492a6","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d8631571ed5b6360e53a8092bff16cfc6776d8533831f025f98beb600ed492a6","first_computed_at":"2026-05-18T00:49:46.973119Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:49:46.973119Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"/CFhpH8oEtCPSjCNZ+Zz/6oFkelb0FTXouKJ54sIlPl8rHKgXxpQtquHrY3uIawM1VzhaWFl9RFmznHBG+UsCg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:49:46.973759Z","signed_message":"canonical_sha256_bytes"},"source_id":"1606.03862","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:91e095222623c511b25873c99d3eb3d11676ba3dc50a597ea9172f3468e81811","sha256:15ba2f0ebeb5b74c0b6d408ceea7a19639c662876cdfc25c9382b8e8c4617854"],"state_sha256":"3c79c2d546354f1c725f07fd8accf7fc5b8e0513c9f28207d0e7de36011f94c4"}