{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:SX2VJ45WNA37JK4QFFFGO5QZ5O","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":"46b39a97cbf53127058b72caef593e51f4e191ef89cd2974137e311ffac3333b","cross_cats_sorted":["math.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2018-02-17T20:00:16Z","title_canon_sha256":"0d36eeff59f4b2568de29d4d92a5226622c3127f0a7e4041f163565ca579f854"},"schema_version":"1.0","source":{"id":"1802.06281","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1802.06281","created_at":"2026-05-18T00:23:03Z"},{"alias_kind":"arxiv_version","alias_value":"1802.06281v1","created_at":"2026-05-18T00:23:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1802.06281","created_at":"2026-05-18T00:23:03Z"},{"alias_kind":"pith_short_12","alias_value":"SX2VJ45WNA37","created_at":"2026-05-18T12:32:53Z"},{"alias_kind":"pith_short_16","alias_value":"SX2VJ45WNA37JK4Q","created_at":"2026-05-18T12:32:53Z"},{"alias_kind":"pith_short_8","alias_value":"SX2VJ45W","created_at":"2026-05-18T12:32:53Z"}],"graph_snapshots":[{"event_id":"sha256:5249190bc729ef783e04b00c3dd2c11cc2c99155486f3e37a4846abad533668e","target":"graph","created_at":"2026-05-18T00:23:03Z","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":"A semigroup S containing a zero element is said to be 0-left cancellative if st = sr \\neq 0 implies that t = r. Given such an S we build an inverse semigroup H(S), called the inverse hull of S. Motivated by the study of certain C*-algebras associated to H(S) (a task that we will address in a subsequent article) we carry out a detailed analysis of the spectrum of the idempotent semilattice E(S) of H(S) with a special interest in identifying the ultra-characters. In order to produce examples of characters on E(S), we introduce the notion of \"strings\" in a semigroup, attempting to make sense of t","authors_text":"B. Steinberg, R. Exel","cross_cats":["math.DS"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2018-02-17T20:00:16Z","title":"Representations of the inverse hull of a 0-left cancellative semigroup"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1802.06281","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":"sha256:7ed327f2f83194c3595d3c3408e51b8790ab3893ba67be4f7348a0628efb9a63","target":"record","created_at":"2026-05-18T00:23:03Z","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":"46b39a97cbf53127058b72caef593e51f4e191ef89cd2974137e311ffac3333b","cross_cats_sorted":["math.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2018-02-17T20:00:16Z","title_canon_sha256":"0d36eeff59f4b2568de29d4d92a5226622c3127f0a7e4041f163565ca579f854"},"schema_version":"1.0","source":{"id":"1802.06281","kind":"arxiv","version":1}},"canonical_sha256":"95f554f3b66837f4ab90294a677619ebacf113ee3be1593e3473b94796a77008","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"95f554f3b66837f4ab90294a677619ebacf113ee3be1593e3473b94796a77008","first_computed_at":"2026-05-18T00:23:03.808889Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:23:03.808889Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"KzlnkqHhNuMwe8svkFUWWMB0bC69Uzj5p2PZDlxI3Kns6aIMZKnG7yydN1/G3DitmwY0+cAnYwdHyRqkQXfaDA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:23:03.809421Z","signed_message":"canonical_sha256_bytes"},"source_id":"1802.06281","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7ed327f2f83194c3595d3c3408e51b8790ab3893ba67be4f7348a0628efb9a63","sha256:5249190bc729ef783e04b00c3dd2c11cc2c99155486f3e37a4846abad533668e"],"state_sha256":"a29dbcf1d0dd743e130cb64ec3dc9ec2bea90cc21e40937c81117e3058b7b5dd"}