{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:5T3REIEZG3C77FW6QS67RNLA6R","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":"0abee93382148922acb65a8590ec4e45cb332bc6090b18cfb33048c492709f01","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2018-02-07T13:49:40Z","title_canon_sha256":"e4b0043259127bf1312a3fe7a715390e694d55605764d7c851932b36613d7c43"},"schema_version":"1.0","source":{"id":"1802.02420","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1802.02420","created_at":"2026-05-17T23:56:38Z"},{"alias_kind":"arxiv_version","alias_value":"1802.02420v2","created_at":"2026-05-17T23:56:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1802.02420","created_at":"2026-05-17T23:56:38Z"},{"alias_kind":"pith_short_12","alias_value":"5T3REIEZG3C7","created_at":"2026-05-18T12:32:08Z"},{"alias_kind":"pith_short_16","alias_value":"5T3REIEZG3C77FW6","created_at":"2026-05-18T12:32:08Z"},{"alias_kind":"pith_short_8","alias_value":"5T3REIEZ","created_at":"2026-05-18T12:32:08Z"}],"graph_snapshots":[{"event_id":"sha256:c7e417d5887c368961cee4c13b0976398050df7f1de3295b2a28ca9e710e376d","target":"graph","created_at":"2026-05-17T23:56:38Z","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":"The set of idempotents of any semigroup carries the structure of a biordered set, which contains a great deal of information concerning the idempotent generated subsemigroup of the semigroup in question. This leads to the construction of a free idempotent generated semigroup $\\mathsf{IG}(\\mathcal{E})$ - the `free-est' semigroup with a given biordered set $\\mathcal{E}$ of idempotents. We show that when $\\mathcal{E}$ is finite, the word problem for $\\mathsf{IG}(\\mathcal{E})$ is equivalent to a family of constraint satisfaction problems involving rational subsets of direct products of pairs of ma","authors_text":"Igor Dolinka, Victoria Gould, Yang Dandan","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2018-02-07T13:49:40Z","title":"A group-theoretical interpretation of the word problem for free idempotent generated semigroups"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1802.02420","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":"sha256:29bd430af78ddbbdf9dc90bd20dac64afb9f417a3c97dce734dfe0784677974c","target":"record","created_at":"2026-05-17T23:56:38Z","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":"0abee93382148922acb65a8590ec4e45cb332bc6090b18cfb33048c492709f01","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2018-02-07T13:49:40Z","title_canon_sha256":"e4b0043259127bf1312a3fe7a715390e694d55605764d7c851932b36613d7c43"},"schema_version":"1.0","source":{"id":"1802.02420","kind":"arxiv","version":2}},"canonical_sha256":"ecf712209936c5ff96de84bdf8b560f45c217f30abd025678409fca6fb2cc6b6","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ecf712209936c5ff96de84bdf8b560f45c217f30abd025678409fca6fb2cc6b6","first_computed_at":"2026-05-17T23:56:38.796354Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:56:38.796354Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"3N1HaT0+MoWdhn6EIgojYHJ8WyrnbklMpgKiYE+iKRgXXRbmpyrKgQzS4jITLFnNG+IbqK14t+z+9hxJxAn+Ag==","signature_status":"signed_v1","signed_at":"2026-05-17T23:56:38.796907Z","signed_message":"canonical_sha256_bytes"},"source_id":"1802.02420","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:29bd430af78ddbbdf9dc90bd20dac64afb9f417a3c97dce734dfe0784677974c","sha256:c7e417d5887c368961cee4c13b0976398050df7f1de3295b2a28ca9e710e376d"],"state_sha256":"0414ef3e6157da834b3ba1801d31e5df710b5387c4a6e7a4f0a392eb6d5d8bcd"}