{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:2JNCKFWJDHU6SR2R3VNRD2LBY5","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":"661786c4b6ca7f62ebcc5fc3be2e4d970522457929087d3debe591758e6d2ad0","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2013-04-05T08:26:12Z","title_canon_sha256":"1e2712208333b85168829aa3658477d2c11b31f2b44c90eb19fdda19df84a240"},"schema_version":"1.0","source":{"id":"1304.1637","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1304.1637","created_at":"2026-05-18T03:28:55Z"},{"alias_kind":"arxiv_version","alias_value":"1304.1637v1","created_at":"2026-05-18T03:28:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1304.1637","created_at":"2026-05-18T03:28:55Z"},{"alias_kind":"pith_short_12","alias_value":"2JNCKFWJDHU6","created_at":"2026-05-18T12:27:30Z"},{"alias_kind":"pith_short_16","alias_value":"2JNCKFWJDHU6SR2R","created_at":"2026-05-18T12:27:30Z"},{"alias_kind":"pith_short_8","alias_value":"2JNCKFWJ","created_at":"2026-05-18T12:27:30Z"}],"graph_snapshots":[{"event_id":"sha256:ca3ae584ee6ec196b665507a0699424e36feed5eb11796871a6e9fe755222e3c","target":"graph","created_at":"2026-05-18T03:28:55Z","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 study the freeness problem for matrix semigroups. We show that the freeness problem is decidable for upper-triangular $2\\times 2$ matrices with rational entries when the products are restricted to certain bounded languages.","authors_text":"\\'Emilie Charlier, Juha Honkala","cross_cats":["math.CO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2013-04-05T08:26:12Z","title":"The freeness problem over matrix semigroups and bounded languages"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1304.1637","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":"sha256:9f0828c8fc21eebd2ad46df81ea36bd0cb84ebd0618c8ae1e425fc049fddf23c","target":"record","created_at":"2026-05-18T03:28:55Z","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":"661786c4b6ca7f62ebcc5fc3be2e4d970522457929087d3debe591758e6d2ad0","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2013-04-05T08:26:12Z","title_canon_sha256":"1e2712208333b85168829aa3658477d2c11b31f2b44c90eb19fdda19df84a240"},"schema_version":"1.0","source":{"id":"1304.1637","kind":"arxiv","version":1}},"canonical_sha256":"d25a2516c919e9e94751dd5b11e961c75752f05ea8345993d7e98e487f4ae02c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d25a2516c919e9e94751dd5b11e961c75752f05ea8345993d7e98e487f4ae02c","first_computed_at":"2026-05-18T03:28:55.107744Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:28:55.107744Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"uvDTAyarFT+Ts3jUgIu+WxpZtZYylK/b7UCoQbLliWfBnWaiy5gmDA8XhdTfWkktC61x7l1I/hvYhAS/Bbs+AA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:28:55.108558Z","signed_message":"canonical_sha256_bytes"},"source_id":"1304.1637","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9f0828c8fc21eebd2ad46df81ea36bd0cb84ebd0618c8ae1e425fc049fddf23c","sha256:ca3ae584ee6ec196b665507a0699424e36feed5eb11796871a6e9fe755222e3c"],"state_sha256":"b0526ab740584ba1043636609e9475ba04c755b23fe7d991a226885832eaa75c"}