{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:AB5LVHTO2COYBZYAJ2WH43UHEA","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":"347c3da963d0e18be17a8c7756dbaf823ba3f07d68bf2388aa1c252aafdf80ca","cross_cats_sorted":["cs.AI","cs.DM","cs.IT","math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2017-04-18T17:46:58Z","title_canon_sha256":"1d8461522c1c04bbdcef0d54dee080cdeb35acfa74949e32819cc1de8d9d1fcb"},"schema_version":"1.0","source":{"id":"1704.05443","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1704.05443","created_at":"2026-05-18T00:46:09Z"},{"alias_kind":"arxiv_version","alias_value":"1704.05443v1","created_at":"2026-05-18T00:46:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1704.05443","created_at":"2026-05-18T00:46:09Z"},{"alias_kind":"pith_short_12","alias_value":"AB5LVHTO2COY","created_at":"2026-05-18T12:31:05Z"},{"alias_kind":"pith_short_16","alias_value":"AB5LVHTO2COYBZYA","created_at":"2026-05-18T12:31:05Z"},{"alias_kind":"pith_short_8","alias_value":"AB5LVHTO","created_at":"2026-05-18T12:31:05Z"}],"graph_snapshots":[{"event_id":"sha256:adf916b7de608633d47e819781ef702f3d17f7c9baecb982eaca100e72188588","target":"graph","created_at":"2026-05-18T00:46:09Z","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":"Not all approximations arise from information systems. The problem of fitting approximations, subjected to some rules (and related data), to information systems in a rough scheme of things is known as the \\emph{inverse problem}. The inverse problem is more general than the duality (or abstract representation) problems and was introduced by the present author in her earlier papers. From the practical perspective, a few (as opposed to one) theoretical frameworks may be suitable for formulating the problem itself. \\emph{Granular operator spaces} have been recently introduced and investigated by t","authors_text":"A. Mani","cross_cats":["cs.AI","cs.DM","cs.IT","math.IT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2017-04-18T17:46:58Z","title":"Approximations from Anywhere and General Rough Sets"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1704.05443","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":"sha256:2303a3b04ecc7c46978e3c09e12236aa695830c2ed5f9fb5117b39e33f54a1ba","target":"record","created_at":"2026-05-18T00:46:09Z","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":"347c3da963d0e18be17a8c7756dbaf823ba3f07d68bf2388aa1c252aafdf80ca","cross_cats_sorted":["cs.AI","cs.DM","cs.IT","math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2017-04-18T17:46:58Z","title_canon_sha256":"1d8461522c1c04bbdcef0d54dee080cdeb35acfa74949e32819cc1de8d9d1fcb"},"schema_version":"1.0","source":{"id":"1704.05443","kind":"arxiv","version":1}},"canonical_sha256":"007aba9e6ed09d80e7004eac7e6e8720133e18b8253d22d89aaf908c9e382fa1","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"007aba9e6ed09d80e7004eac7e6e8720133e18b8253d22d89aaf908c9e382fa1","first_computed_at":"2026-05-18T00:46:09.224358Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:46:09.224358Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"mA5rRfZf7uHUiUVDkUaREa89Lglx3D5Xbv9WDwi63nIoeiIV2KR/M16uaRMd7p4s9HhCzdI2MFUlRE5TArYVAA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:46:09.224786Z","signed_message":"canonical_sha256_bytes"},"source_id":"1704.05443","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2303a3b04ecc7c46978e3c09e12236aa695830c2ed5f9fb5117b39e33f54a1ba","sha256:adf916b7de608633d47e819781ef702f3d17f7c9baecb982eaca100e72188588"],"state_sha256":"ae5cf07fad7c85addc68ac0e5adbfb04ba5f59baee1f4ec4f55b76c336859dd0"}