{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:4IJEW4RCHKZMQCPXOJN24K45FQ","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":"c9dbe0d2deb41aba68c30bbf2d3f2d3209d36f641776f5fada4f90542af5916f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2013-03-06T14:59:48Z","title_canon_sha256":"75c3f179f1435b22e4ada66f7887898bff00fd897f5522d7c35a10be628a575b"},"schema_version":"1.0","source":{"id":"1303.1344","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1303.1344","created_at":"2026-05-18T03:31:43Z"},{"alias_kind":"arxiv_version","alias_value":"1303.1344v1","created_at":"2026-05-18T03:31:43Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1303.1344","created_at":"2026-05-18T03:31:43Z"},{"alias_kind":"pith_short_12","alias_value":"4IJEW4RCHKZM","created_at":"2026-05-18T12:27:34Z"},{"alias_kind":"pith_short_16","alias_value":"4IJEW4RCHKZMQCPX","created_at":"2026-05-18T12:27:34Z"},{"alias_kind":"pith_short_8","alias_value":"4IJEW4RC","created_at":"2026-05-18T12:27:34Z"}],"graph_snapshots":[{"event_id":"sha256:2e7ca1dfe90ed109cf80680341ae17be616c3355bb1032f68d0d3bbf7223f22f","target":"graph","created_at":"2026-05-18T03:31:43Z","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 have studied the concept of bipolarity of information in the soft sets. We have defined bipolar soft sets and basic operations of union, intersection and complementation for bipolar soft sets. Examples of bipolar soft sets and an application of bipolar soft sets in a decision making problem with general algorithms have also been presented at the end.","authors_text":"Muhammad Shabir, Munazza Naz","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2013-03-06T14:59:48Z","title":"On Bipolar Soft Sets"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1303.1344","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":"sha256:4745e23e0df3c71ec2a27a061ea0404c2008fcecb0ac47412a683cd104c7300b","target":"record","created_at":"2026-05-18T03:31:43Z","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":"c9dbe0d2deb41aba68c30bbf2d3f2d3209d36f641776f5fada4f90542af5916f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2013-03-06T14:59:48Z","title_canon_sha256":"75c3f179f1435b22e4ada66f7887898bff00fd897f5522d7c35a10be628a575b"},"schema_version":"1.0","source":{"id":"1303.1344","kind":"arxiv","version":1}},"canonical_sha256":"e2124b72223ab2c809f7725bae2b9d2c035ece4857bcc8498abbf05cded8ff77","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e2124b72223ab2c809f7725bae2b9d2c035ece4857bcc8498abbf05cded8ff77","first_computed_at":"2026-05-18T03:31:43.792271Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:31:43.792271Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"aPLaTCLL1/GVilEr18UQoRCwSDdnzwmZq9dWQ4JU8EFjJibZ5+gFqalfg0n8Y0iXvoeYqhRw7AjWCUFwomQ4Ag==","signature_status":"signed_v1","signed_at":"2026-05-18T03:31:43.792990Z","signed_message":"canonical_sha256_bytes"},"source_id":"1303.1344","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4745e23e0df3c71ec2a27a061ea0404c2008fcecb0ac47412a683cd104c7300b","sha256:2e7ca1dfe90ed109cf80680341ae17be616c3355bb1032f68d0d3bbf7223f22f"],"state_sha256":"d1bdd4e136fb07b3b2dc3a8cf40f98cba443afe23bf97000d403b32970b7283f"}