{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:MM6HAWAES34RJXNOUHLLEJFUCO","short_pith_number":"pith:MM6HAWAE","canonical_record":{"source":{"id":"1302.4568","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2013-02-19T10:29:15Z","cross_cats_sorted":[],"title_canon_sha256":"4208688e7ea592e1d3641a926c1d9a389f223d927cd556b14519820c813af084","abstract_canon_sha256":"ea0b9da22ad2af8c079c9f737eb2a06802cb7d4d4274bde24af7a63f16929fec"},"schema_version":"1.0"},"canonical_sha256":"633c70580496f914ddaea1d6b224b4138a6fdbdd3ec08513e66919c693e1bbf2","source":{"kind":"arxiv","id":"1302.4568","version":4},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1302.4568","created_at":"2026-05-18T03:19:01Z"},{"alias_kind":"arxiv_version","alias_value":"1302.4568v4","created_at":"2026-05-18T03:19:01Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1302.4568","created_at":"2026-05-18T03:19:01Z"},{"alias_kind":"pith_short_12","alias_value":"MM6HAWAES34R","created_at":"2026-05-18T12:27:52Z"},{"alias_kind":"pith_short_16","alias_value":"MM6HAWAES34RJXNO","created_at":"2026-05-18T12:27:52Z"},{"alias_kind":"pith_short_8","alias_value":"MM6HAWAE","created_at":"2026-05-18T12:27:52Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:MM6HAWAES34RJXNOUHLLEJFUCO","target":"record","payload":{"canonical_record":{"source":{"id":"1302.4568","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2013-02-19T10:29:15Z","cross_cats_sorted":[],"title_canon_sha256":"4208688e7ea592e1d3641a926c1d9a389f223d927cd556b14519820c813af084","abstract_canon_sha256":"ea0b9da22ad2af8c079c9f737eb2a06802cb7d4d4274bde24af7a63f16929fec"},"schema_version":"1.0"},"canonical_sha256":"633c70580496f914ddaea1d6b224b4138a6fdbdd3ec08513e66919c693e1bbf2","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:19:01.316912Z","signature_b64":"K631M+ATLL3zMIpsooqIrVr+gw9AJ9CeULeCaeMjLjSon2favui7121BLT8krQNHuLYWVjIn/zFyJa+H9In7Dw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"633c70580496f914ddaea1d6b224b4138a6fdbdd3ec08513e66919c693e1bbf2","last_reissued_at":"2026-05-18T03:19:01.316332Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:19:01.316332Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1302.4568","source_version":4,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:19:01Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"E/KEv1jSvqcts0MlNmpFnYPuMd7NtOCSOE5icrrLKiFwzLqWJftYIe5sWFA/vvDMg8JAe7GO15koWsmBXZ6kCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T04:57:15.942049Z"},"content_sha256":"3cd27ef0e2dd477626ae4b3f0d2f0d0359712da22a5c93df26b20ae74236f0da","schema_version":"1.0","event_id":"sha256:3cd27ef0e2dd477626ae4b3f0d2f0d0359712da22a5c93df26b20ae74236f0da"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:MM6HAWAES34RJXNOUHLLEJFUCO","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Soft Games","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.LO","authors_text":"\\.Irfan Deli, Naim \\c{C}a\\u{g}man","submitted_at":"2013-02-19T10:29:15Z","abstract_excerpt":"In this work, after given the definition of soft sets and their basic operations we define two person soft games which can apply to problems contain vagueness and uncertainty. We then give four solution methods of the games which are soft saddle points, soft lover and soft upper values, soft dominated strategies and soft Nash equilibrium. We also give an example from the real world which shows that the methods can be successfully applied to a financial problem. Finally, we extended the two person soft games to n-person soft games."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1302.4568","kind":"arxiv","version":4},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:19:01Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"hhiqw40TgyJFmGYE7svHkXWCeJ5DGu9UwjrosbTAVFT/eVUGhm/mpLkuvSamhAXbKcegdMQPBS4qaQbl1nn1Bw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T04:57:15.942711Z"},"content_sha256":"a3e75b047ef16ed4c48f30a7dd8fcca499c9b226ea42a6ccc4c3cc387881951d","schema_version":"1.0","event_id":"sha256:a3e75b047ef16ed4c48f30a7dd8fcca499c9b226ea42a6ccc4c3cc387881951d"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/MM6HAWAES34RJXNOUHLLEJFUCO/bundle.json","state_url":"https://pith.science/pith/MM6HAWAES34RJXNOUHLLEJFUCO/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/MM6HAWAES34RJXNOUHLLEJFUCO/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-07T04:57:15Z","links":{"resolver":"https://pith.science/pith/MM6HAWAES34RJXNOUHLLEJFUCO","bundle":"https://pith.science/pith/MM6HAWAES34RJXNOUHLLEJFUCO/bundle.json","state":"https://pith.science/pith/MM6HAWAES34RJXNOUHLLEJFUCO/state.json","well_known_bundle":"https://pith.science/.well-known/pith/MM6HAWAES34RJXNOUHLLEJFUCO/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:MM6HAWAES34RJXNOUHLLEJFUCO","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":"ea0b9da22ad2af8c079c9f737eb2a06802cb7d4d4274bde24af7a63f16929fec","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2013-02-19T10:29:15Z","title_canon_sha256":"4208688e7ea592e1d3641a926c1d9a389f223d927cd556b14519820c813af084"},"schema_version":"1.0","source":{"id":"1302.4568","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1302.4568","created_at":"2026-05-18T03:19:01Z"},{"alias_kind":"arxiv_version","alias_value":"1302.4568v4","created_at":"2026-05-18T03:19:01Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1302.4568","created_at":"2026-05-18T03:19:01Z"},{"alias_kind":"pith_short_12","alias_value":"MM6HAWAES34R","created_at":"2026-05-18T12:27:52Z"},{"alias_kind":"pith_short_16","alias_value":"MM6HAWAES34RJXNO","created_at":"2026-05-18T12:27:52Z"},{"alias_kind":"pith_short_8","alias_value":"MM6HAWAE","created_at":"2026-05-18T12:27:52Z"}],"graph_snapshots":[{"event_id":"sha256:a3e75b047ef16ed4c48f30a7dd8fcca499c9b226ea42a6ccc4c3cc387881951d","target":"graph","created_at":"2026-05-18T03:19:01Z","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":"In this work, after given the definition of soft sets and their basic operations we define two person soft games which can apply to problems contain vagueness and uncertainty. We then give four solution methods of the games which are soft saddle points, soft lover and soft upper values, soft dominated strategies and soft Nash equilibrium. We also give an example from the real world which shows that the methods can be successfully applied to a financial problem. Finally, we extended the two person soft games to n-person soft games.","authors_text":"\\.Irfan Deli, Naim \\c{C}a\\u{g}man","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2013-02-19T10:29:15Z","title":"Soft Games"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1302.4568","kind":"arxiv","version":4},"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":"sha256:3cd27ef0e2dd477626ae4b3f0d2f0d0359712da22a5c93df26b20ae74236f0da","target":"record","created_at":"2026-05-18T03:19:01Z","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":"ea0b9da22ad2af8c079c9f737eb2a06802cb7d4d4274bde24af7a63f16929fec","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2013-02-19T10:29:15Z","title_canon_sha256":"4208688e7ea592e1d3641a926c1d9a389f223d927cd556b14519820c813af084"},"schema_version":"1.0","source":{"id":"1302.4568","kind":"arxiv","version":4}},"canonical_sha256":"633c70580496f914ddaea1d6b224b4138a6fdbdd3ec08513e66919c693e1bbf2","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"633c70580496f914ddaea1d6b224b4138a6fdbdd3ec08513e66919c693e1bbf2","first_computed_at":"2026-05-18T03:19:01.316332Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:19:01.316332Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"K631M+ATLL3zMIpsooqIrVr+gw9AJ9CeULeCaeMjLjSon2favui7121BLT8krQNHuLYWVjIn/zFyJa+H9In7Dw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:19:01.316912Z","signed_message":"canonical_sha256_bytes"},"source_id":"1302.4568","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3cd27ef0e2dd477626ae4b3f0d2f0d0359712da22a5c93df26b20ae74236f0da","sha256:a3e75b047ef16ed4c48f30a7dd8fcca499c9b226ea42a6ccc4c3cc387881951d"],"state_sha256":"9fcd37654207bb48842d974656a909caf861336e3f39b44aed358fb4cc54d59b"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"JS+hlU7Gp0teNOCWXHUEVOzVD1duoAhe4lXv7vYA45EvzaDx1tSOXNCTDZsg6Ocy5eqS5MnhNcA+Nyt9jfahCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-07T04:57:15.945186Z","bundle_sha256":"27b09bca27b5b2d68cd493eb2eea3969e67d37b0210f06eba17ee269ccc2ba9b"}}