{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:U4JFYM6YV2UKWRXGLVUARBSCY3","short_pith_number":"pith:U4JFYM6Y","canonical_record":{"source":{"id":"1102.0169","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GM","submitted_at":"2011-02-01T14:46:50Z","cross_cats_sorted":[],"title_canon_sha256":"638e0b25b870e78d3fd032ef2712308586a11b6123fbffb85062ae9a2745d899","abstract_canon_sha256":"8a91af94c8518813131b8ab0fe8a5139d1de1a5bc85c969808c72bc9e527cd4f"},"schema_version":"1.0"},"canonical_sha256":"a7125c33d8aea8ab46e65d68088642c6e158656c87ce60b56572e2c22b1b9a4b","source":{"kind":"arxiv","id":"1102.0169","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1102.0169","created_at":"2026-05-18T04:30:13Z"},{"alias_kind":"arxiv_version","alias_value":"1102.0169v1","created_at":"2026-05-18T04:30:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1102.0169","created_at":"2026-05-18T04:30:13Z"},{"alias_kind":"pith_short_12","alias_value":"U4JFYM6YV2UK","created_at":"2026-05-18T12:26:42Z"},{"alias_kind":"pith_short_16","alias_value":"U4JFYM6YV2UKWRXG","created_at":"2026-05-18T12:26:42Z"},{"alias_kind":"pith_short_8","alias_value":"U4JFYM6Y","created_at":"2026-05-18T12:26:42Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:U4JFYM6YV2UKWRXGLVUARBSCY3","target":"record","payload":{"canonical_record":{"source":{"id":"1102.0169","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GM","submitted_at":"2011-02-01T14:46:50Z","cross_cats_sorted":[],"title_canon_sha256":"638e0b25b870e78d3fd032ef2712308586a11b6123fbffb85062ae9a2745d899","abstract_canon_sha256":"8a91af94c8518813131b8ab0fe8a5139d1de1a5bc85c969808c72bc9e527cd4f"},"schema_version":"1.0"},"canonical_sha256":"a7125c33d8aea8ab46e65d68088642c6e158656c87ce60b56572e2c22b1b9a4b","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:30:13.036772Z","signature_b64":"2XKOVBaD6LpUgjxzxo9THaLEEl6E0LAXhc25DcDf6JCZW3PJ5WbZKBumzCud6BSVuqD7lWJDZNq8re6E9CdwDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a7125c33d8aea8ab46e65d68088642c6e158656c87ce60b56572e2c22b1b9a4b","last_reissued_at":"2026-05-18T04:30:13.036350Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:30:13.036350Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1102.0169","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T04:30:13Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"07e0KQOfrdvCaj+C6rjWZgjjyrSzmJU1yrLnCmGTbxoC1YXY2bpbjsZV4KC+GiFDtmIz0uJdIaDID7fEo/wYCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-08T06:09:39.719126Z"},"content_sha256":"98ce029fa017d330b42de99a5d5e7181e9241c12117359e95934ce20a076246d","schema_version":"1.0","event_id":"sha256:98ce029fa017d330b42de99a5d5e7181e9241c12117359e95934ce20a076246d"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:U4JFYM6YV2UKWRXGLVUARBSCY3","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"(Alpha, Beta)-Fuzzy Subsemigroup and (Alpha, Beta)-Fuzzy Bi-ideal in Gamma- Semigroups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GM","authors_text":"Bijan Davvaz, Samit Kumar Majumder, Soumitra Kayal, Sujit Kumar Sardar","submitted_at":"2011-02-01T14:46:50Z","abstract_excerpt":"In this paper, using the idea of quasi-coincidence of a fuzzy point with a fuzzy set, the concepts of (epsilon, epsilon join q)- fuzzy subsemigroup and (epsilon, epsilon join q)- fuzzy bi-ideal in a gamma-semigroup have been introduced and some related properties have been investigated."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1102.0169","kind":"arxiv","version":1},"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":"2026-05-18T04:30:13Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"o7FirNOPeiTgdR2KC+54xSUA2wnM7s31eLBYvwSnQ6l1Tf/U+0AiKhcmiRuvemuM8gSfasoGtjsBAgCf7fEvBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-08T06:09:39.719841Z"},"content_sha256":"506af8b7e788feaf00b24a1349d76785609bb928155607265a40c20605596ca2","schema_version":"1.0","event_id":"sha256:506af8b7e788feaf00b24a1349d76785609bb928155607265a40c20605596ca2"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/U4JFYM6YV2UKWRXGLVUARBSCY3/bundle.json","state_url":"https://pith.science/pith/U4JFYM6YV2UKWRXGLVUARBSCY3/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/U4JFYM6YV2UKWRXGLVUARBSCY3/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":"2026-06-08T06:09:39Z","links":{"resolver":"https://pith.science/pith/U4JFYM6YV2UKWRXGLVUARBSCY3","bundle":"https://pith.science/pith/U4JFYM6YV2UKWRXGLVUARBSCY3/bundle.json","state":"https://pith.science/pith/U4JFYM6YV2UKWRXGLVUARBSCY3/state.json","well_known_bundle":"https://pith.science/.well-known/pith/U4JFYM6YV2UKWRXGLVUARBSCY3/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:U4JFYM6YV2UKWRXGLVUARBSCY3","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":"8a91af94c8518813131b8ab0fe8a5139d1de1a5bc85c969808c72bc9e527cd4f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GM","submitted_at":"2011-02-01T14:46:50Z","title_canon_sha256":"638e0b25b870e78d3fd032ef2712308586a11b6123fbffb85062ae9a2745d899"},"schema_version":"1.0","source":{"id":"1102.0169","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1102.0169","created_at":"2026-05-18T04:30:13Z"},{"alias_kind":"arxiv_version","alias_value":"1102.0169v1","created_at":"2026-05-18T04:30:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1102.0169","created_at":"2026-05-18T04:30:13Z"},{"alias_kind":"pith_short_12","alias_value":"U4JFYM6YV2UK","created_at":"2026-05-18T12:26:42Z"},{"alias_kind":"pith_short_16","alias_value":"U4JFYM6YV2UKWRXG","created_at":"2026-05-18T12:26:42Z"},{"alias_kind":"pith_short_8","alias_value":"U4JFYM6Y","created_at":"2026-05-18T12:26:42Z"}],"graph_snapshots":[{"event_id":"sha256:506af8b7e788feaf00b24a1349d76785609bb928155607265a40c20605596ca2","target":"graph","created_at":"2026-05-18T04:30:13Z","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 paper, using the idea of quasi-coincidence of a fuzzy point with a fuzzy set, the concepts of (epsilon, epsilon join q)- fuzzy subsemigroup and (epsilon, epsilon join q)- fuzzy bi-ideal in a gamma-semigroup have been introduced and some related properties have been investigated.","authors_text":"Bijan Davvaz, Samit Kumar Majumder, Soumitra Kayal, Sujit Kumar Sardar","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GM","submitted_at":"2011-02-01T14:46:50Z","title":"(Alpha, Beta)-Fuzzy Subsemigroup and (Alpha, Beta)-Fuzzy Bi-ideal in Gamma- Semigroups"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1102.0169","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":"sha256:98ce029fa017d330b42de99a5d5e7181e9241c12117359e95934ce20a076246d","target":"record","created_at":"2026-05-18T04:30:13Z","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":"8a91af94c8518813131b8ab0fe8a5139d1de1a5bc85c969808c72bc9e527cd4f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GM","submitted_at":"2011-02-01T14:46:50Z","title_canon_sha256":"638e0b25b870e78d3fd032ef2712308586a11b6123fbffb85062ae9a2745d899"},"schema_version":"1.0","source":{"id":"1102.0169","kind":"arxiv","version":1}},"canonical_sha256":"a7125c33d8aea8ab46e65d68088642c6e158656c87ce60b56572e2c22b1b9a4b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a7125c33d8aea8ab46e65d68088642c6e158656c87ce60b56572e2c22b1b9a4b","first_computed_at":"2026-05-18T04:30:13.036350Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:30:13.036350Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"2XKOVBaD6LpUgjxzxo9THaLEEl6E0LAXhc25DcDf6JCZW3PJ5WbZKBumzCud6BSVuqD7lWJDZNq8re6E9CdwDg==","signature_status":"signed_v1","signed_at":"2026-05-18T04:30:13.036772Z","signed_message":"canonical_sha256_bytes"},"source_id":"1102.0169","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:98ce029fa017d330b42de99a5d5e7181e9241c12117359e95934ce20a076246d","sha256:506af8b7e788feaf00b24a1349d76785609bb928155607265a40c20605596ca2"],"state_sha256":"214eff4cdf984badcd7e56ee2099149627ff00729a5771ed310b14ae0223b9b5"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"7TzTihZawHxRTxliKX1mvoDGliJD7XuzxMnIb5jZ1t8HAYjpTOqkMLVmeewUhW3qg3FMHJrSjO2QdLjqzg71AA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-08T06:09:39.723351Z","bundle_sha256":"db530f38450935d3eb3b485000861759b7606502ce78a42c65dd851e2811f05f"}}