{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:AP2IVCL6GBWE3BINFOM53OY34V","short_pith_number":"pith:AP2IVCL6","canonical_record":{"source":{"id":"1101.3081","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GM","submitted_at":"2011-01-16T17:30:30Z","cross_cats_sorted":[],"title_canon_sha256":"469b4e11a3c42dccd132bc8b2f9b8096f67c9d537d6e663c25c4482ae7f76ff0","abstract_canon_sha256":"9dd43fca90c3100c519ebb25176615103474e3668176057fc1d73f8f198ed4ea"},"schema_version":"1.0"},"canonical_sha256":"03f48a897e306c4d850d2b99ddbb1be54c6571349688f664de30278397bd5334","source":{"kind":"arxiv","id":"1101.3081","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1101.3081","created_at":"2026-05-18T04:30:25Z"},{"alias_kind":"arxiv_version","alias_value":"1101.3081v1","created_at":"2026-05-18T04:30:25Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1101.3081","created_at":"2026-05-18T04:30:25Z"},{"alias_kind":"pith_short_12","alias_value":"AP2IVCL6GBWE","created_at":"2026-05-18T12:26:24Z"},{"alias_kind":"pith_short_16","alias_value":"AP2IVCL6GBWE3BIN","created_at":"2026-05-18T12:26:24Z"},{"alias_kind":"pith_short_8","alias_value":"AP2IVCL6","created_at":"2026-05-18T12:26:24Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:AP2IVCL6GBWE3BINFOM53OY34V","target":"record","payload":{"canonical_record":{"source":{"id":"1101.3081","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GM","submitted_at":"2011-01-16T17:30:30Z","cross_cats_sorted":[],"title_canon_sha256":"469b4e11a3c42dccd132bc8b2f9b8096f67c9d537d6e663c25c4482ae7f76ff0","abstract_canon_sha256":"9dd43fca90c3100c519ebb25176615103474e3668176057fc1d73f8f198ed4ea"},"schema_version":"1.0"},"canonical_sha256":"03f48a897e306c4d850d2b99ddbb1be54c6571349688f664de30278397bd5334","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:30:25.229503Z","signature_b64":"7d7YmCWIiyyiyOvgFWDjhss/B5ugnyeZ/VGrQ49Hze1bzzSSlx2f3hJyim2qSQW+/I2hWjztGmmxLysMC7odDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"03f48a897e306c4d850d2b99ddbb1be54c6571349688f664de30278397bd5334","last_reissued_at":"2026-05-18T04:30:25.228924Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:30:25.228924Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1101.3081","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":"2026-05-18T04:30:25Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"48fxIQI58SrTW+honk38f/zanvOHfWhnPT3LEmFU4pd86znGcII4sj/bPItH0TlNu/4MHyWwVd7wHvvNTCOxDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T04:54:34.397540Z"},"content_sha256":"b4db8e6363c3610e33524eda52b39a78b6791775d2a0016f75eb3a5cd360e0a2","schema_version":"1.0","event_id":"sha256:b4db8e6363c3610e33524eda52b39a78b6791775d2a0016f75eb3a5cd360e0a2"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:AP2IVCL6GBWE3BINFOM53OY34V","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Study of Gamma Semigroups via its Operator Semigroups in terms of Atanassov's Intuitionistic Fuzzy Ideals","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GM","authors_text":"Manasi Mandal, Samit Kumar Majumder, Sujit Kumar Sardar","submitted_at":"2011-01-16T17:30:30Z","abstract_excerpt":"In this paper some fundamental relationships of a gamma semigroup and its operator semigroups in terms of intuitionistic fuzzy subsets, intuitionistic fuzzy ideals, intuitionistic fuzzy prime(semiprime) ideals, intuitionistic fuzzy ideal extensions are obtained. These are then used to obtain some important characterization theorems of gamma semigroups in terms of intuitionistic fuzzy subsets so as to highlight the role of operator semigroups in the study of gamma semigroups in terms of intuitionistic fuzzy subsets."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1101.3081","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":"2026-05-18T04:30:25Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"nOAVg150AEtvf+ofjA5CJY0tgbRszlstx6i++OpmW1RC9rNF3chSA5iZWyb8nNsy1y7eqXObLQqiv4yc3GNNDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T04:54:34.397886Z"},"content_sha256":"2d5f7198bca3f08ea702d5266c3b6e6bfd36385e4a4d7a878fed1db7e806fde6","schema_version":"1.0","event_id":"sha256:2d5f7198bca3f08ea702d5266c3b6e6bfd36385e4a4d7a878fed1db7e806fde6"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/AP2IVCL6GBWE3BINFOM53OY34V/bundle.json","state_url":"https://pith.science/pith/AP2IVCL6GBWE3BINFOM53OY34V/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/AP2IVCL6GBWE3BINFOM53OY34V/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":"2026-06-24T04:54:34Z","links":{"resolver":"https://pith.science/pith/AP2IVCL6GBWE3BINFOM53OY34V","bundle":"https://pith.science/pith/AP2IVCL6GBWE3BINFOM53OY34V/bundle.json","state":"https://pith.science/pith/AP2IVCL6GBWE3BINFOM53OY34V/state.json","well_known_bundle":"https://pith.science/.well-known/pith/AP2IVCL6GBWE3BINFOM53OY34V/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:AP2IVCL6GBWE3BINFOM53OY34V","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":"9dd43fca90c3100c519ebb25176615103474e3668176057fc1d73f8f198ed4ea","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GM","submitted_at":"2011-01-16T17:30:30Z","title_canon_sha256":"469b4e11a3c42dccd132bc8b2f9b8096f67c9d537d6e663c25c4482ae7f76ff0"},"schema_version":"1.0","source":{"id":"1101.3081","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1101.3081","created_at":"2026-05-18T04:30:25Z"},{"alias_kind":"arxiv_version","alias_value":"1101.3081v1","created_at":"2026-05-18T04:30:25Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1101.3081","created_at":"2026-05-18T04:30:25Z"},{"alias_kind":"pith_short_12","alias_value":"AP2IVCL6GBWE","created_at":"2026-05-18T12:26:24Z"},{"alias_kind":"pith_short_16","alias_value":"AP2IVCL6GBWE3BIN","created_at":"2026-05-18T12:26:24Z"},{"alias_kind":"pith_short_8","alias_value":"AP2IVCL6","created_at":"2026-05-18T12:26:24Z"}],"graph_snapshots":[{"event_id":"sha256:2d5f7198bca3f08ea702d5266c3b6e6bfd36385e4a4d7a878fed1db7e806fde6","target":"graph","created_at":"2026-05-18T04:30:25Z","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 some fundamental relationships of a gamma semigroup and its operator semigroups in terms of intuitionistic fuzzy subsets, intuitionistic fuzzy ideals, intuitionistic fuzzy prime(semiprime) ideals, intuitionistic fuzzy ideal extensions are obtained. These are then used to obtain some important characterization theorems of gamma semigroups in terms of intuitionistic fuzzy subsets so as to highlight the role of operator semigroups in the study of gamma semigroups in terms of intuitionistic fuzzy subsets.","authors_text":"Manasi Mandal, Samit Kumar Majumder, Sujit Kumar Sardar","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GM","submitted_at":"2011-01-16T17:30:30Z","title":"Study of Gamma Semigroups via its Operator Semigroups in terms of Atanassov's Intuitionistic Fuzzy Ideals"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1101.3081","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:b4db8e6363c3610e33524eda52b39a78b6791775d2a0016f75eb3a5cd360e0a2","target":"record","created_at":"2026-05-18T04:30:25Z","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":"9dd43fca90c3100c519ebb25176615103474e3668176057fc1d73f8f198ed4ea","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GM","submitted_at":"2011-01-16T17:30:30Z","title_canon_sha256":"469b4e11a3c42dccd132bc8b2f9b8096f67c9d537d6e663c25c4482ae7f76ff0"},"schema_version":"1.0","source":{"id":"1101.3081","kind":"arxiv","version":1}},"canonical_sha256":"03f48a897e306c4d850d2b99ddbb1be54c6571349688f664de30278397bd5334","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"03f48a897e306c4d850d2b99ddbb1be54c6571349688f664de30278397bd5334","first_computed_at":"2026-05-18T04:30:25.228924Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:30:25.228924Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"7d7YmCWIiyyiyOvgFWDjhss/B5ugnyeZ/VGrQ49Hze1bzzSSlx2f3hJyim2qSQW+/I2hWjztGmmxLysMC7odDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T04:30:25.229503Z","signed_message":"canonical_sha256_bytes"},"source_id":"1101.3081","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b4db8e6363c3610e33524eda52b39a78b6791775d2a0016f75eb3a5cd360e0a2","sha256:2d5f7198bca3f08ea702d5266c3b6e6bfd36385e4a4d7a878fed1db7e806fde6"],"state_sha256":"0beb7d3f7d21f3404ae75b784ef3b6326a4b18d45260be370793ae72fc7af68a"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"qHCeSNl+EIZs/GhM/28O/I987oVLKY9mkHThNWs5y8GFKM/Mp9qfYwY8VlLMhPta5EBB4YEklQUOmFuFyjjcCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-24T04:54:34.399851Z","bundle_sha256":"955a24ca933b29e32c3a4da312ff3edc35bf82fbabba00fdc7355c80fce62d3a"}}