{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:NCGEOFPYVHKXNVXJ5ST3FUL5LU","short_pith_number":"pith:NCGEOFPY","canonical_record":{"source":{"id":"1401.0821","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2014-01-04T15:41:27Z","cross_cats_sorted":[],"title_canon_sha256":"fe20b16646f9a0ed3030c2fa3c6902a2c28a831173bf347c0346844c7c1c1421","abstract_canon_sha256":"bbe52f198e2d2bd73bca0d5fcd278a86a5b04efc4a0138c72522b196f1d5db17"},"schema_version":"1.0"},"canonical_sha256":"688c4715f8a9d576d6e9eca7b2d17d5d1386d8cac610db6cc993b6509a5bc61d","source":{"kind":"arxiv","id":"1401.0821","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1401.0821","created_at":"2026-05-18T03:03:11Z"},{"alias_kind":"arxiv_version","alias_value":"1401.0821v1","created_at":"2026-05-18T03:03:11Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1401.0821","created_at":"2026-05-18T03:03:11Z"},{"alias_kind":"pith_short_12","alias_value":"NCGEOFPYVHKX","created_at":"2026-05-18T12:28:41Z"},{"alias_kind":"pith_short_16","alias_value":"NCGEOFPYVHKXNVXJ","created_at":"2026-05-18T12:28:41Z"},{"alias_kind":"pith_short_8","alias_value":"NCGEOFPY","created_at":"2026-05-18T12:28:41Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:NCGEOFPYVHKXNVXJ5ST3FUL5LU","target":"record","payload":{"canonical_record":{"source":{"id":"1401.0821","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2014-01-04T15:41:27Z","cross_cats_sorted":[],"title_canon_sha256":"fe20b16646f9a0ed3030c2fa3c6902a2c28a831173bf347c0346844c7c1c1421","abstract_canon_sha256":"bbe52f198e2d2bd73bca0d5fcd278a86a5b04efc4a0138c72522b196f1d5db17"},"schema_version":"1.0"},"canonical_sha256":"688c4715f8a9d576d6e9eca7b2d17d5d1386d8cac610db6cc993b6509a5bc61d","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:03:11.894035Z","signature_b64":"6VoSqyx2vXm49d8o3rGnMEa8T0XAuGeEbSdMkLkuovEqxHGuQGiWyddojuFar0E1rAsgrC7qOAbKtCpCChAaAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"688c4715f8a9d576d6e9eca7b2d17d5d1386d8cac610db6cc993b6509a5bc61d","last_reissued_at":"2026-05-18T03:03:11.893200Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:03:11.893200Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1401.0821","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":"2026-05-18T03:03:11Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"e05v9zsy57+OfeSrPbnPmFVj4UnXb/mSw6PyDGVmhO4rWK5PXPjdUDq6MW/QtpHURdO20Zx9tanCKl5mLMnsCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-12T10:25:31.401031Z"},"content_sha256":"caad600662ebb85e684d3613cf2e8196ec9e5b8bb6b7870baacf378c5ceed070","schema_version":"1.0","event_id":"sha256:caad600662ebb85e684d3613cf2e8196ec9e5b8bb6b7870baacf378c5ceed070"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:NCGEOFPYVHKXNVXJ5ST3FUL5LU","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Intuitionistic Fuzzy Linear Transformations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DM","authors_text":"Madhumangal Pal, Rajkumar Pradhan","submitted_at":"2014-01-04T15:41:27Z","abstract_excerpt":"In this paper, we discussed about the intuitionistic fuzzy linear transformations (IFLT) and shown that the set of all linear transformations L(V) defined over an intuitionistic fuzzy vector space V does not form an vector space. Here we determine the unique intuitionistic fuzzy matrix associated with an intuitionistic fuzzy linear transformation with respect to an ordered standard basis for an intuitionistic fuzzy vector space. We introduced the concept of the inverse of an IFLT."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1401.0821","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":"2026-05-18T03:03:11Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"XaAyBWlZy0xn/IJdg/hA0dVMdJwSkDkc/14aXGw70qShSngrzgsL1S/qVxdB2tSl7S5/Ljad0646H3RM0960Bw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-12T10:25:31.401383Z"},"content_sha256":"34510527cba22b4034c9a30e2e1336b2ecc813708ad5ef11ea098ad8d5e2a127","schema_version":"1.0","event_id":"sha256:34510527cba22b4034c9a30e2e1336b2ecc813708ad5ef11ea098ad8d5e2a127"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/NCGEOFPYVHKXNVXJ5ST3FUL5LU/bundle.json","state_url":"https://pith.science/pith/NCGEOFPYVHKXNVXJ5ST3FUL5LU/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/NCGEOFPYVHKXNVXJ5ST3FUL5LU/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":"2026-06-12T10:25:31Z","links":{"resolver":"https://pith.science/pith/NCGEOFPYVHKXNVXJ5ST3FUL5LU","bundle":"https://pith.science/pith/NCGEOFPYVHKXNVXJ5ST3FUL5LU/bundle.json","state":"https://pith.science/pith/NCGEOFPYVHKXNVXJ5ST3FUL5LU/state.json","well_known_bundle":"https://pith.science/.well-known/pith/NCGEOFPYVHKXNVXJ5ST3FUL5LU/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:NCGEOFPYVHKXNVXJ5ST3FUL5LU","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":"bbe52f198e2d2bd73bca0d5fcd278a86a5b04efc4a0138c72522b196f1d5db17","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2014-01-04T15:41:27Z","title_canon_sha256":"fe20b16646f9a0ed3030c2fa3c6902a2c28a831173bf347c0346844c7c1c1421"},"schema_version":"1.0","source":{"id":"1401.0821","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1401.0821","created_at":"2026-05-18T03:03:11Z"},{"alias_kind":"arxiv_version","alias_value":"1401.0821v1","created_at":"2026-05-18T03:03:11Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1401.0821","created_at":"2026-05-18T03:03:11Z"},{"alias_kind":"pith_short_12","alias_value":"NCGEOFPYVHKX","created_at":"2026-05-18T12:28:41Z"},{"alias_kind":"pith_short_16","alias_value":"NCGEOFPYVHKXNVXJ","created_at":"2026-05-18T12:28:41Z"},{"alias_kind":"pith_short_8","alias_value":"NCGEOFPY","created_at":"2026-05-18T12:28:41Z"}],"graph_snapshots":[{"event_id":"sha256:34510527cba22b4034c9a30e2e1336b2ecc813708ad5ef11ea098ad8d5e2a127","target":"graph","created_at":"2026-05-18T03:03:11Z","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, we discussed about the intuitionistic fuzzy linear transformations (IFLT) and shown that the set of all linear transformations L(V) defined over an intuitionistic fuzzy vector space V does not form an vector space. Here we determine the unique intuitionistic fuzzy matrix associated with an intuitionistic fuzzy linear transformation with respect to an ordered standard basis for an intuitionistic fuzzy vector space. We introduced the concept of the inverse of an IFLT.","authors_text":"Madhumangal Pal, Rajkumar Pradhan","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2014-01-04T15:41:27Z","title":"Intuitionistic Fuzzy Linear Transformations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1401.0821","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:caad600662ebb85e684d3613cf2e8196ec9e5b8bb6b7870baacf378c5ceed070","target":"record","created_at":"2026-05-18T03:03:11Z","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":"bbe52f198e2d2bd73bca0d5fcd278a86a5b04efc4a0138c72522b196f1d5db17","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2014-01-04T15:41:27Z","title_canon_sha256":"fe20b16646f9a0ed3030c2fa3c6902a2c28a831173bf347c0346844c7c1c1421"},"schema_version":"1.0","source":{"id":"1401.0821","kind":"arxiv","version":1}},"canonical_sha256":"688c4715f8a9d576d6e9eca7b2d17d5d1386d8cac610db6cc993b6509a5bc61d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"688c4715f8a9d576d6e9eca7b2d17d5d1386d8cac610db6cc993b6509a5bc61d","first_computed_at":"2026-05-18T03:03:11.893200Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:03:11.893200Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"6VoSqyx2vXm49d8o3rGnMEa8T0XAuGeEbSdMkLkuovEqxHGuQGiWyddojuFar0E1rAsgrC7qOAbKtCpCChAaAA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:03:11.894035Z","signed_message":"canonical_sha256_bytes"},"source_id":"1401.0821","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:caad600662ebb85e684d3613cf2e8196ec9e5b8bb6b7870baacf378c5ceed070","sha256:34510527cba22b4034c9a30e2e1336b2ecc813708ad5ef11ea098ad8d5e2a127"],"state_sha256":"328c056900737643b62e289a2ee1e4f4fcb7c11a771e6c78fa46a5bf2e5b2ee8"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Obf61YS1lXhSPyY6igbwSCmSOFUZvc/MGUmKU4an0yEG+j9+nypzaQ9dpIXrvZ+GXfH8/4VQlexZbZqSfKFiCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-12T10:25:31.403495Z","bundle_sha256":"4e89bc9aa68c9c3e57c21ee5bb9588ae8f960072b91631695734cf8a3148b3a0"}}