{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:D33NNOD2ZO6TYOIXIFNSJIKACJ","short_pith_number":"pith:D33NNOD2","canonical_record":{"source":{"id":"1512.03771","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GN","submitted_at":"2015-12-11T19:46:25Z","cross_cats_sorted":[],"title_canon_sha256":"ebc7dea05a7d2d9d69a591e10a5d8ec4531028106c462831e1954fda54048ac7","abstract_canon_sha256":"6fd32c94f8bf80a8513a005fcbe0efd30b0878f10ea76e17ba26d7982c8fe2f8"},"schema_version":"1.0"},"canonical_sha256":"1ef6d6b87acbbd3c3917415b24a140126bdcdf459cef46da7bdffa06cf34ad2e","source":{"kind":"arxiv","id":"1512.03771","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1512.03771","created_at":"2026-05-18T01:24:31Z"},{"alias_kind":"arxiv_version","alias_value":"1512.03771v1","created_at":"2026-05-18T01:24:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1512.03771","created_at":"2026-05-18T01:24:31Z"},{"alias_kind":"pith_short_12","alias_value":"D33NNOD2ZO6T","created_at":"2026-05-18T12:29:17Z"},{"alias_kind":"pith_short_16","alias_value":"D33NNOD2ZO6TYOIX","created_at":"2026-05-18T12:29:17Z"},{"alias_kind":"pith_short_8","alias_value":"D33NNOD2","created_at":"2026-05-18T12:29:17Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:D33NNOD2ZO6TYOIXIFNSJIKACJ","target":"record","payload":{"canonical_record":{"source":{"id":"1512.03771","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GN","submitted_at":"2015-12-11T19:46:25Z","cross_cats_sorted":[],"title_canon_sha256":"ebc7dea05a7d2d9d69a591e10a5d8ec4531028106c462831e1954fda54048ac7","abstract_canon_sha256":"6fd32c94f8bf80a8513a005fcbe0efd30b0878f10ea76e17ba26d7982c8fe2f8"},"schema_version":"1.0"},"canonical_sha256":"1ef6d6b87acbbd3c3917415b24a140126bdcdf459cef46da7bdffa06cf34ad2e","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:24:31.410816Z","signature_b64":"58rhAWXTQvDaagsyKbbCxc+lsJ41vra9eHp46PISk0uPAjXe4Ml2jXX1gfrAh5uhX9xvx2Nnh5GRqkARivNcAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1ef6d6b87acbbd3c3917415b24a140126bdcdf459cef46da7bdffa06cf34ad2e","last_reissued_at":"2026-05-18T01:24:31.410156Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:24:31.410156Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1512.03771","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":"2026-05-18T01:24:31Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"dXliE3tx3Gs9Znh38H7EfPeyzKtn/oZ+sBR5Ovx4SlKv9ie7J0iHnbFrBpAt9IyBE5aNPsliMTzxKkp6mGByBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T12:07:05.028767Z"},"content_sha256":"6b49f90ffa225db24bfd2e0e8d62055d8e914a3360203f65aa0fd49b038fb80a","schema_version":"1.0","event_id":"sha256:6b49f90ffa225db24bfd2e0e8d62055d8e914a3360203f65aa0fd49b038fb80a"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:D33NNOD2ZO6TYOIXIFNSJIKACJ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Remarks on Multiplicative Metric Spaces and Related Fixed Points","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GN","authors_text":"A. Pitea, K. Abodayeh, T. Abdeljawad, W. Shatanawi","submitted_at":"2015-12-11T19:46:25Z","abstract_excerpt":"In this article we studied the relationship between metric spaces and multiplicative metric spaces. Also, we pointed out some fixed and common fixed point results under some contractive conditions in multiplicative metric spaces can be obtained from the corresponding results in standard metric spaces."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1512.03771","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":"2026-05-18T01:24:31Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"nPG+iGEnZPiLtcRJLIu8AN7k3UCJ5Zxj/yYefLBQ6XIA+zn9+g/89vGk8Ti1s7IuVS6bvm8yIS37LgJdzJt4DA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T12:07:05.029108Z"},"content_sha256":"51791f62c28aa210f595509f8d07fa29e43a3b5ede63733f4e4b70ecbc99c564","schema_version":"1.0","event_id":"sha256:51791f62c28aa210f595509f8d07fa29e43a3b5ede63733f4e4b70ecbc99c564"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/D33NNOD2ZO6TYOIXIFNSJIKACJ/bundle.json","state_url":"https://pith.science/pith/D33NNOD2ZO6TYOIXIFNSJIKACJ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/D33NNOD2ZO6TYOIXIFNSJIKACJ/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":"2026-06-02T12:07:05Z","links":{"resolver":"https://pith.science/pith/D33NNOD2ZO6TYOIXIFNSJIKACJ","bundle":"https://pith.science/pith/D33NNOD2ZO6TYOIXIFNSJIKACJ/bundle.json","state":"https://pith.science/pith/D33NNOD2ZO6TYOIXIFNSJIKACJ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/D33NNOD2ZO6TYOIXIFNSJIKACJ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:D33NNOD2ZO6TYOIXIFNSJIKACJ","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":"6fd32c94f8bf80a8513a005fcbe0efd30b0878f10ea76e17ba26d7982c8fe2f8","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GN","submitted_at":"2015-12-11T19:46:25Z","title_canon_sha256":"ebc7dea05a7d2d9d69a591e10a5d8ec4531028106c462831e1954fda54048ac7"},"schema_version":"1.0","source":{"id":"1512.03771","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1512.03771","created_at":"2026-05-18T01:24:31Z"},{"alias_kind":"arxiv_version","alias_value":"1512.03771v1","created_at":"2026-05-18T01:24:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1512.03771","created_at":"2026-05-18T01:24:31Z"},{"alias_kind":"pith_short_12","alias_value":"D33NNOD2ZO6T","created_at":"2026-05-18T12:29:17Z"},{"alias_kind":"pith_short_16","alias_value":"D33NNOD2ZO6TYOIX","created_at":"2026-05-18T12:29:17Z"},{"alias_kind":"pith_short_8","alias_value":"D33NNOD2","created_at":"2026-05-18T12:29:17Z"}],"graph_snapshots":[{"event_id":"sha256:51791f62c28aa210f595509f8d07fa29e43a3b5ede63733f4e4b70ecbc99c564","target":"graph","created_at":"2026-05-18T01:24:31Z","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 article we studied the relationship between metric spaces and multiplicative metric spaces. Also, we pointed out some fixed and common fixed point results under some contractive conditions in multiplicative metric spaces can be obtained from the corresponding results in standard metric spaces.","authors_text":"A. Pitea, K. Abodayeh, T. Abdeljawad, W. Shatanawi","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GN","submitted_at":"2015-12-11T19:46:25Z","title":"Remarks on Multiplicative Metric Spaces and Related Fixed Points"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1512.03771","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":"sha256:6b49f90ffa225db24bfd2e0e8d62055d8e914a3360203f65aa0fd49b038fb80a","target":"record","created_at":"2026-05-18T01:24:31Z","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":"6fd32c94f8bf80a8513a005fcbe0efd30b0878f10ea76e17ba26d7982c8fe2f8","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GN","submitted_at":"2015-12-11T19:46:25Z","title_canon_sha256":"ebc7dea05a7d2d9d69a591e10a5d8ec4531028106c462831e1954fda54048ac7"},"schema_version":"1.0","source":{"id":"1512.03771","kind":"arxiv","version":1}},"canonical_sha256":"1ef6d6b87acbbd3c3917415b24a140126bdcdf459cef46da7bdffa06cf34ad2e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1ef6d6b87acbbd3c3917415b24a140126bdcdf459cef46da7bdffa06cf34ad2e","first_computed_at":"2026-05-18T01:24:31.410156Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:24:31.410156Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"58rhAWXTQvDaagsyKbbCxc+lsJ41vra9eHp46PISk0uPAjXe4Ml2jXX1gfrAh5uhX9xvx2Nnh5GRqkARivNcAA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:24:31.410816Z","signed_message":"canonical_sha256_bytes"},"source_id":"1512.03771","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6b49f90ffa225db24bfd2e0e8d62055d8e914a3360203f65aa0fd49b038fb80a","sha256:51791f62c28aa210f595509f8d07fa29e43a3b5ede63733f4e4b70ecbc99c564"],"state_sha256":"2e0a921bb91e141cbdcf6151695e4394428e90964ba98baafa2d512a7565f166"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"NSmWkUmlf8Grfjsj2P0cRusS/rD1wGbVRi0VaYugb1GS3qQKCaX9nlHwxcedO1NJ1+fUbsctXwZ/f+XoH6bUAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-02T12:07:05.030992Z","bundle_sha256":"852a5f1f42fce0e9377d5e077f1af2f29ca041270fde9c92a8b935adc278591c"}}