{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:QUVZWYGILVUZD3YG7DQ5LDA4KA","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":"be65445c83d60d2cffb3d20ea152608a883ff8c03899d8e51bb188015e7cd396","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2018-06-15T10:27:56Z","title_canon_sha256":"8e223f90832106612ac65514fe9eddf23ab5b1fc6dbbf2f2e3d1fe81d0f7d4e6"},"schema_version":"1.0","source":{"id":"1806.05890","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1806.05890","created_at":"2026-05-18T00:13:09Z"},{"alias_kind":"arxiv_version","alias_value":"1806.05890v1","created_at":"2026-05-18T00:13:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1806.05890","created_at":"2026-05-18T00:13:09Z"},{"alias_kind":"pith_short_12","alias_value":"QUVZWYGILVUZ","created_at":"2026-05-18T12:32:46Z"},{"alias_kind":"pith_short_16","alias_value":"QUVZWYGILVUZD3YG","created_at":"2026-05-18T12:32:46Z"},{"alias_kind":"pith_short_8","alias_value":"QUVZWYGI","created_at":"2026-05-18T12:32:46Z"}],"graph_snapshots":[{"event_id":"sha256:0692691fc84d833581e9114f2e37ee5d0e984625c12d4be194311d0af04ef378","target":"graph","created_at":"2026-05-18T00:13:09Z","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 manuscript, we claim that the newly introduced $\\mathcal{F}$-metric spaces are Hausdorff and also first countable. Moreover, we assert that every separable $\\mathcal{F}$-metric space is second countable. Additionally, we acquire some interesting fixed point results concerning altering distance functions for contractive-type mappings and Kannan-type contractive mappings in this exciting context. However, most of the findings are well-furnished by several non-trivial numerical examples. Finally, we raise an open problem regarding the metrizability of such kind of spaces.","authors_text":"Ankush Chanda, Ashis Bera, Hiranmoy Garai, Lakshmi Kanta Dey","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2018-06-15T10:27:56Z","title":"Topological developments of $\\mathcal{F}$-metric spaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1806.05890","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":"sha256:6f0215b58854b2fdb5ad2f9c43d002b369e0d1e4db52d0cb673f792051021b82","target":"record","created_at":"2026-05-18T00:13:09Z","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":"be65445c83d60d2cffb3d20ea152608a883ff8c03899d8e51bb188015e7cd396","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2018-06-15T10:27:56Z","title_canon_sha256":"8e223f90832106612ac65514fe9eddf23ab5b1fc6dbbf2f2e3d1fe81d0f7d4e6"},"schema_version":"1.0","source":{"id":"1806.05890","kind":"arxiv","version":1}},"canonical_sha256":"852b9b60c85d6991ef06f8e1d58c1c5022ea2a442235d4ab3d20b96756e14e68","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"852b9b60c85d6991ef06f8e1d58c1c5022ea2a442235d4ab3d20b96756e14e68","first_computed_at":"2026-05-18T00:13:09.135040Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:13:09.135040Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"4DT0YITHiCqb06KpAdf3f/3qOxm8Zhx2SE8OjKKzHhgzSPStlrcNedW+c3t4F5Tgi9kUy4iMsCEI1L5mRcPRDA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:13:09.135780Z","signed_message":"canonical_sha256_bytes"},"source_id":"1806.05890","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6f0215b58854b2fdb5ad2f9c43d002b369e0d1e4db52d0cb673f792051021b82","sha256:0692691fc84d833581e9114f2e37ee5d0e984625c12d4be194311d0af04ef378"],"state_sha256":"a9f29ad62b0c21924832a3acc125151a87b66c1034db5d3884ac7e0ca8e3844e"}