{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:62EDVM5DAK63POU24FWPBFVOBE","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":"bd59545971ed8b866605800b85fe161627d3a411b057c6899cf59e7c619ca151","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2016-06-08T21:37:15Z","title_canon_sha256":"0d8e543a687617af424b3ffa25557e1ad26abac028fe2801cb9ec290ac3fe927"},"schema_version":"1.0","source":{"id":"1606.02763","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1606.02763","created_at":"2026-05-18T01:12:40Z"},{"alias_kind":"arxiv_version","alias_value":"1606.02763v1","created_at":"2026-05-18T01:12:40Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1606.02763","created_at":"2026-05-18T01:12:40Z"},{"alias_kind":"pith_short_12","alias_value":"62EDVM5DAK63","created_at":"2026-05-18T12:30:01Z"},{"alias_kind":"pith_short_16","alias_value":"62EDVM5DAK63POU2","created_at":"2026-05-18T12:30:01Z"},{"alias_kind":"pith_short_8","alias_value":"62EDVM5D","created_at":"2026-05-18T12:30:01Z"}],"graph_snapshots":[{"event_id":"sha256:870080d95250b280876cf5a868c850487c56fec12cd08c10805ca9e90c983ea1","target":"graph","created_at":"2026-05-18T01:12:40Z","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":"The sufficient condition for partial function from the cartesian square of the finite set to the reals to be compatible with some metric on this set is given. It is then shown, that when afforementioned set and function are respectively a space of binary words of length n and probalities of receiving some word after sending the other word through Binary Assymetric Channel the condition is satisfied so the required metrics exist.","authors_text":"Artur Poplawski","cross_cats":["math.IT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2016-06-08T21:37:15Z","title":"On Matched Metric and Channel Problem"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1606.02763","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":"sha256:8f4ef3f120a248b0cf38561e7a4cb7d829a2619701cee65533f3d1175c295544","target":"record","created_at":"2026-05-18T01:12:40Z","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":"bd59545971ed8b866605800b85fe161627d3a411b057c6899cf59e7c619ca151","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2016-06-08T21:37:15Z","title_canon_sha256":"0d8e543a687617af424b3ffa25557e1ad26abac028fe2801cb9ec290ac3fe927"},"schema_version":"1.0","source":{"id":"1606.02763","kind":"arxiv","version":1}},"canonical_sha256":"f6883ab3a302bdb7ba9ae16cf096ae0900ae608b6dbdb7df9c90212b38e49d22","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f6883ab3a302bdb7ba9ae16cf096ae0900ae608b6dbdb7df9c90212b38e49d22","first_computed_at":"2026-05-18T01:12:40.071458Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:12:40.071458Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"PbGbiXkqIJbCPjOar125IRmk9AK50hO6tGzpoFM7YG8CgUraVx2ZnINJds9Z7mf+ZeLcFHrgH3FfZb2WZ5GBCg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:12:40.071804Z","signed_message":"canonical_sha256_bytes"},"source_id":"1606.02763","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8f4ef3f120a248b0cf38561e7a4cb7d829a2619701cee65533f3d1175c295544","sha256:870080d95250b280876cf5a868c850487c56fec12cd08c10805ca9e90c983ea1"],"state_sha256":"88d6c5217bd70c6d3978300f73552b74a01c6cd7b3e7a7592d2c9ddb07c52cf2"}