{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2020:EBB5M4GJWJ6WMTLUIHJ5TQL73O","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":"44145d330fe42db3c62ff2e148d13902a7901233fb6c62b358b2de2a9eb85c8d","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2020-01-30T16:42:55Z","title_canon_sha256":"6c8373df067eb74daae0b7d47f1eea1db6404d2811ba93ccc5ee0fbffc6718c7"},"schema_version":"1.0","source":{"id":"2001.11442","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2001.11442","created_at":"2026-07-05T01:37:33Z"},{"alias_kind":"arxiv_version","alias_value":"2001.11442v3","created_at":"2026-07-05T01:37:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2001.11442","created_at":"2026-07-05T01:37:33Z"},{"alias_kind":"pith_short_12","alias_value":"EBB5M4GJWJ6W","created_at":"2026-07-05T01:37:33Z"},{"alias_kind":"pith_short_16","alias_value":"EBB5M4GJWJ6WMTLU","created_at":"2026-07-05T01:37:33Z"},{"alias_kind":"pith_short_8","alias_value":"EBB5M4GJ","created_at":"2026-07-05T01:37:33Z"}],"graph_snapshots":[{"event_id":"sha256:0b9d3160865d837f97b89ffb2194e96381e8bec0d7724cf721c340443cec1df5","target":"graph","created_at":"2026-07-05T01:37:33Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2001.11442/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"The zero-error capacity of a discrete classical channel was first defined by Shannon as the least upper bound of rates for which one transmits information with zero probability of error. The problem of finding the zero-error capacity $C_0$, which assigns a capacity to each channel as a function, was reformulated in terms of graph theory as a function $\\Theta$, which assigns a value to each simple graph. This paper studies the computability of the zero-error capacity. For the computability, the concept of a Turing machine and a Kolmogorov oracle is used. It is unknown if the zero-error capacity","authors_text":"Christian Deppe, Holger Boche","cross_cats":["math.IT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2020-01-30T16:42:55Z","title":"Computability of the Zero-Error capacity with Kolmogorov Oracle"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2001.11442","kind":"arxiv","version":3},"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":"sha256:3bf4a485f65db27dfc38383e7bbcd49493fbd73c598680239eacdd0866ba1c83","target":"record","created_at":"2026-07-05T01:37:33Z","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":"44145d330fe42db3c62ff2e148d13902a7901233fb6c62b358b2de2a9eb85c8d","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2020-01-30T16:42:55Z","title_canon_sha256":"6c8373df067eb74daae0b7d47f1eea1db6404d2811ba93ccc5ee0fbffc6718c7"},"schema_version":"1.0","source":{"id":"2001.11442","kind":"arxiv","version":3}},"canonical_sha256":"2043d670c9b27d664d7441d3d9c17fdbae600b5f0feffeba56b7f4209342cde2","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2043d670c9b27d664d7441d3d9c17fdbae600b5f0feffeba56b7f4209342cde2","first_computed_at":"2026-07-05T01:37:33.935487Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T01:37:33.935487Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"G84clDcJRYr2ZTviGC8zKE/LSyR1a8f5N+oPIIEq8w21q0bikJZb6jKpexI9OhhoyPGs/o/Ne/3nUHZ+BhLEBw==","signature_status":"signed_v1","signed_at":"2026-07-05T01:37:33.935910Z","signed_message":"canonical_sha256_bytes"},"source_id":"2001.11442","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3bf4a485f65db27dfc38383e7bbcd49493fbd73c598680239eacdd0866ba1c83","sha256:0b9d3160865d837f97b89ffb2194e96381e8bec0d7724cf721c340443cec1df5"],"state_sha256":"0e6871b005f5b5d691b1a7fa2a9ce5fa53f538007d9e50ececa5e3e16daf5fe9"}