{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:LFIVTTVVUTCPBDRQXXMEG7MFRP","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":"82b404e39afc715cab67211d414a861d2f3bfa62f88ce4d574df21959174725a","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2013-03-26T08:37:05Z","title_canon_sha256":"47bf5426dd1775214549650b9f28c337d63e32200cbf9bef56240e5e67a9f19c"},"schema_version":"1.0","source":{"id":"1303.6409","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1303.6409","created_at":"2026-05-18T03:27:44Z"},{"alias_kind":"arxiv_version","alias_value":"1303.6409v2","created_at":"2026-05-18T03:27:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1303.6409","created_at":"2026-05-18T03:27:44Z"},{"alias_kind":"pith_short_12","alias_value":"LFIVTTVVUTCP","created_at":"2026-05-18T12:27:51Z"},{"alias_kind":"pith_short_16","alias_value":"LFIVTTVVUTCPBDRQ","created_at":"2026-05-18T12:27:51Z"},{"alias_kind":"pith_short_8","alias_value":"LFIVTTVV","created_at":"2026-05-18T12:27:51Z"}],"graph_snapshots":[{"event_id":"sha256:da4f0d434f92c98cecb9ec2125bc6d85cdbf6d567133d9bb144ca061b4af0bc8","target":"graph","created_at":"2026-05-18T03:27:44Z","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 work the information loss in deterministic, memoryless systems is investigated by evaluating the conditional entropy of the input random variable given the output random variable. It is shown that for a large class of systems the information loss is finite, even if the input is continuously distributed. Based on this finiteness, the problem of perfectly reconstructing the input is addressed and Fano-type bounds between the information loss and the reconstruction error probability are derived.\n  For systems with infinite information loss a relative measure is defined and shown to be tig","authors_text":"Bernhard C. Geiger, Gernot Kubin","cross_cats":["math.IT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2013-03-26T08:37:05Z","title":"Information Measures for Deterministic Input-Output Systems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1303.6409","kind":"arxiv","version":2},"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:fb1963e6a00295dcb5fd8a993c9bf63877e97daf75fa3e9cc8d1bea4f84225aa","target":"record","created_at":"2026-05-18T03:27:44Z","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":"82b404e39afc715cab67211d414a861d2f3bfa62f88ce4d574df21959174725a","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2013-03-26T08:37:05Z","title_canon_sha256":"47bf5426dd1775214549650b9f28c337d63e32200cbf9bef56240e5e67a9f19c"},"schema_version":"1.0","source":{"id":"1303.6409","kind":"arxiv","version":2}},"canonical_sha256":"595159ceb5a4c4f08e30bdd8437d858bf7d5a60e8461ee82d172d1c8ac7adc92","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"595159ceb5a4c4f08e30bdd8437d858bf7d5a60e8461ee82d172d1c8ac7adc92","first_computed_at":"2026-05-18T03:27:44.416335Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:27:44.416335Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"t5XXBNSVXljHl1u1A9uUjCPTSmCUgWoU+YGKArj8xkZMFuwefxHRuEU25O7XOm6+zq4xKUH4dnpFIohkTGVwDA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:27:44.417030Z","signed_message":"canonical_sha256_bytes"},"source_id":"1303.6409","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:fb1963e6a00295dcb5fd8a993c9bf63877e97daf75fa3e9cc8d1bea4f84225aa","sha256:da4f0d434f92c98cecb9ec2125bc6d85cdbf6d567133d9bb144ca061b4af0bc8"],"state_sha256":"9b84a0d825102dc7e593fd1b616e7903e9354578a94c6c1a39cecd17e45ab6f0"}