{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:BUGVJABBLQA6ZEGNANPSDUHNKS","short_pith_number":"pith:BUGVJABB","canonical_record":{"source":{"id":"1304.5075","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2013-04-18T10:38:28Z","cross_cats_sorted":["math.IT"],"title_canon_sha256":"d77dbcbe7e5f2f498ca5b84ad227743f1324cd0d4fa5ab1364f31f4c240aacac","abstract_canon_sha256":"20663c1184a85d838d6fe530a91e48ec78bdbf3fa16b0c9c8b606e54d88df383"},"schema_version":"1.0"},"canonical_sha256":"0d0d5480215c01ec90cd035f21d0ed54a7565b8c90ac30ed9c2ee40bbffcc96f","source":{"kind":"arxiv","id":"1304.5075","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1304.5075","created_at":"2026-05-18T03:27:41Z"},{"alias_kind":"arxiv_version","alias_value":"1304.5075v1","created_at":"2026-05-18T03:27:41Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1304.5075","created_at":"2026-05-18T03:27:41Z"},{"alias_kind":"pith_short_12","alias_value":"BUGVJABBLQA6","created_at":"2026-05-18T12:27:40Z"},{"alias_kind":"pith_short_16","alias_value":"BUGVJABBLQA6ZEGN","created_at":"2026-05-18T12:27:40Z"},{"alias_kind":"pith_short_8","alias_value":"BUGVJABB","created_at":"2026-05-18T12:27:40Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:BUGVJABBLQA6ZEGNANPSDUHNKS","target":"record","payload":{"canonical_record":{"source":{"id":"1304.5075","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2013-04-18T10:38:28Z","cross_cats_sorted":["math.IT"],"title_canon_sha256":"d77dbcbe7e5f2f498ca5b84ad227743f1324cd0d4fa5ab1364f31f4c240aacac","abstract_canon_sha256":"20663c1184a85d838d6fe530a91e48ec78bdbf3fa16b0c9c8b606e54d88df383"},"schema_version":"1.0"},"canonical_sha256":"0d0d5480215c01ec90cd035f21d0ed54a7565b8c90ac30ed9c2ee40bbffcc96f","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:27:41.869710Z","signature_b64":"sgoipjij80Zj79FNi0D9ArnPecdlwXZxd0LpohRTTPOG3psFhSa5lbwqT+6jBaVxwbM55ZcxHUqRcFMjb7QkCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0d0d5480215c01ec90cd035f21d0ed54a7565b8c90ac30ed9c2ee40bbffcc96f","last_reissued_at":"2026-05-18T03:27:41.868901Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:27:41.868901Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1304.5075","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":"2026-05-18T03:27:41Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"YsDcbSbyJXxo8eGRCdaBIb5/LQW7/MbVFvHcp2cJ+VtOaXunObV1rcGJ19EV1oHJvN9pOhNSR1gz3nUPdxxOAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T12:56:22.586367Z"},"content_sha256":"d585f2cffd5ba8c30bbcbd7a45c9f0d7dcd5474205a10f1854bedd9370803df7","schema_version":"1.0","event_id":"sha256:d585f2cffd5ba8c30bbcbd7a45c9f0d7dcd5474205a10f1854bedd9370803df7"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:BUGVJABBLQA6ZEGNANPSDUHNKS","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On the Rate of Information Loss in Memoryless Systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"Bernhard C. Geiger, Gernot Kubin","submitted_at":"2013-04-18T10:38:28Z","abstract_excerpt":"In this work we present results about the rate of (relative) information loss induced by passing a real-valued, stationary stochastic process through a memoryless system. We show that for a special class of systems the information loss rate is closely related to the difference of differential entropy rates of the input and output processes. It is further shown that the rate of (relative) information loss is bounded from above by the (relative) information loss the system induces on a random variable distributed according to the process's marginal distribution.\n  As a side result, in this work "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1304.5075","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":"2026-05-18T03:27:41Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/CXPXI8gqJ0jCLXFIfhuWheZWeD3zmehTs+jq5Hug6kTWNRsa58K5bfczqQvyIUkb6FiZQQpWohBLcQvwI3/Bw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T12:56:22.587048Z"},"content_sha256":"8fec3b1f68da84ff4fd91cbc215893f9bb643a636a3995f8aa1d8ad06706f67b","schema_version":"1.0","event_id":"sha256:8fec3b1f68da84ff4fd91cbc215893f9bb643a636a3995f8aa1d8ad06706f67b"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/BUGVJABBLQA6ZEGNANPSDUHNKS/bundle.json","state_url":"https://pith.science/pith/BUGVJABBLQA6ZEGNANPSDUHNKS/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/BUGVJABBLQA6ZEGNANPSDUHNKS/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":"2026-05-31T12:56:22Z","links":{"resolver":"https://pith.science/pith/BUGVJABBLQA6ZEGNANPSDUHNKS","bundle":"https://pith.science/pith/BUGVJABBLQA6ZEGNANPSDUHNKS/bundle.json","state":"https://pith.science/pith/BUGVJABBLQA6ZEGNANPSDUHNKS/state.json","well_known_bundle":"https://pith.science/.well-known/pith/BUGVJABBLQA6ZEGNANPSDUHNKS/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:BUGVJABBLQA6ZEGNANPSDUHNKS","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":"20663c1184a85d838d6fe530a91e48ec78bdbf3fa16b0c9c8b606e54d88df383","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2013-04-18T10:38:28Z","title_canon_sha256":"d77dbcbe7e5f2f498ca5b84ad227743f1324cd0d4fa5ab1364f31f4c240aacac"},"schema_version":"1.0","source":{"id":"1304.5075","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1304.5075","created_at":"2026-05-18T03:27:41Z"},{"alias_kind":"arxiv_version","alias_value":"1304.5075v1","created_at":"2026-05-18T03:27:41Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1304.5075","created_at":"2026-05-18T03:27:41Z"},{"alias_kind":"pith_short_12","alias_value":"BUGVJABBLQA6","created_at":"2026-05-18T12:27:40Z"},{"alias_kind":"pith_short_16","alias_value":"BUGVJABBLQA6ZEGN","created_at":"2026-05-18T12:27:40Z"},{"alias_kind":"pith_short_8","alias_value":"BUGVJABB","created_at":"2026-05-18T12:27:40Z"}],"graph_snapshots":[{"event_id":"sha256:8fec3b1f68da84ff4fd91cbc215893f9bb643a636a3995f8aa1d8ad06706f67b","target":"graph","created_at":"2026-05-18T03:27:41Z","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 we present results about the rate of (relative) information loss induced by passing a real-valued, stationary stochastic process through a memoryless system. We show that for a special class of systems the information loss rate is closely related to the difference of differential entropy rates of the input and output processes. It is further shown that the rate of (relative) information loss is bounded from above by the (relative) information loss the system induces on a random variable distributed according to the process's marginal distribution.\n  As a side result, in this work ","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":"2013-04-18T10:38:28Z","title":"On the Rate of Information Loss in Memoryless Systems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1304.5075","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:d585f2cffd5ba8c30bbcbd7a45c9f0d7dcd5474205a10f1854bedd9370803df7","target":"record","created_at":"2026-05-18T03:27:41Z","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":"20663c1184a85d838d6fe530a91e48ec78bdbf3fa16b0c9c8b606e54d88df383","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2013-04-18T10:38:28Z","title_canon_sha256":"d77dbcbe7e5f2f498ca5b84ad227743f1324cd0d4fa5ab1364f31f4c240aacac"},"schema_version":"1.0","source":{"id":"1304.5075","kind":"arxiv","version":1}},"canonical_sha256":"0d0d5480215c01ec90cd035f21d0ed54a7565b8c90ac30ed9c2ee40bbffcc96f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0d0d5480215c01ec90cd035f21d0ed54a7565b8c90ac30ed9c2ee40bbffcc96f","first_computed_at":"2026-05-18T03:27:41.868901Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:27:41.868901Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"sgoipjij80Zj79FNi0D9ArnPecdlwXZxd0LpohRTTPOG3psFhSa5lbwqT+6jBaVxwbM55ZcxHUqRcFMjb7QkCw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:27:41.869710Z","signed_message":"canonical_sha256_bytes"},"source_id":"1304.5075","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d585f2cffd5ba8c30bbcbd7a45c9f0d7dcd5474205a10f1854bedd9370803df7","sha256:8fec3b1f68da84ff4fd91cbc215893f9bb643a636a3995f8aa1d8ad06706f67b"],"state_sha256":"137fcf43099eb179b64ff1c3be0a973ed10241588e7f0360e72c6555954f77b7"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"jHqMiyxjElzL4aZcQJFERLvM2VSQ6ORMByJFNLH6kWO7jW5fU8YLEl6XH3sNHvx1pQsG/b5AnlEZ9VhsdkckAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-31T12:56:22.590643Z","bundle_sha256":"3b42f485d9a44e067c609b9476ea8f996187f9a8a6f24a5b365f9bcb0ba60664"}}