{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:J54BEVWOGEBCOPROGRAFVYZB2I","short_pith_number":"pith:J54BEVWO","canonical_record":{"source":{"id":"1202.0895","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/3.0/","primary_cat":"cs.IT","submitted_at":"2012-02-04T13:23:32Z","cross_cats_sorted":["math.FA","math.IT","math.PR"],"title_canon_sha256":"687517bb41ec110591ffe0af823c442b10983df9b414d9b35725828735aa260b","abstract_canon_sha256":"7ef7c93e91d1091b629f1c42933a1e2b5e881cc7aa6f73a39b24fcb01bf09b52"},"schema_version":"1.0"},"canonical_sha256":"4f781256ce3102273e2e34405ae321d22168224f69b5ae0caddc5a4b463d345b","source":{"kind":"arxiv","id":"1202.0895","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1202.0895","created_at":"2026-05-18T04:03:05Z"},{"alias_kind":"arxiv_version","alias_value":"1202.0895v1","created_at":"2026-05-18T04:03:05Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1202.0895","created_at":"2026-05-18T04:03:05Z"},{"alias_kind":"pith_short_12","alias_value":"J54BEVWOGEBC","created_at":"2026-05-18T12:27:09Z"},{"alias_kind":"pith_short_16","alias_value":"J54BEVWOGEBCOPRO","created_at":"2026-05-18T12:27:09Z"},{"alias_kind":"pith_short_8","alias_value":"J54BEVWO","created_at":"2026-05-18T12:27:09Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:J54BEVWOGEBCOPROGRAFVYZB2I","target":"record","payload":{"canonical_record":{"source":{"id":"1202.0895","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/3.0/","primary_cat":"cs.IT","submitted_at":"2012-02-04T13:23:32Z","cross_cats_sorted":["math.FA","math.IT","math.PR"],"title_canon_sha256":"687517bb41ec110591ffe0af823c442b10983df9b414d9b35725828735aa260b","abstract_canon_sha256":"7ef7c93e91d1091b629f1c42933a1e2b5e881cc7aa6f73a39b24fcb01bf09b52"},"schema_version":"1.0"},"canonical_sha256":"4f781256ce3102273e2e34405ae321d22168224f69b5ae0caddc5a4b463d345b","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:03:05.848391Z","signature_b64":"fnWeL47JUnjc6MPSipfk7cK53sAmGzqTWmabkHZ5OidvB/cM73UNS8b/nX5dLhfDLCF0UcLh7piGvQouebEiDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4f781256ce3102273e2e34405ae321d22168224f69b5ae0caddc5a4b463d345b","last_reissued_at":"2026-05-18T04:03:05.847488Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:03:05.847488Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1202.0895","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":"2026-05-18T04:03:05Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"92poKE/TL//a18KPGLmNvUsBzkD3XtIoEuilIbXSfXHi3xa+zXLyDizXchQfbHbROq309KwUK3AMzB+Sa45SCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T03:24:37.930807Z"},"content_sha256":"77132bccf77eeeec37ab2053805ce6b0a7e770bfea629910e209465512f0a978","schema_version":"1.0","event_id":"sha256:77132bccf77eeeec37ab2053805ce6b0a7e770bfea629910e209465512f0a978"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:J54BEVWOGEBCOPROGRAFVYZB2I","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Causal Rate Distortion Function on Abstract Alphabets: Optimal Reconstruction and Properties","license":"http://creativecommons.org/licenses/by/3.0/","headline":"","cross_cats":["math.FA","math.IT","math.PR"],"primary_cat":"cs.IT","authors_text":"Charalambos D. Charalambous, Christos K. Kourtellaris, Photios A. Stavrou","submitted_at":"2012-02-04T13:23:32Z","abstract_excerpt":"A causal rate distortion function with a general fidelity criterion is formulated on abstract alphabets and a coding theorem is derived. Existence of the minimizing kernel is shown using the topology of weak convergence of probability measures. The optimal reconstruction kernel is derived, which is causal, and certain properties of the causal rate distortion function are presented."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1202.0895","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":"2026-05-18T04:03:05Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Fse/9Xt9IaB9aaIMAXr9z5XjQO8Ua7Pcka/l2xjoQg7khDo0OWVsrBr+C/7A4hXxwvaEObaT6akzQDGB5CrPDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T03:24:37.931142Z"},"content_sha256":"9dd99a8f08d5b8aec62a838640026d476945284cffcf52d248eb0ba439ace014","schema_version":"1.0","event_id":"sha256:9dd99a8f08d5b8aec62a838640026d476945284cffcf52d248eb0ba439ace014"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/J54BEVWOGEBCOPROGRAFVYZB2I/bundle.json","state_url":"https://pith.science/pith/J54BEVWOGEBCOPROGRAFVYZB2I/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/J54BEVWOGEBCOPROGRAFVYZB2I/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":"2026-06-03T03:24:37Z","links":{"resolver":"https://pith.science/pith/J54BEVWOGEBCOPROGRAFVYZB2I","bundle":"https://pith.science/pith/J54BEVWOGEBCOPROGRAFVYZB2I/bundle.json","state":"https://pith.science/pith/J54BEVWOGEBCOPROGRAFVYZB2I/state.json","well_known_bundle":"https://pith.science/.well-known/pith/J54BEVWOGEBCOPROGRAFVYZB2I/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:J54BEVWOGEBCOPROGRAFVYZB2I","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":"7ef7c93e91d1091b629f1c42933a1e2b5e881cc7aa6f73a39b24fcb01bf09b52","cross_cats_sorted":["math.FA","math.IT","math.PR"],"license":"http://creativecommons.org/licenses/by/3.0/","primary_cat":"cs.IT","submitted_at":"2012-02-04T13:23:32Z","title_canon_sha256":"687517bb41ec110591ffe0af823c442b10983df9b414d9b35725828735aa260b"},"schema_version":"1.0","source":{"id":"1202.0895","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1202.0895","created_at":"2026-05-18T04:03:05Z"},{"alias_kind":"arxiv_version","alias_value":"1202.0895v1","created_at":"2026-05-18T04:03:05Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1202.0895","created_at":"2026-05-18T04:03:05Z"},{"alias_kind":"pith_short_12","alias_value":"J54BEVWOGEBC","created_at":"2026-05-18T12:27:09Z"},{"alias_kind":"pith_short_16","alias_value":"J54BEVWOGEBCOPRO","created_at":"2026-05-18T12:27:09Z"},{"alias_kind":"pith_short_8","alias_value":"J54BEVWO","created_at":"2026-05-18T12:27:09Z"}],"graph_snapshots":[{"event_id":"sha256:9dd99a8f08d5b8aec62a838640026d476945284cffcf52d248eb0ba439ace014","target":"graph","created_at":"2026-05-18T04:03:05Z","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":"A causal rate distortion function with a general fidelity criterion is formulated on abstract alphabets and a coding theorem is derived. Existence of the minimizing kernel is shown using the topology of weak convergence of probability measures. The optimal reconstruction kernel is derived, which is causal, and certain properties of the causal rate distortion function are presented.","authors_text":"Charalambos D. Charalambous, Christos K. Kourtellaris, Photios A. Stavrou","cross_cats":["math.FA","math.IT","math.PR"],"headline":"","license":"http://creativecommons.org/licenses/by/3.0/","primary_cat":"cs.IT","submitted_at":"2012-02-04T13:23:32Z","title":"Causal Rate Distortion Function on Abstract Alphabets: Optimal Reconstruction and Properties"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1202.0895","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":"sha256:77132bccf77eeeec37ab2053805ce6b0a7e770bfea629910e209465512f0a978","target":"record","created_at":"2026-05-18T04:03:05Z","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":"7ef7c93e91d1091b629f1c42933a1e2b5e881cc7aa6f73a39b24fcb01bf09b52","cross_cats_sorted":["math.FA","math.IT","math.PR"],"license":"http://creativecommons.org/licenses/by/3.0/","primary_cat":"cs.IT","submitted_at":"2012-02-04T13:23:32Z","title_canon_sha256":"687517bb41ec110591ffe0af823c442b10983df9b414d9b35725828735aa260b"},"schema_version":"1.0","source":{"id":"1202.0895","kind":"arxiv","version":1}},"canonical_sha256":"4f781256ce3102273e2e34405ae321d22168224f69b5ae0caddc5a4b463d345b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4f781256ce3102273e2e34405ae321d22168224f69b5ae0caddc5a4b463d345b","first_computed_at":"2026-05-18T04:03:05.847488Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:03:05.847488Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"fnWeL47JUnjc6MPSipfk7cK53sAmGzqTWmabkHZ5OidvB/cM73UNS8b/nX5dLhfDLCF0UcLh7piGvQouebEiDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T04:03:05.848391Z","signed_message":"canonical_sha256_bytes"},"source_id":"1202.0895","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:77132bccf77eeeec37ab2053805ce6b0a7e770bfea629910e209465512f0a978","sha256:9dd99a8f08d5b8aec62a838640026d476945284cffcf52d248eb0ba439ace014"],"state_sha256":"05e4d0fff59bb63bb3293837a75ab20c4f7971f0be009af6ac9a6e6353c75efc"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"gUIwoBCmHUHI0xXwFtSd2PjDDE2qg6AtYnD6J6zf/jjaJlHlepF3YVFFnHgLmA7Y8sRxNQGKd+SsPJml/K4xDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-03T03:24:37.932953Z","bundle_sha256":"d06f09b0c57464df09d11cfdf57295ec2d7d24a8cb0ded119b23b70a65d5b2e8"}}