{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2007:D5C7BL7PVW7DGRKECQTS2MLRH2","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":"86a9ba8d576a48b028ab574485dd792af8f55fdd18ffe5974cf06bdf31f8035a","cross_cats_sorted":["math.IT"],"license":"","primary_cat":"cs.IT","submitted_at":"2007-11-16T18:58:45Z","title_canon_sha256":"5e37b757473d81444ccbf4d6ee65be24335a997c19d1a24e24eaddb9528f4213"},"schema_version":"1.0","source":{"id":"0711.2666","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0711.2666","created_at":"2026-05-18T03:36:16Z"},{"alias_kind":"arxiv_version","alias_value":"0711.2666v1","created_at":"2026-05-18T03:36:16Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0711.2666","created_at":"2026-05-18T03:36:16Z"},{"alias_kind":"pith_short_12","alias_value":"D5C7BL7PVW7D","created_at":"2026-05-18T12:25:55Z"},{"alias_kind":"pith_short_16","alias_value":"D5C7BL7PVW7DGRKE","created_at":"2026-05-18T12:25:55Z"},{"alias_kind":"pith_short_8","alias_value":"D5C7BL7P","created_at":"2026-05-18T12:25:55Z"}],"graph_snapshots":[{"event_id":"sha256:c8081a699ae9c7ee2c6f52928197b6da9b2ba961be4bb6e3877856ef2b10ee8d","target":"graph","created_at":"2026-05-18T03:36:16Z","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":"Suppose a string $X_1^n=(X_1,X_2,...,X_n)$ generated by a memoryless source $(X_n)_{n\\geq 1}$ with distribution $P$ is to be compressed with distortion no greater than $D\\geq 0$, using a memoryless random codebook with distribution $Q$. The compression performance is determined by the ``generalized asymptotic equipartition property'' (AEP), which states that the probability of finding a $D$-close match between $X_1^n$ and any given codeword $Y_1^n$, is approximately $2^{-n R(P,Q,D)}$, where the rate function $R(P,Q,D)$ can be expressed as an infimum of relative entropies. The main purpose here","authors_text":"Matthew T. Harrison","cross_cats":["math.IT"],"headline":"","license":"","primary_cat":"cs.IT","submitted_at":"2007-11-16T18:58:45Z","title":"The Generalized Asymptotic Equipartition Property: Necessary and Sufficient Conditions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0711.2666","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:a347884bbda72470927377f5e4fb6d4c5ac6dbf0d9be57842144d87ded7114d3","target":"record","created_at":"2026-05-18T03:36:16Z","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":"86a9ba8d576a48b028ab574485dd792af8f55fdd18ffe5974cf06bdf31f8035a","cross_cats_sorted":["math.IT"],"license":"","primary_cat":"cs.IT","submitted_at":"2007-11-16T18:58:45Z","title_canon_sha256":"5e37b757473d81444ccbf4d6ee65be24335a997c19d1a24e24eaddb9528f4213"},"schema_version":"1.0","source":{"id":"0711.2666","kind":"arxiv","version":1}},"canonical_sha256":"1f45f0afefadbe33454414272d31713eac7074ad828ec577a5590793cbb4835a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1f45f0afefadbe33454414272d31713eac7074ad828ec577a5590793cbb4835a","first_computed_at":"2026-05-18T03:36:16.517376Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:36:16.517376Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"tZtSuyISnYG3h4RiR9Zs1lZzh/x9cgQTfarfXNhU37w2p/VioZYNmjeZBvIfW6yhOoJ8XLO0h74zg8oPVYMDDg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:36:16.518053Z","signed_message":"canonical_sha256_bytes"},"source_id":"0711.2666","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a347884bbda72470927377f5e4fb6d4c5ac6dbf0d9be57842144d87ded7114d3","sha256:c8081a699ae9c7ee2c6f52928197b6da9b2ba961be4bb6e3877856ef2b10ee8d"],"state_sha256":"9fac132e93935018065fbe27e4ccd60dc6e20ab484bcdf2c72965cba0136c9a1"}