{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2007:STJ2KSIR6DUTTKEMFKOUNEDRTY","short_pith_number":"pith:STJ2KSIR","canonical_record":{"source":{"id":"0708.2575","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2007-08-20T01:32:42Z","cross_cats_sorted":["math.IT"],"title_canon_sha256":"87da3c34958bbe596facd719e6b2253c43c9b3e63809382f37884b9f1bd8dff4","abstract_canon_sha256":"51bf04dd7d817f4177096c27bc55e7b8419c9105ba73a10ece2d4116d2ba669c"},"schema_version":"1.0"},"canonical_sha256":"94d3a54911f0e939a88c2a9d4690719e32c61c24deb2049a764bfaa8416d2c60","source":{"kind":"arxiv","id":"0708.2575","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0708.2575","created_at":"2026-05-18T04:20:39Z"},{"alias_kind":"arxiv_version","alias_value":"0708.2575v2","created_at":"2026-05-18T04:20:39Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0708.2575","created_at":"2026-05-18T04:20:39Z"},{"alias_kind":"pith_short_12","alias_value":"STJ2KSIR6DUT","created_at":"2026-05-18T12:25:56Z"},{"alias_kind":"pith_short_16","alias_value":"STJ2KSIR6DUTTKEM","created_at":"2026-05-18T12:25:56Z"},{"alias_kind":"pith_short_8","alias_value":"STJ2KSIR","created_at":"2026-05-18T12:25:56Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2007:STJ2KSIR6DUTTKEMFKOUNEDRTY","target":"record","payload":{"canonical_record":{"source":{"id":"0708.2575","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2007-08-20T01:32:42Z","cross_cats_sorted":["math.IT"],"title_canon_sha256":"87da3c34958bbe596facd719e6b2253c43c9b3e63809382f37884b9f1bd8dff4","abstract_canon_sha256":"51bf04dd7d817f4177096c27bc55e7b8419c9105ba73a10ece2d4116d2ba669c"},"schema_version":"1.0"},"canonical_sha256":"94d3a54911f0e939a88c2a9d4690719e32c61c24deb2049a764bfaa8416d2c60","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:20:39.515678Z","signature_b64":"HiMegothb6jCBljSBZJMfApU0x1oAIMyFb+kWux92yD0b4WoJqZcs4BRV1KqqX/TjOTIOybI66XvU7oFthLoDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"94d3a54911f0e939a88c2a9d4690719e32c61c24deb2049a764bfaa8416d2c60","last_reissued_at":"2026-05-18T04:20:39.514956Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:20:39.514956Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"0708.2575","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T04:20:39Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"pjGm7VTVcIXMm1LGIlzinjgVHtcGQvyqpBBh+LW2dFlLVVdAXPh1ep+6AnrvLv4l6GPDcnV3XxN3FaIqB3EKAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T02:33:27.100671Z"},"content_sha256":"28ecd66659f1f440dba23f63ce0fbba9598d473c365cadaee46ffdbe36783ac7","schema_version":"1.0","event_id":"sha256:28ecd66659f1f440dba23f63ce0fbba9598d473c365cadaee46ffdbe36783ac7"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2007:STJ2KSIR6DUTTKEMFKOUNEDRTY","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Rateless Coding for Gaussian Channels","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"Gregory W. Wornell, Mitchell D. Trott, Uri Erez","submitted_at":"2007-08-20T01:32:42Z","abstract_excerpt":"A rateless code-i.e., a rate-compatible family of codes-has the property that codewords of the higher rate codes are prefixes of those of the lower rate ones. A perfect family of such codes is one in which each of the codes in the family is capacity-achieving. We show by construction that perfect rateless codes with low-complexity decoding algorithms exist for additive white Gaussian noise channels. Our construction involves the use of layered encoding and successive decoding, together with repetition using time-varying layer weights. As an illustration of our framework, we design a practical "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0708.2575","kind":"arxiv","version":2},"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":"2026-05-18T04:20:39Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"gJOJ9cKCm7b4LAN8E6JSPcK436VEcR5EVDi9+pzFGuP0OLVIleKlMGOB2BBf3b8W6zpMbiu+onRo/egcTlZKCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T02:33:27.101371Z"},"content_sha256":"a25945843b490adfb59cbdf7f9f8e62c12b90bdb371f82260a239555fbad6ccc","schema_version":"1.0","event_id":"sha256:a25945843b490adfb59cbdf7f9f8e62c12b90bdb371f82260a239555fbad6ccc"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/STJ2KSIR6DUTTKEMFKOUNEDRTY/bundle.json","state_url":"https://pith.science/pith/STJ2KSIR6DUTTKEMFKOUNEDRTY/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/STJ2KSIR6DUTTKEMFKOUNEDRTY/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":"2026-06-01T02:33:27Z","links":{"resolver":"https://pith.science/pith/STJ2KSIR6DUTTKEMFKOUNEDRTY","bundle":"https://pith.science/pith/STJ2KSIR6DUTTKEMFKOUNEDRTY/bundle.json","state":"https://pith.science/pith/STJ2KSIR6DUTTKEMFKOUNEDRTY/state.json","well_known_bundle":"https://pith.science/.well-known/pith/STJ2KSIR6DUTTKEMFKOUNEDRTY/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2007:STJ2KSIR6DUTTKEMFKOUNEDRTY","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":"51bf04dd7d817f4177096c27bc55e7b8419c9105ba73a10ece2d4116d2ba669c","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2007-08-20T01:32:42Z","title_canon_sha256":"87da3c34958bbe596facd719e6b2253c43c9b3e63809382f37884b9f1bd8dff4"},"schema_version":"1.0","source":{"id":"0708.2575","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0708.2575","created_at":"2026-05-18T04:20:39Z"},{"alias_kind":"arxiv_version","alias_value":"0708.2575v2","created_at":"2026-05-18T04:20:39Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0708.2575","created_at":"2026-05-18T04:20:39Z"},{"alias_kind":"pith_short_12","alias_value":"STJ2KSIR6DUT","created_at":"2026-05-18T12:25:56Z"},{"alias_kind":"pith_short_16","alias_value":"STJ2KSIR6DUTTKEM","created_at":"2026-05-18T12:25:56Z"},{"alias_kind":"pith_short_8","alias_value":"STJ2KSIR","created_at":"2026-05-18T12:25:56Z"}],"graph_snapshots":[{"event_id":"sha256:a25945843b490adfb59cbdf7f9f8e62c12b90bdb371f82260a239555fbad6ccc","target":"graph","created_at":"2026-05-18T04:20:39Z","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 rateless code-i.e., a rate-compatible family of codes-has the property that codewords of the higher rate codes are prefixes of those of the lower rate ones. A perfect family of such codes is one in which each of the codes in the family is capacity-achieving. We show by construction that perfect rateless codes with low-complexity decoding algorithms exist for additive white Gaussian noise channels. Our construction involves the use of layered encoding and successive decoding, together with repetition using time-varying layer weights. As an illustration of our framework, we design a practical ","authors_text":"Gregory W. Wornell, Mitchell D. Trott, Uri Erez","cross_cats":["math.IT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2007-08-20T01:32:42Z","title":"Rateless Coding for Gaussian Channels"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0708.2575","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":"sha256:28ecd66659f1f440dba23f63ce0fbba9598d473c365cadaee46ffdbe36783ac7","target":"record","created_at":"2026-05-18T04:20:39Z","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":"51bf04dd7d817f4177096c27bc55e7b8419c9105ba73a10ece2d4116d2ba669c","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2007-08-20T01:32:42Z","title_canon_sha256":"87da3c34958bbe596facd719e6b2253c43c9b3e63809382f37884b9f1bd8dff4"},"schema_version":"1.0","source":{"id":"0708.2575","kind":"arxiv","version":2}},"canonical_sha256":"94d3a54911f0e939a88c2a9d4690719e32c61c24deb2049a764bfaa8416d2c60","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"94d3a54911f0e939a88c2a9d4690719e32c61c24deb2049a764bfaa8416d2c60","first_computed_at":"2026-05-18T04:20:39.514956Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:20:39.514956Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"HiMegothb6jCBljSBZJMfApU0x1oAIMyFb+kWux92yD0b4WoJqZcs4BRV1KqqX/TjOTIOybI66XvU7oFthLoDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T04:20:39.515678Z","signed_message":"canonical_sha256_bytes"},"source_id":"0708.2575","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:28ecd66659f1f440dba23f63ce0fbba9598d473c365cadaee46ffdbe36783ac7","sha256:a25945843b490adfb59cbdf7f9f8e62c12b90bdb371f82260a239555fbad6ccc"],"state_sha256":"a43cdaaf68572720717b94997aebcecf0a5bb971fe6a0d4e16dc0d8f51b9ff73"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"QWDo9xGdgyUXL/z0zGg7Qq9+cei1cxUWfuFl3/vZflkJ9zyuC5qYvvbQ8Y1RkqSq0W2bptV3Zj675JgdnzI+DQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-01T02:33:27.106039Z","bundle_sha256":"c490473d262e41292baa8bb6942dbc901db050c46246cf47d320d8fe097dc507"}}