{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:5GQ2TFODS5MUR2ISUZI6TD4OC3","short_pith_number":"pith:5GQ2TFOD","canonical_record":{"source":{"id":"1303.0572","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2013-03-03T21:32:43Z","cross_cats_sorted":["math.IT"],"title_canon_sha256":"e8e22a05b5d1aedf0b128e079236f3039be6b8c3dc8c6559c2784fbdf20cede6","abstract_canon_sha256":"d664a2073a73f56c46d5861f162dbe44d815fb5ee8e2128fc9019b6bb15bf417"},"schema_version":"1.0"},"canonical_sha256":"e9a1a995c3975948e912a651e98f8e16c43daca3400923dd6189cfdf925320bd","source":{"kind":"arxiv","id":"1303.0572","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1303.0572","created_at":"2026-05-18T03:31:55Z"},{"alias_kind":"arxiv_version","alias_value":"1303.0572v1","created_at":"2026-05-18T03:31:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1303.0572","created_at":"2026-05-18T03:31:55Z"},{"alias_kind":"pith_short_12","alias_value":"5GQ2TFODS5MU","created_at":"2026-05-18T12:27:34Z"},{"alias_kind":"pith_short_16","alias_value":"5GQ2TFODS5MUR2IS","created_at":"2026-05-18T12:27:34Z"},{"alias_kind":"pith_short_8","alias_value":"5GQ2TFOD","created_at":"2026-05-18T12:27:34Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:5GQ2TFODS5MUR2ISUZI6TD4OC3","target":"record","payload":{"canonical_record":{"source":{"id":"1303.0572","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2013-03-03T21:32:43Z","cross_cats_sorted":["math.IT"],"title_canon_sha256":"e8e22a05b5d1aedf0b128e079236f3039be6b8c3dc8c6559c2784fbdf20cede6","abstract_canon_sha256":"d664a2073a73f56c46d5861f162dbe44d815fb5ee8e2128fc9019b6bb15bf417"},"schema_version":"1.0"},"canonical_sha256":"e9a1a995c3975948e912a651e98f8e16c43daca3400923dd6189cfdf925320bd","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:31:55.544141Z","signature_b64":"XuVvBNiRq0i4pYtcRiTFVi15yOdaJN7XWHKee5QN9tPm6l82SzqoCT/ZgOqTrmgQ0/rcgCywz1Ps06tq2aV4BA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e9a1a995c3975948e912a651e98f8e16c43daca3400923dd6189cfdf925320bd","last_reissued_at":"2026-05-18T03:31:55.543356Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:31:55.543356Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1303.0572","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":"2026-05-18T03:31:55Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"4u4v6Qf3nPaqDPIEnnwKRv2Gb8cfBRRbkNKgwTj/bIyy84tC3VgQQ+zzL4Mb6boXEC/XXxxPI1z49hIIy/wxDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T22:08:06.744349Z"},"content_sha256":"03fdfa8a579d76a8bfdc15a7fad3845d83518c5b3b7881699a9c40f7a4cdeb58","schema_version":"1.0","event_id":"sha256:03fdfa8a579d76a8bfdc15a7fad3845d83518c5b3b7881699a9c40f7a4cdeb58"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:5GQ2TFODS5MUR2ISUZI6TD4OC3","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"New Non-asymptotic Random Channel Coding Theorems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"En-hui Yang, Jin Meng","submitted_at":"2013-03-03T21:32:43Z","abstract_excerpt":"New non-asymptotic random coding theorems (with error probability $\\epsilon$ and finite block length $n$) based on Gallager parity check ensemble and Shannon random code ensemble with a fixed codeword type are established for discrete input arbitrary output channels. The resulting non-asymptotic achievability bounds, when combined with non-asymptotic equipartition properties developed in the paper, can be easily computed. Analytically, these non-asymptotic achievability bounds are shown to be asymptotically tight up to the second order of the coding rate as $n$ goes to infinity with either con"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1303.0572","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":"2026-05-18T03:31:55Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ZWjQYFXvwWZFMnp3z3q4zlUXM9z8pPOsjuQUUlJGAUabYyOHwUw61akgLE4L34e+KiRoF/Wba9FlWuQJX+HxCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T22:08:06.745093Z"},"content_sha256":"c573747cf65feb940f9c6e4df5785c37dc0f00fd7426708fadcfd2131b908836","schema_version":"1.0","event_id":"sha256:c573747cf65feb940f9c6e4df5785c37dc0f00fd7426708fadcfd2131b908836"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/5GQ2TFODS5MUR2ISUZI6TD4OC3/bundle.json","state_url":"https://pith.science/pith/5GQ2TFODS5MUR2ISUZI6TD4OC3/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/5GQ2TFODS5MUR2ISUZI6TD4OC3/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":"2026-06-07T22:08:06Z","links":{"resolver":"https://pith.science/pith/5GQ2TFODS5MUR2ISUZI6TD4OC3","bundle":"https://pith.science/pith/5GQ2TFODS5MUR2ISUZI6TD4OC3/bundle.json","state":"https://pith.science/pith/5GQ2TFODS5MUR2ISUZI6TD4OC3/state.json","well_known_bundle":"https://pith.science/.well-known/pith/5GQ2TFODS5MUR2ISUZI6TD4OC3/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:5GQ2TFODS5MUR2ISUZI6TD4OC3","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":"d664a2073a73f56c46d5861f162dbe44d815fb5ee8e2128fc9019b6bb15bf417","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2013-03-03T21:32:43Z","title_canon_sha256":"e8e22a05b5d1aedf0b128e079236f3039be6b8c3dc8c6559c2784fbdf20cede6"},"schema_version":"1.0","source":{"id":"1303.0572","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1303.0572","created_at":"2026-05-18T03:31:55Z"},{"alias_kind":"arxiv_version","alias_value":"1303.0572v1","created_at":"2026-05-18T03:31:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1303.0572","created_at":"2026-05-18T03:31:55Z"},{"alias_kind":"pith_short_12","alias_value":"5GQ2TFODS5MU","created_at":"2026-05-18T12:27:34Z"},{"alias_kind":"pith_short_16","alias_value":"5GQ2TFODS5MUR2IS","created_at":"2026-05-18T12:27:34Z"},{"alias_kind":"pith_short_8","alias_value":"5GQ2TFOD","created_at":"2026-05-18T12:27:34Z"}],"graph_snapshots":[{"event_id":"sha256:c573747cf65feb940f9c6e4df5785c37dc0f00fd7426708fadcfd2131b908836","target":"graph","created_at":"2026-05-18T03:31:55Z","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":"New non-asymptotic random coding theorems (with error probability $\\epsilon$ and finite block length $n$) based on Gallager parity check ensemble and Shannon random code ensemble with a fixed codeword type are established for discrete input arbitrary output channels. The resulting non-asymptotic achievability bounds, when combined with non-asymptotic equipartition properties developed in the paper, can be easily computed. Analytically, these non-asymptotic achievability bounds are shown to be asymptotically tight up to the second order of the coding rate as $n$ goes to infinity with either con","authors_text":"En-hui Yang, Jin Meng","cross_cats":["math.IT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2013-03-03T21:32:43Z","title":"New Non-asymptotic Random Channel Coding Theorems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1303.0572","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":"sha256:03fdfa8a579d76a8bfdc15a7fad3845d83518c5b3b7881699a9c40f7a4cdeb58","target":"record","created_at":"2026-05-18T03:31:55Z","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":"d664a2073a73f56c46d5861f162dbe44d815fb5ee8e2128fc9019b6bb15bf417","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2013-03-03T21:32:43Z","title_canon_sha256":"e8e22a05b5d1aedf0b128e079236f3039be6b8c3dc8c6559c2784fbdf20cede6"},"schema_version":"1.0","source":{"id":"1303.0572","kind":"arxiv","version":1}},"canonical_sha256":"e9a1a995c3975948e912a651e98f8e16c43daca3400923dd6189cfdf925320bd","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e9a1a995c3975948e912a651e98f8e16c43daca3400923dd6189cfdf925320bd","first_computed_at":"2026-05-18T03:31:55.543356Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:31:55.543356Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"XuVvBNiRq0i4pYtcRiTFVi15yOdaJN7XWHKee5QN9tPm6l82SzqoCT/ZgOqTrmgQ0/rcgCywz1Ps06tq2aV4BA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:31:55.544141Z","signed_message":"canonical_sha256_bytes"},"source_id":"1303.0572","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:03fdfa8a579d76a8bfdc15a7fad3845d83518c5b3b7881699a9c40f7a4cdeb58","sha256:c573747cf65feb940f9c6e4df5785c37dc0f00fd7426708fadcfd2131b908836"],"state_sha256":"9060345c0f604abcba98f2b8ea76a488b6a0d6143ecd02cebb6821840a8ff2c7"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"2BWK4JPvTF04ACOjlSVkZR6x+C0b7J3ojBo8iV4O+6IBKsxBzvZLm5W31pJHFtNYonrfKNfZcGrGmgMg7dH7AA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-07T22:08:06.748857Z","bundle_sha256":"8adc4ce5393709ad17561ea4ac2369c46a792d483f23cceffb2465e8bee6f1f5"}}