{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:MXGEPFJYKQKIAEGREE6TORP7RT","short_pith_number":"pith:MXGEPFJY","canonical_record":{"source":{"id":"1501.02444","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2015-01-11T11:20:35Z","cross_cats_sorted":["math.IT"],"title_canon_sha256":"c257627870ef44dac3f7055a21c5836d440efa2c214ba32d4a1dbd2cb7dd8cb1","abstract_canon_sha256":"02e179c69d24b11f9badf1dbad7b31cfa0faf1212fd394408a06fa532e66573a"},"schema_version":"1.0"},"canonical_sha256":"65cc47953854148010d1213d3745ff8cc0d5c796c180ee6ebac38eae5bf96fcf","source":{"kind":"arxiv","id":"1501.02444","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1501.02444","created_at":"2026-05-18T01:09:55Z"},{"alias_kind":"arxiv_version","alias_value":"1501.02444v3","created_at":"2026-05-18T01:09:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1501.02444","created_at":"2026-05-18T01:09:55Z"},{"alias_kind":"pith_short_12","alias_value":"MXGEPFJYKQKI","created_at":"2026-05-18T12:29:32Z"},{"alias_kind":"pith_short_16","alias_value":"MXGEPFJYKQKIAEGR","created_at":"2026-05-18T12:29:32Z"},{"alias_kind":"pith_short_8","alias_value":"MXGEPFJY","created_at":"2026-05-18T12:29:32Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:MXGEPFJYKQKIAEGREE6TORP7RT","target":"record","payload":{"canonical_record":{"source":{"id":"1501.02444","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2015-01-11T11:20:35Z","cross_cats_sorted":["math.IT"],"title_canon_sha256":"c257627870ef44dac3f7055a21c5836d440efa2c214ba32d4a1dbd2cb7dd8cb1","abstract_canon_sha256":"02e179c69d24b11f9badf1dbad7b31cfa0faf1212fd394408a06fa532e66573a"},"schema_version":"1.0"},"canonical_sha256":"65cc47953854148010d1213d3745ff8cc0d5c796c180ee6ebac38eae5bf96fcf","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:09:55.447442Z","signature_b64":"vLoI4LaIoUcK9mM+DAjMZLZdw5pobWWPikOoPEZZrk/PPNcvDBZ7ApvphnJ2350Z6io9eRucfuPvdZjW6/xzDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"65cc47953854148010d1213d3745ff8cc0d5c796c180ee6ebac38eae5bf96fcf","last_reissued_at":"2026-05-18T01:09:55.446829Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:09:55.446829Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1501.02444","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:09:55Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"FFx4glQj6Z9MIKKu2Uqx23tchBa+lChOrBBxclBU0d2pgmrnVWn2pdek9K6s5oHuTRTFRIYABknjg+9ZTmykAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-22T02:29:02.953443Z"},"content_sha256":"4bb9029e7183cdaf29e168f13e9eedd9a0c6dbba5a3b0f14683f61e43764f1a9","schema_version":"1.0","event_id":"sha256:4bb9029e7183cdaf29e168f13e9eedd9a0c6dbba5a3b0f14683f61e43764f1a9"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:MXGEPFJYKQKIAEGREE6TORP7RT","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Unified Scaling of Polar Codes: Error Exponent, Scaling Exponent, Moderate Deviations, and Error Floors","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"Marco Mondelli, R\\\"udiger Urbanke, S. Hamed Hassani","submitted_at":"2015-01-11T11:20:35Z","abstract_excerpt":"Consider the transmission of a polar code of block length $N$ and rate $R$ over a binary memoryless symmetric channel $W$ and let $P_e$ be the block error probability under successive cancellation decoding. In this paper, we develop new bounds that characterize the relationship of the parameters $R$, $N$, $P_e$, and the quality of the channel $W$ quantified by its capacity $I(W)$ and its Bhattacharyya parameter $Z(W)$.\n  In previous work, two main regimes were studied. In the error exponent regime, the channel $W$ and the rate $R<I(W)$ are fixed, and it was proved that the error probability $P"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1501.02444","kind":"arxiv","version":3},"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":"2026-05-18T01:09:55Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"imZ4wk0AMB2RvgDUlTA99ygeerimVt3YG85rzPabeve8fjjP0sM1lNhh9fgyMzuetUxgQOYz/yDG5A5dam3pCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-22T02:29:02.954089Z"},"content_sha256":"e8c114b5dbcb4db63bba89855df19500c93ccd549e7df4910f20ea046cafe5f2","schema_version":"1.0","event_id":"sha256:e8c114b5dbcb4db63bba89855df19500c93ccd549e7df4910f20ea046cafe5f2"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/MXGEPFJYKQKIAEGREE6TORP7RT/bundle.json","state_url":"https://pith.science/pith/MXGEPFJYKQKIAEGREE6TORP7RT/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/MXGEPFJYKQKIAEGREE6TORP7RT/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":"2026-05-22T02:29:02Z","links":{"resolver":"https://pith.science/pith/MXGEPFJYKQKIAEGREE6TORP7RT","bundle":"https://pith.science/pith/MXGEPFJYKQKIAEGREE6TORP7RT/bundle.json","state":"https://pith.science/pith/MXGEPFJYKQKIAEGREE6TORP7RT/state.json","well_known_bundle":"https://pith.science/.well-known/pith/MXGEPFJYKQKIAEGREE6TORP7RT/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:MXGEPFJYKQKIAEGREE6TORP7RT","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":"02e179c69d24b11f9badf1dbad7b31cfa0faf1212fd394408a06fa532e66573a","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2015-01-11T11:20:35Z","title_canon_sha256":"c257627870ef44dac3f7055a21c5836d440efa2c214ba32d4a1dbd2cb7dd8cb1"},"schema_version":"1.0","source":{"id":"1501.02444","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1501.02444","created_at":"2026-05-18T01:09:55Z"},{"alias_kind":"arxiv_version","alias_value":"1501.02444v3","created_at":"2026-05-18T01:09:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1501.02444","created_at":"2026-05-18T01:09:55Z"},{"alias_kind":"pith_short_12","alias_value":"MXGEPFJYKQKI","created_at":"2026-05-18T12:29:32Z"},{"alias_kind":"pith_short_16","alias_value":"MXGEPFJYKQKIAEGR","created_at":"2026-05-18T12:29:32Z"},{"alias_kind":"pith_short_8","alias_value":"MXGEPFJY","created_at":"2026-05-18T12:29:32Z"}],"graph_snapshots":[{"event_id":"sha256:e8c114b5dbcb4db63bba89855df19500c93ccd549e7df4910f20ea046cafe5f2","target":"graph","created_at":"2026-05-18T01:09:55Z","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":"Consider the transmission of a polar code of block length $N$ and rate $R$ over a binary memoryless symmetric channel $W$ and let $P_e$ be the block error probability under successive cancellation decoding. In this paper, we develop new bounds that characterize the relationship of the parameters $R$, $N$, $P_e$, and the quality of the channel $W$ quantified by its capacity $I(W)$ and its Bhattacharyya parameter $Z(W)$.\n  In previous work, two main regimes were studied. In the error exponent regime, the channel $W$ and the rate $R<I(W)$ are fixed, and it was proved that the error probability $P","authors_text":"Marco Mondelli, R\\\"udiger Urbanke, S. Hamed Hassani","cross_cats":["math.IT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2015-01-11T11:20:35Z","title":"Unified Scaling of Polar Codes: Error Exponent, Scaling Exponent, Moderate Deviations, and Error Floors"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1501.02444","kind":"arxiv","version":3},"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":"sha256:4bb9029e7183cdaf29e168f13e9eedd9a0c6dbba5a3b0f14683f61e43764f1a9","target":"record","created_at":"2026-05-18T01:09:55Z","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":"02e179c69d24b11f9badf1dbad7b31cfa0faf1212fd394408a06fa532e66573a","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2015-01-11T11:20:35Z","title_canon_sha256":"c257627870ef44dac3f7055a21c5836d440efa2c214ba32d4a1dbd2cb7dd8cb1"},"schema_version":"1.0","source":{"id":"1501.02444","kind":"arxiv","version":3}},"canonical_sha256":"65cc47953854148010d1213d3745ff8cc0d5c796c180ee6ebac38eae5bf96fcf","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"65cc47953854148010d1213d3745ff8cc0d5c796c180ee6ebac38eae5bf96fcf","first_computed_at":"2026-05-18T01:09:55.446829Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:09:55.446829Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"vLoI4LaIoUcK9mM+DAjMZLZdw5pobWWPikOoPEZZrk/PPNcvDBZ7ApvphnJ2350Z6io9eRucfuPvdZjW6/xzDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:09:55.447442Z","signed_message":"canonical_sha256_bytes"},"source_id":"1501.02444","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4bb9029e7183cdaf29e168f13e9eedd9a0c6dbba5a3b0f14683f61e43764f1a9","sha256:e8c114b5dbcb4db63bba89855df19500c93ccd549e7df4910f20ea046cafe5f2"],"state_sha256":"63337860e822a2879bd27c8ace7281480374554feba4768874ec5f0e1e8b23bc"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"osJA+WvPS0AYHWsYxBN3yKLPqhGHaJS1Xw7NUTAyHxcDdBXHY/Z3falKxJjWF9DfI2sAxgeJtsKjWbMZ9Q7kBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-22T02:29:02.957233Z","bundle_sha256":"123cb7666f00c169235316b92c2859827458260c39f6f9fe7aacb3b6802df7fe"}}