{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:YLIJSVYD2DX4Y4POPPLH5SFXED","short_pith_number":"pith:YLIJSVYD","canonical_record":{"source":{"id":"1605.02175","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2016-05-07T11:42:26Z","cross_cats_sorted":["math.IT"],"title_canon_sha256":"a74a0b92bcd7c22388901c5e4fbdb8de2bf2c91d8ecc574e49849c8c8ae9e16e","abstract_canon_sha256":"9447432df07d7e3b8703237f69d5c2e3877f41bf6af6ea3f146c580c1acad784"},"schema_version":"1.0"},"canonical_sha256":"c2d0995703d0efcc71ee7bd67ec8b720c04e0e16c0c1ef562803c09433de9e8d","source":{"kind":"arxiv","id":"1605.02175","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1605.02175","created_at":"2026-05-18T01:15:21Z"},{"alias_kind":"arxiv_version","alias_value":"1605.02175v1","created_at":"2026-05-18T01:15:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1605.02175","created_at":"2026-05-18T01:15:21Z"},{"alias_kind":"pith_short_12","alias_value":"YLIJSVYD2DX4","created_at":"2026-05-18T12:30:53Z"},{"alias_kind":"pith_short_16","alias_value":"YLIJSVYD2DX4Y4PO","created_at":"2026-05-18T12:30:53Z"},{"alias_kind":"pith_short_8","alias_value":"YLIJSVYD","created_at":"2026-05-18T12:30:53Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:YLIJSVYD2DX4Y4POPPLH5SFXED","target":"record","payload":{"canonical_record":{"source":{"id":"1605.02175","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2016-05-07T11:42:26Z","cross_cats_sorted":["math.IT"],"title_canon_sha256":"a74a0b92bcd7c22388901c5e4fbdb8de2bf2c91d8ecc574e49849c8c8ae9e16e","abstract_canon_sha256":"9447432df07d7e3b8703237f69d5c2e3877f41bf6af6ea3f146c580c1acad784"},"schema_version":"1.0"},"canonical_sha256":"c2d0995703d0efcc71ee7bd67ec8b720c04e0e16c0c1ef562803c09433de9e8d","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:15:21.868836Z","signature_b64":"jIqXDJJInzans0iIlql6vZE6ImVBzaPEou8KKL39TEw+EYePLTl/mXgseZdIt6wKxYVoQwCHph6OVPxNPrGuDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c2d0995703d0efcc71ee7bd67ec8b720c04e0e16c0c1ef562803c09433de9e8d","last_reissued_at":"2026-05-18T01:15:21.868059Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:15:21.868059Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1605.02175","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":"2026-05-18T01:15:21Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"gHBKM4QSo8TTsENltCj7ilwqrLTlxDvX4gb20pTtPnZGlsFNLHV/nI0quSbwpKL/MCfLkkULVvOY9cEY1YnzAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T04:28:01.984686Z"},"content_sha256":"2476b04e538fe81de584067b1eb9fc12810a88b7a8f6f38601a36981407c217d","schema_version":"1.0","event_id":"sha256:2476b04e538fe81de584067b1eb9fc12810a88b7a8f6f38601a36981407c217d"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:YLIJSVYD2DX4Y4POPPLH5SFXED","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Asymptotics of Input-Constrained Erasure Channel Capacity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"Guangyue Han, Yonglong Li","submitted_at":"2016-05-07T11:42:26Z","abstract_excerpt":"In this paper, we examine an input-constrained erasure channel and we characterize the asymptotics of its capacity when the erasure rate is low. More specifically, for a general memoryless erasure channel with its input supported on an irreducible finite-type constraint, we derive partial asymptotics of its capacity, using some series expansion type formulas of its mutual information rate; and for a binary erasure channel with its first-order Markovian input supported on the $(1, \\infty)$-RLL constraint, based on the concavity of its mutual information rate with respect to some parameterizatio"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1605.02175","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":"2026-05-18T01:15:21Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"H7jVvGQRfONXMhuvgHuVcmrJWfQxa7R/tn/GGUGRTNEV77ZwZ00I+3Fs/lix7l+Zl6EsugqTMRZIzFkHV/3CDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T04:28:01.985054Z"},"content_sha256":"c1be4f7b8512c5c374aba757623aa7196a2bc54f655261d58c9da611a2211b2b","schema_version":"1.0","event_id":"sha256:c1be4f7b8512c5c374aba757623aa7196a2bc54f655261d58c9da611a2211b2b"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/YLIJSVYD2DX4Y4POPPLH5SFXED/bundle.json","state_url":"https://pith.science/pith/YLIJSVYD2DX4Y4POPPLH5SFXED/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/YLIJSVYD2DX4Y4POPPLH5SFXED/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":"2026-06-23T04:28:01Z","links":{"resolver":"https://pith.science/pith/YLIJSVYD2DX4Y4POPPLH5SFXED","bundle":"https://pith.science/pith/YLIJSVYD2DX4Y4POPPLH5SFXED/bundle.json","state":"https://pith.science/pith/YLIJSVYD2DX4Y4POPPLH5SFXED/state.json","well_known_bundle":"https://pith.science/.well-known/pith/YLIJSVYD2DX4Y4POPPLH5SFXED/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:YLIJSVYD2DX4Y4POPPLH5SFXED","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":"9447432df07d7e3b8703237f69d5c2e3877f41bf6af6ea3f146c580c1acad784","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2016-05-07T11:42:26Z","title_canon_sha256":"a74a0b92bcd7c22388901c5e4fbdb8de2bf2c91d8ecc574e49849c8c8ae9e16e"},"schema_version":"1.0","source":{"id":"1605.02175","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1605.02175","created_at":"2026-05-18T01:15:21Z"},{"alias_kind":"arxiv_version","alias_value":"1605.02175v1","created_at":"2026-05-18T01:15:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1605.02175","created_at":"2026-05-18T01:15:21Z"},{"alias_kind":"pith_short_12","alias_value":"YLIJSVYD2DX4","created_at":"2026-05-18T12:30:53Z"},{"alias_kind":"pith_short_16","alias_value":"YLIJSVYD2DX4Y4PO","created_at":"2026-05-18T12:30:53Z"},{"alias_kind":"pith_short_8","alias_value":"YLIJSVYD","created_at":"2026-05-18T12:30:53Z"}],"graph_snapshots":[{"event_id":"sha256:c1be4f7b8512c5c374aba757623aa7196a2bc54f655261d58c9da611a2211b2b","target":"graph","created_at":"2026-05-18T01:15:21Z","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":"In this paper, we examine an input-constrained erasure channel and we characterize the asymptotics of its capacity when the erasure rate is low. More specifically, for a general memoryless erasure channel with its input supported on an irreducible finite-type constraint, we derive partial asymptotics of its capacity, using some series expansion type formulas of its mutual information rate; and for a binary erasure channel with its first-order Markovian input supported on the $(1, \\infty)$-RLL constraint, based on the concavity of its mutual information rate with respect to some parameterizatio","authors_text":"Guangyue Han, Yonglong Li","cross_cats":["math.IT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2016-05-07T11:42:26Z","title":"Asymptotics of Input-Constrained Erasure Channel Capacity"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1605.02175","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":"sha256:2476b04e538fe81de584067b1eb9fc12810a88b7a8f6f38601a36981407c217d","target":"record","created_at":"2026-05-18T01:15:21Z","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":"9447432df07d7e3b8703237f69d5c2e3877f41bf6af6ea3f146c580c1acad784","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2016-05-07T11:42:26Z","title_canon_sha256":"a74a0b92bcd7c22388901c5e4fbdb8de2bf2c91d8ecc574e49849c8c8ae9e16e"},"schema_version":"1.0","source":{"id":"1605.02175","kind":"arxiv","version":1}},"canonical_sha256":"c2d0995703d0efcc71ee7bd67ec8b720c04e0e16c0c1ef562803c09433de9e8d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c2d0995703d0efcc71ee7bd67ec8b720c04e0e16c0c1ef562803c09433de9e8d","first_computed_at":"2026-05-18T01:15:21.868059Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:15:21.868059Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"jIqXDJJInzans0iIlql6vZE6ImVBzaPEou8KKL39TEw+EYePLTl/mXgseZdIt6wKxYVoQwCHph6OVPxNPrGuDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:15:21.868836Z","signed_message":"canonical_sha256_bytes"},"source_id":"1605.02175","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2476b04e538fe81de584067b1eb9fc12810a88b7a8f6f38601a36981407c217d","sha256:c1be4f7b8512c5c374aba757623aa7196a2bc54f655261d58c9da611a2211b2b"],"state_sha256":"385e146770f5cc8c31c7a206730e5f1129ff4df37dbd673d8ba73c56caf26256"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"8lmdv695Lv6f+6+gVYazOTDuuKH+56uj9YT/BSUGDl1bg+cTP2G+yW4kjBtmT3KYWfVZCV7sDzMVn7tA4tFeCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-23T04:28:01.987087Z","bundle_sha256":"b306a37f1d33e63c2e361a83b4f52e2a36244bcbc2250c7c71407075be850737"}}