{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2025:HPTUU7APBNBCCZZ2HFLNKMCUDO","short_pith_number":"pith:HPTUU7AP","canonical_record":{"source":{"id":"2507.23180","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2025-07-31T01:21:06Z","cross_cats_sorted":["math.IT"],"title_canon_sha256":"730198a0f37b0e88d5dae5fe18b95f08ece3201db8863658345de36a6a9261c0","abstract_canon_sha256":"ec0d52df8421bd5b8b3d3c0bf2a216c58fc64da872d6d2071b8e36201a77f88e"},"schema_version":"1.0"},"canonical_sha256":"3be74a7c0f0b4221673a3956d530541bbcfcf85d03dc86268ea812353a3e832a","source":{"kind":"arxiv","id":"2507.23180","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2507.23180","created_at":"2026-05-17T23:39:17Z"},{"alias_kind":"arxiv_version","alias_value":"2507.23180v2","created_at":"2026-05-17T23:39:17Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2507.23180","created_at":"2026-05-17T23:39:17Z"},{"alias_kind":"pith_short_12","alias_value":"HPTUU7APBNBC","created_at":"2026-05-18T12:33:37Z"},{"alias_kind":"pith_short_16","alias_value":"HPTUU7APBNBCCZZ2","created_at":"2026-05-18T12:33:37Z"},{"alias_kind":"pith_short_8","alias_value":"HPTUU7AP","created_at":"2026-05-18T12:33:37Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2025:HPTUU7APBNBCCZZ2HFLNKMCUDO","target":"record","payload":{"canonical_record":{"source":{"id":"2507.23180","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2025-07-31T01:21:06Z","cross_cats_sorted":["math.IT"],"title_canon_sha256":"730198a0f37b0e88d5dae5fe18b95f08ece3201db8863658345de36a6a9261c0","abstract_canon_sha256":"ec0d52df8421bd5b8b3d3c0bf2a216c58fc64da872d6d2071b8e36201a77f88e"},"schema_version":"1.0"},"canonical_sha256":"3be74a7c0f0b4221673a3956d530541bbcfcf85d03dc86268ea812353a3e832a","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:39:17.790839Z","signature_b64":"YrqOHMJJ/9Y5n/8B8k3LYJ9IyRG00ZYJN0i3alwkvasRdCQBKq0i8MswOlxybYlhocRUln2m3/rUSmOSerFDDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3be74a7c0f0b4221673a3956d530541bbcfcf85d03dc86268ea812353a3e832a","last_reissued_at":"2026-05-17T23:39:17.790104Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:39:17.790104Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2507.23180","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":"2026-05-17T23:39:17Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"fNeEsuKsdBM43ma1bRM80xdROgMW8hVlk0i9sz6WsblQ6HJgkYTC08l9DO/ReySkU0q3o5JFauv3OLTWAmOyAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-21T10:08:02.900983Z"},"content_sha256":"c4cb20568cf0daf8a22a1eaa362e751a12b7c8f0e325a37f9fba924ae3b9a128","schema_version":"1.0","event_id":"sha256:c4cb20568cf0daf8a22a1eaa362e751a12b7c8f0e325a37f9fba924ae3b9a128"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2025:HPTUU7APBNBCCZZ2HFLNKMCUDO","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The Construction of Near-optimal Universal Coding of Integers","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"Wei Yan, Yunghsiang S. Han","submitted_at":"2025-07-31T01:21:06Z","abstract_excerpt":"The Universal Coding of Integers~(UCI) is suitable for discrete memoryless sources with unknown probability distributions and infinitely countable alphabet sizes. A UCI is a class of prefix codes for which the ratio of the average codeword length to $\\max\\{1,H(P)\\}$ is within a constant expansion factor \\textcolor{red}{$C_{\\mathcal{C}}$} for any decreasing probability distribution $P$, where $H(P)$ is the entropy of $P$. For any UCI code $\\mathcal{C}$, \\emph{the minimum expansion factor} \\textcolor{red}{$C_{\\mathcal{C}}^{*}$} is defined to represent the infimum of the set of extension factors "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2507.23180","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":"2026-05-17T23:39:17Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"MkRfpzjkVL3eMsIaBxLY8j7NFabQlNVM497eAClEePPxf+TpRgBkvmC9/stMVGYnxf8FAz+1dLH8s+6rq5ZwCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-21T10:08:02.901344Z"},"content_sha256":"623a43582589345dbdcd7e8e3ed644c00fc17bfaa0d0bc6cfc309cf597b24d1f","schema_version":"1.0","event_id":"sha256:623a43582589345dbdcd7e8e3ed644c00fc17bfaa0d0bc6cfc309cf597b24d1f"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/HPTUU7APBNBCCZZ2HFLNKMCUDO/bundle.json","state_url":"https://pith.science/pith/HPTUU7APBNBCCZZ2HFLNKMCUDO/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/HPTUU7APBNBCCZZ2HFLNKMCUDO/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":"2026-05-21T10:08:02Z","links":{"resolver":"https://pith.science/pith/HPTUU7APBNBCCZZ2HFLNKMCUDO","bundle":"https://pith.science/pith/HPTUU7APBNBCCZZ2HFLNKMCUDO/bundle.json","state":"https://pith.science/pith/HPTUU7APBNBCCZZ2HFLNKMCUDO/state.json","well_known_bundle":"https://pith.science/.well-known/pith/HPTUU7APBNBCCZZ2HFLNKMCUDO/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:HPTUU7APBNBCCZZ2HFLNKMCUDO","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":"ec0d52df8421bd5b8b3d3c0bf2a216c58fc64da872d6d2071b8e36201a77f88e","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2025-07-31T01:21:06Z","title_canon_sha256":"730198a0f37b0e88d5dae5fe18b95f08ece3201db8863658345de36a6a9261c0"},"schema_version":"1.0","source":{"id":"2507.23180","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2507.23180","created_at":"2026-05-17T23:39:17Z"},{"alias_kind":"arxiv_version","alias_value":"2507.23180v2","created_at":"2026-05-17T23:39:17Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2507.23180","created_at":"2026-05-17T23:39:17Z"},{"alias_kind":"pith_short_12","alias_value":"HPTUU7APBNBC","created_at":"2026-05-18T12:33:37Z"},{"alias_kind":"pith_short_16","alias_value":"HPTUU7APBNBCCZZ2","created_at":"2026-05-18T12:33:37Z"},{"alias_kind":"pith_short_8","alias_value":"HPTUU7AP","created_at":"2026-05-18T12:33:37Z"}],"graph_snapshots":[{"event_id":"sha256:623a43582589345dbdcd7e8e3ed644c00fc17bfaa0d0bc6cfc309cf597b24d1f","target":"graph","created_at":"2026-05-17T23:39:17Z","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":"The Universal Coding of Integers~(UCI) is suitable for discrete memoryless sources with unknown probability distributions and infinitely countable alphabet sizes. A UCI is a class of prefix codes for which the ratio of the average codeword length to $\\max\\{1,H(P)\\}$ is within a constant expansion factor \\textcolor{red}{$C_{\\mathcal{C}}$} for any decreasing probability distribution $P$, where $H(P)$ is the entropy of $P$. For any UCI code $\\mathcal{C}$, \\emph{the minimum expansion factor} \\textcolor{red}{$C_{\\mathcal{C}}^{*}$} is defined to represent the infimum of the set of extension factors ","authors_text":"Wei Yan, Yunghsiang S. Han","cross_cats":["math.IT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2025-07-31T01:21:06Z","title":"The Construction of Near-optimal Universal Coding of Integers"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2507.23180","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:c4cb20568cf0daf8a22a1eaa362e751a12b7c8f0e325a37f9fba924ae3b9a128","target":"record","created_at":"2026-05-17T23:39:17Z","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":"ec0d52df8421bd5b8b3d3c0bf2a216c58fc64da872d6d2071b8e36201a77f88e","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2025-07-31T01:21:06Z","title_canon_sha256":"730198a0f37b0e88d5dae5fe18b95f08ece3201db8863658345de36a6a9261c0"},"schema_version":"1.0","source":{"id":"2507.23180","kind":"arxiv","version":2}},"canonical_sha256":"3be74a7c0f0b4221673a3956d530541bbcfcf85d03dc86268ea812353a3e832a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3be74a7c0f0b4221673a3956d530541bbcfcf85d03dc86268ea812353a3e832a","first_computed_at":"2026-05-17T23:39:17.790104Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:39:17.790104Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"YrqOHMJJ/9Y5n/8B8k3LYJ9IyRG00ZYJN0i3alwkvasRdCQBKq0i8MswOlxybYlhocRUln2m3/rUSmOSerFDDg==","signature_status":"signed_v1","signed_at":"2026-05-17T23:39:17.790839Z","signed_message":"canonical_sha256_bytes"},"source_id":"2507.23180","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c4cb20568cf0daf8a22a1eaa362e751a12b7c8f0e325a37f9fba924ae3b9a128","sha256:623a43582589345dbdcd7e8e3ed644c00fc17bfaa0d0bc6cfc309cf597b24d1f"],"state_sha256":"19765d2c07b09d7fb05b249b0add2f80e2bbb9484d78458ca2c5743659eb9d1c"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"mEfyceJu8I2zdaKSrHKFU9eC1KUKVQs8V0RraC7gnMIoYSRluVFRE14m+TW+iMWywjuoptuORfuV4xtem7ubDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-21T10:08:02.903363Z","bundle_sha256":"bd8e4fc223eb0d9584b7ae6b71c18624cede6336ea66bae0976f46c3284bb272"}}