{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2007:UQGJSG7KVJ6QGYSQPBQB7YJGLL","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":"206e9332a7b1e86358bc46d74cd657dc1ce46bd0aca390065ec32b85f3312f3a","cross_cats_sorted":["cs.DS","math.IT"],"license":"","primary_cat":"cs.IT","submitted_at":"2007-01-03T03:42:09Z","title_canon_sha256":"4613969d4ac6f853d09bfc0ab37f142c14eb7b2f227a6a22e402ff419ccbbb41"},"schema_version":"1.0","source":{"id":"cs/0701012","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"cs/0701012","created_at":"2026-07-04T15:02:54Z"},{"alias_kind":"arxiv_version","alias_value":"cs/0701012v2","created_at":"2026-07-04T15:02:54Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.cs/0701012","created_at":"2026-07-04T15:02:54Z"},{"alias_kind":"pith_short_12","alias_value":"UQGJSG7KVJ6Q","created_at":"2026-07-04T15:02:54Z"},{"alias_kind":"pith_short_16","alias_value":"UQGJSG7KVJ6QGYSQ","created_at":"2026-07-04T15:02:54Z"},{"alias_kind":"pith_short_8","alias_value":"UQGJSG7K","created_at":"2026-07-04T15:02:54Z"}],"graph_snapshots":[{"event_id":"sha256:7f1f132c5070376cfe28ab610014cac3d0f68ed96df05c63ceb38a993ae89f1a","target":"graph","created_at":"2026-07-04T15:02:54Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/cs/0701012/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Efficient optimal prefix coding has long been accomplished via the Huffman algorithm. However, there is still room for improvement and exploration regarding variants of the Huffman problem. Length-limited Huffman coding, useful for many practical applications, is one such variant, in which codes are restricted to the set of codes in which none of the $n$ codewords is longer than a given length, $l_{\\max}$. Binary length-limited coding can be done in $O(n l_{\\max})$ time and O(n) space via the widely used Package-Merge algorithm. In this paper the Package-Merge approach is generalized without i","authors_text":"Michael B. Baer","cross_cats":["cs.DS","math.IT"],"headline":"","license":"","primary_cat":"cs.IT","submitted_at":"2007-01-03T03:42:09Z","title":"$D$-ary Bounded-Length Huffman Coding"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"cs/0701012","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:defc5d126ed1df61f337b72a3a33a4df63bd9579f90cc447f1c90e570677c78e","target":"record","created_at":"2026-07-04T15:02:54Z","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":"206e9332a7b1e86358bc46d74cd657dc1ce46bd0aca390065ec32b85f3312f3a","cross_cats_sorted":["cs.DS","math.IT"],"license":"","primary_cat":"cs.IT","submitted_at":"2007-01-03T03:42:09Z","title_canon_sha256":"4613969d4ac6f853d09bfc0ab37f142c14eb7b2f227a6a22e402ff419ccbbb41"},"schema_version":"1.0","source":{"id":"cs/0701012","kind":"arxiv","version":2}},"canonical_sha256":"a40c991beaaa7d03625078601fe1265adc09c76709694adbc1f70bb553d14246","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a40c991beaaa7d03625078601fe1265adc09c76709694adbc1f70bb553d14246","first_computed_at":"2026-07-04T15:02:54.816737Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-04T15:02:54.816737Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"TMvSd1ZwQ7Eqx6Dk4chgdb2m2oOUEZI7WYqWSqOuKIc/0cU2E6tfK5RaX/1C1brGYwflf+QakQWw06Tu3BYiBw==","signature_status":"signed_v1","signed_at":"2026-07-04T15:02:54.817140Z","signed_message":"canonical_sha256_bytes"},"source_id":"cs/0701012","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:defc5d126ed1df61f337b72a3a33a4df63bd9579f90cc447f1c90e570677c78e","sha256:7f1f132c5070376cfe28ab610014cac3d0f68ed96df05c63ceb38a993ae89f1a"],"state_sha256":"bc8615b1bb18d83f224fa79ef377a650dcdde2a21f53021741baa064789100ac"}