{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:EUHYJ5UD4P4UY6GOPK3B3PNKRN","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":"c242ee0114c1dc47e8448fc37850a58c863e65cda39923cda7caed4793452143","cross_cats_sorted":["cs.DM","math.NT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2011-08-30T14:16:08Z","title_canon_sha256":"a43ccbd9ff2dd78b833457eaafb4c041fb552d3a8175872e4cf7847ca67d3582"},"schema_version":"1.0","source":{"id":"1108.5964","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1108.5964","created_at":"2026-05-18T03:28:54Z"},{"alias_kind":"arxiv_version","alias_value":"1108.5964v1","created_at":"2026-05-18T03:28:54Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1108.5964","created_at":"2026-05-18T03:28:54Z"},{"alias_kind":"pith_short_12","alias_value":"EUHYJ5UD4P4U","created_at":"2026-05-18T12:26:28Z"},{"alias_kind":"pith_short_16","alias_value":"EUHYJ5UD4P4UY6GO","created_at":"2026-05-18T12:26:28Z"},{"alias_kind":"pith_short_8","alias_value":"EUHYJ5UD","created_at":"2026-05-18T12:26:28Z"}],"graph_snapshots":[{"event_id":"sha256:a42dc9c32abdce49db1f2699fa99bb992f2cd015ef0472d4b4c44d685fabc1da","target":"graph","created_at":"2026-05-18T03:28:54Z","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"},"paper":{"abstract_excerpt":"The number of \"nonequivalent\" Huffman codes of length r over an alphabet of size t has been studied frequently. Equivalently, the number of \"nonequivalent\" complete t-ary trees has been examined. We first survey the literature, unifying several independent approaches to the problem. Then, improving on earlier work we prove a very precise asymptotic result on the counting function, consisting of two main terms and an error term.","authors_text":"Christian Elsholtz, Clemens Heuberger, Helmut Prodinger","cross_cats":["cs.DM","math.NT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2011-08-30T14:16:08Z","title":"The number of Huffman codes, compact trees, and sums of unit fractions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1108.5964","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:a86961d7e93e641503056273bb4a7a5898bbb874096a4ed03302766deb91f75c","target":"record","created_at":"2026-05-18T03:28:54Z","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":"c242ee0114c1dc47e8448fc37850a58c863e65cda39923cda7caed4793452143","cross_cats_sorted":["cs.DM","math.NT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2011-08-30T14:16:08Z","title_canon_sha256":"a43ccbd9ff2dd78b833457eaafb4c041fb552d3a8175872e4cf7847ca67d3582"},"schema_version":"1.0","source":{"id":"1108.5964","kind":"arxiv","version":1}},"canonical_sha256":"250f84f683e3f94c78ce7ab61dbdaa8b7187789c244a77dff4ff5927c04169cf","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"250f84f683e3f94c78ce7ab61dbdaa8b7187789c244a77dff4ff5927c04169cf","first_computed_at":"2026-05-18T03:28:54.228615Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:28:54.228615Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"cc2yiNDrtYAX/owYysckOeoQjnMgodJV67K5cc9nTFZWQbepgabeCvfwcHiUyZierUfx3SdHQ5AmMbmUZIjABw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:28:54.229271Z","signed_message":"canonical_sha256_bytes"},"source_id":"1108.5964","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a86961d7e93e641503056273bb4a7a5898bbb874096a4ed03302766deb91f75c","sha256:a42dc9c32abdce49db1f2699fa99bb992f2cd015ef0472d4b4c44d685fabc1da"],"state_sha256":"180502dd257b68c7f6379a22dd6508c09a182e5da1c2f11e9fa06c065aa58cdb"}