{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:42CAWFWAM7BRIXQ5R327BI5YIA","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":"7c34c86f583636bf77f88e6ea1c37a9fcd677e04bd3414bcf3bfce16ae7cbaa5","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-11-26T01:45:33Z","title_canon_sha256":"82c0a5489e368be092dc1dc010ff5c99a0165acf357139035fbf566b2a79033e"},"schema_version":"1.0","source":{"id":"1511.08267","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1511.08267","created_at":"2026-05-18T01:25:56Z"},{"alias_kind":"arxiv_version","alias_value":"1511.08267v1","created_at":"2026-05-18T01:25:56Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1511.08267","created_at":"2026-05-18T01:25:56Z"},{"alias_kind":"pith_short_12","alias_value":"42CAWFWAM7BR","created_at":"2026-05-18T12:29:02Z"},{"alias_kind":"pith_short_16","alias_value":"42CAWFWAM7BRIXQ5","created_at":"2026-05-18T12:29:02Z"},{"alias_kind":"pith_short_8","alias_value":"42CAWFWA","created_at":"2026-05-18T12:29:02Z"}],"graph_snapshots":[{"event_id":"sha256:ae514a092ef51c7dbee0c88ffea1077b5d418a690f464521259654225376549d","target":"graph","created_at":"2026-05-18T01:25:56Z","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":"Using methods developed by Coons and Tyler, we give a new proof of a recent result of Defant, by determining the maximal order of the number of hyper-($b$-ary)-expansions of a nonnegative integer $n$ for general integral bases $b\\geqslant 2$.","authors_text":"Lukas Spiegelhofer, Michael Coons","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-11-26T01:45:33Z","title":"The maximal order of hyper-($b$-ary)-expansions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1511.08267","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:cd39435f7b7c1f55c99b246de110c2b9f6e797f7b2234d77ca0d71d2a6277398","target":"record","created_at":"2026-05-18T01:25:56Z","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":"7c34c86f583636bf77f88e6ea1c37a9fcd677e04bd3414bcf3bfce16ae7cbaa5","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-11-26T01:45:33Z","title_canon_sha256":"82c0a5489e368be092dc1dc010ff5c99a0165acf357139035fbf566b2a79033e"},"schema_version":"1.0","source":{"id":"1511.08267","kind":"arxiv","version":1}},"canonical_sha256":"e6840b16c067c3145e1d8ef5f0a3b8403473dc96e013183ce0ffd5411aab90b0","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e6840b16c067c3145e1d8ef5f0a3b8403473dc96e013183ce0ffd5411aab90b0","first_computed_at":"2026-05-18T01:25:56.170488Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:25:56.170488Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"g5Sq2N+q1p/+mG2vwq6I4xTlooUEJG0YWLEexhfnSVwMLEngzzElUf682zpeuNarEI9wtT/oLTpN6Pc4gMwICw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:25:56.171221Z","signed_message":"canonical_sha256_bytes"},"source_id":"1511.08267","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:cd39435f7b7c1f55c99b246de110c2b9f6e797f7b2234d77ca0d71d2a6277398","sha256:ae514a092ef51c7dbee0c88ffea1077b5d418a690f464521259654225376549d"],"state_sha256":"e8179ceec0417f0517bdb4f61812354304e9353f4be0aa457eee534b0a1c1428"}