{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2009:BDJNQ75ZDUEXURTFDQYURXOWJG","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":"7641a283ea8786ec9a38e615952ec7a52384144a3a72d7210207dcb690e57f89","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2009-12-06T18:01:57Z","title_canon_sha256":"99d503c409bd730c90d4ca24eaf4f84784386f0daca5af152d5f8f043599ec3f"},"schema_version":"1.0","source":{"id":"0912.1039","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0912.1039","created_at":"2026-05-18T04:18:23Z"},{"alias_kind":"arxiv_version","alias_value":"0912.1039v1","created_at":"2026-05-18T04:18:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0912.1039","created_at":"2026-05-18T04:18:23Z"},{"alias_kind":"pith_short_12","alias_value":"BDJNQ75ZDUEX","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_16","alias_value":"BDJNQ75ZDUEXURTF","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_8","alias_value":"BDJNQ75Z","created_at":"2026-05-18T12:25:58Z"}],"graph_snapshots":[{"event_id":"sha256:be61830cad7e5968e6b4b9854390068023ae03b8c9ce000d9918ede6130e6dae","target":"graph","created_at":"2026-05-18T04:18:23Z","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":"This paper continues investigations on the integral transforms of the Minkowski question mark function. In this work we finally establish the long-sought formula for the moments, which does not explicitly involve regular continued fractions, though it has a hidden nice interpretation in terms of semi-regular continued fractions. The proof is self-contained and does not rely on previous results by the author.","authors_text":"Giedrius Alkauskas","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2009-12-06T18:01:57Z","title":"Semi-regular continued fractions and an exact formula for the moments of the Minkowski question mark function"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0912.1039","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":"sha256:27e7885181c6de44d4d53ed5287e741fa191bdc7b449f5b3e98bacc837db5508","target":"record","created_at":"2026-05-18T04:18:23Z","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":"7641a283ea8786ec9a38e615952ec7a52384144a3a72d7210207dcb690e57f89","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2009-12-06T18:01:57Z","title_canon_sha256":"99d503c409bd730c90d4ca24eaf4f84784386f0daca5af152d5f8f043599ec3f"},"schema_version":"1.0","source":{"id":"0912.1039","kind":"arxiv","version":1}},"canonical_sha256":"08d2d87fb91d097a46651c3148ddd649b20f55d5264e3dfdb8ed36ef2f1b67f7","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"08d2d87fb91d097a46651c3148ddd649b20f55d5264e3dfdb8ed36ef2f1b67f7","first_computed_at":"2026-05-18T04:18:23.626549Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:18:23.626549Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"M8nAoTn5yxjbRDLDAGye1sUy696ULUSQaPnp/VOaSsZ8TkM6dqC4Ulr2R1K+f0PgRiid7fp+xhvyNpOKkBkwBA==","signature_status":"signed_v1","signed_at":"2026-05-18T04:18:23.627208Z","signed_message":"canonical_sha256_bytes"},"source_id":"0912.1039","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:27e7885181c6de44d4d53ed5287e741fa191bdc7b449f5b3e98bacc837db5508","sha256:be61830cad7e5968e6b4b9854390068023ae03b8c9ce000d9918ede6130e6dae"],"state_sha256":"d8338adba7585ad791f2b3f6fec2690a137ad9457a97cfd7cd81181148718e8a"}