{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:IGYDOH2LLSGKODTGHLPCZBAFNI","short_pith_number":"pith:IGYDOH2L","canonical_record":{"source":{"id":"1603.05815","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2016-03-18T10:10:57Z","cross_cats_sorted":["math.DS","math.NA","math.NT"],"title_canon_sha256":"25061d2dad6381b01a21f7a52326d114bcbae2645762a9a8055867bdde105daf","abstract_canon_sha256":"c6d1b37b1f9bbecf9c3311ab5ddd05e4b7e449a7871433f0b1e29eb57251771f"},"schema_version":"1.0"},"canonical_sha256":"41b0371f4b5c8ca70e663ade2c84056a1203a9701c0262ad554f23ec03aac806","source":{"kind":"arxiv","id":"1603.05815","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1603.05815","created_at":"2026-05-18T01:01:00Z"},{"alias_kind":"arxiv_version","alias_value":"1603.05815v2","created_at":"2026-05-18T01:01:00Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1603.05815","created_at":"2026-05-18T01:01:00Z"},{"alias_kind":"pith_short_12","alias_value":"IGYDOH2LLSGK","created_at":"2026-05-18T12:30:22Z"},{"alias_kind":"pith_short_16","alias_value":"IGYDOH2LLSGKODTG","created_at":"2026-05-18T12:30:22Z"},{"alias_kind":"pith_short_8","alias_value":"IGYDOH2L","created_at":"2026-05-18T12:30:22Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:IGYDOH2LLSGKODTGHLPCZBAFNI","target":"record","payload":{"canonical_record":{"source":{"id":"1603.05815","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2016-03-18T10:10:57Z","cross_cats_sorted":["math.DS","math.NA","math.NT"],"title_canon_sha256":"25061d2dad6381b01a21f7a52326d114bcbae2645762a9a8055867bdde105daf","abstract_canon_sha256":"c6d1b37b1f9bbecf9c3311ab5ddd05e4b7e449a7871433f0b1e29eb57251771f"},"schema_version":"1.0"},"canonical_sha256":"41b0371f4b5c8ca70e663ade2c84056a1203a9701c0262ad554f23ec03aac806","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:01:00.248275Z","signature_b64":"RvXAUN2i8Ngc0J0WZpq2tzdjmVZCg+0Ven8BucnYs3GZqYuo4GRUQFZ+a+h0oUbbVPRixSKVGLnR775UJ8eCBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"41b0371f4b5c8ca70e663ade2c84056a1203a9701c0262ad554f23ec03aac806","last_reissued_at":"2026-05-18T01:01:00.247550Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:01:00.247550Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1603.05815","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":"2026-05-18T01:01:00Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"sVXtwkuZuljqMH4bYzi1g8AhX3/LdSn3hV20KJD+tjRuZrxy0iHJzP4MZzE7gX5bYvuLLellfqfiMbdmLsS6BA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-08T22:11:26.062885Z"},"content_sha256":"bb9ac7f7d00f779dea7beae083261e6cd475944edcecb24fb4bde708d7b0ff62","schema_version":"1.0","event_id":"sha256:bb9ac7f7d00f779dea7beae083261e6cd475944edcecb24fb4bde708d7b0ff62"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:IGYDOH2LLSGKODTGHLPCZBAFNI","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Minkowski's Question Mark Measure","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DS","math.NA","math.NT"],"primary_cat":"math.CA","authors_text":"Giorgio Mantica","submitted_at":"2016-03-18T10:10:57Z","abstract_excerpt":"Minkowski's question mark function is the distribution function of a singular continuous measure: we study this measure from the point of view of logarithmic potential theory and orthogonal polynomials. We conjecture that it is regular, in the sense of Ullman--Stahl--Totik and moreover it belongs to a Nevai class: we provide numerical evidence of the validity of these conjectures. In addition, we study the zeros of its orthogonal polynomials and the associated Christoffel functions, for which asymptotic formulae are derived. Rigorous results and numerical techniques are based upon Iterated Fun"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1603.05815","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":"2026-05-18T01:01:00Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"NmbL2vAVe38uA7bVXcmRBVdQ6XyhkCKAuNKehc6n6X2GD1Fza1lCiTwuPD3oFmDjNY8v2OPmFmE1fRTiDL82Ag==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-08T22:11:26.063226Z"},"content_sha256":"11e0f36f688f928e9ffada07cd9917884b9ac96d3967b98cd572662011cf43ec","schema_version":"1.0","event_id":"sha256:11e0f36f688f928e9ffada07cd9917884b9ac96d3967b98cd572662011cf43ec"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/IGYDOH2LLSGKODTGHLPCZBAFNI/bundle.json","state_url":"https://pith.science/pith/IGYDOH2LLSGKODTGHLPCZBAFNI/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/IGYDOH2LLSGKODTGHLPCZBAFNI/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":"2026-06-08T22:11:26Z","links":{"resolver":"https://pith.science/pith/IGYDOH2LLSGKODTGHLPCZBAFNI","bundle":"https://pith.science/pith/IGYDOH2LLSGKODTGHLPCZBAFNI/bundle.json","state":"https://pith.science/pith/IGYDOH2LLSGKODTGHLPCZBAFNI/state.json","well_known_bundle":"https://pith.science/.well-known/pith/IGYDOH2LLSGKODTGHLPCZBAFNI/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:IGYDOH2LLSGKODTGHLPCZBAFNI","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":"c6d1b37b1f9bbecf9c3311ab5ddd05e4b7e449a7871433f0b1e29eb57251771f","cross_cats_sorted":["math.DS","math.NA","math.NT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2016-03-18T10:10:57Z","title_canon_sha256":"25061d2dad6381b01a21f7a52326d114bcbae2645762a9a8055867bdde105daf"},"schema_version":"1.0","source":{"id":"1603.05815","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1603.05815","created_at":"2026-05-18T01:01:00Z"},{"alias_kind":"arxiv_version","alias_value":"1603.05815v2","created_at":"2026-05-18T01:01:00Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1603.05815","created_at":"2026-05-18T01:01:00Z"},{"alias_kind":"pith_short_12","alias_value":"IGYDOH2LLSGK","created_at":"2026-05-18T12:30:22Z"},{"alias_kind":"pith_short_16","alias_value":"IGYDOH2LLSGKODTG","created_at":"2026-05-18T12:30:22Z"},{"alias_kind":"pith_short_8","alias_value":"IGYDOH2L","created_at":"2026-05-18T12:30:22Z"}],"graph_snapshots":[{"event_id":"sha256:11e0f36f688f928e9ffada07cd9917884b9ac96d3967b98cd572662011cf43ec","target":"graph","created_at":"2026-05-18T01:01:00Z","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":"Minkowski's question mark function is the distribution function of a singular continuous measure: we study this measure from the point of view of logarithmic potential theory and orthogonal polynomials. We conjecture that it is regular, in the sense of Ullman--Stahl--Totik and moreover it belongs to a Nevai class: we provide numerical evidence of the validity of these conjectures. In addition, we study the zeros of its orthogonal polynomials and the associated Christoffel functions, for which asymptotic formulae are derived. Rigorous results and numerical techniques are based upon Iterated Fun","authors_text":"Giorgio Mantica","cross_cats":["math.DS","math.NA","math.NT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2016-03-18T10:10:57Z","title":"Minkowski's Question Mark Measure"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1603.05815","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:bb9ac7f7d00f779dea7beae083261e6cd475944edcecb24fb4bde708d7b0ff62","target":"record","created_at":"2026-05-18T01:01:00Z","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":"c6d1b37b1f9bbecf9c3311ab5ddd05e4b7e449a7871433f0b1e29eb57251771f","cross_cats_sorted":["math.DS","math.NA","math.NT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2016-03-18T10:10:57Z","title_canon_sha256":"25061d2dad6381b01a21f7a52326d114bcbae2645762a9a8055867bdde105daf"},"schema_version":"1.0","source":{"id":"1603.05815","kind":"arxiv","version":2}},"canonical_sha256":"41b0371f4b5c8ca70e663ade2c84056a1203a9701c0262ad554f23ec03aac806","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"41b0371f4b5c8ca70e663ade2c84056a1203a9701c0262ad554f23ec03aac806","first_computed_at":"2026-05-18T01:01:00.247550Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:01:00.247550Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"RvXAUN2i8Ngc0J0WZpq2tzdjmVZCg+0Ven8BucnYs3GZqYuo4GRUQFZ+a+h0oUbbVPRixSKVGLnR775UJ8eCBw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:01:00.248275Z","signed_message":"canonical_sha256_bytes"},"source_id":"1603.05815","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:bb9ac7f7d00f779dea7beae083261e6cd475944edcecb24fb4bde708d7b0ff62","sha256:11e0f36f688f928e9ffada07cd9917884b9ac96d3967b98cd572662011cf43ec"],"state_sha256":"a087361bd85f7067967599bc769c485b344b34b07c32d4856fe0e93656c3359a"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"tNZptRP/FXkq2/f3IOUlT3ogJoIb53ppQF3JUbSI062FeaGI15S5PVSeIMxM+4RQTs7uxc5KCtsCOI0EobpuAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-08T22:11:26.065075Z","bundle_sha256":"4c6c4e2040f82e714f44c7119015957475ef80f0f89775420bde4cae56d88fd4"}}