{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:ZPT4B5GS22H77OLJAOKBJ2OW5A","short_pith_number":"pith:ZPT4B5GS","canonical_record":{"source":{"id":"1707.06677","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2017-07-20T19:03:19Z","cross_cats_sorted":[],"title_canon_sha256":"39190edc6ca0aea33f994fffacc2470451420c22f0c5d611ee8ab0efb8e9502a","abstract_canon_sha256":"fcb0ea604a72c031c2de8f13ac2452b0f34969a5b48c0d451ade1c27d09a870f"},"schema_version":"1.0"},"canonical_sha256":"cbe7c0f4d2d68fffb969039414e9d6e81786c447ca5601dc834f23863d7d3ece","source":{"kind":"arxiv","id":"1707.06677","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1707.06677","created_at":"2026-05-18T00:39:52Z"},{"alias_kind":"arxiv_version","alias_value":"1707.06677v1","created_at":"2026-05-18T00:39:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1707.06677","created_at":"2026-05-18T00:39:52Z"},{"alias_kind":"pith_short_12","alias_value":"ZPT4B5GS22H7","created_at":"2026-05-18T12:31:59Z"},{"alias_kind":"pith_short_16","alias_value":"ZPT4B5GS22H77OLJ","created_at":"2026-05-18T12:31:59Z"},{"alias_kind":"pith_short_8","alias_value":"ZPT4B5GS","created_at":"2026-05-18T12:31:59Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:ZPT4B5GS22H77OLJAOKBJ2OW5A","target":"record","payload":{"canonical_record":{"source":{"id":"1707.06677","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2017-07-20T19:03:19Z","cross_cats_sorted":[],"title_canon_sha256":"39190edc6ca0aea33f994fffacc2470451420c22f0c5d611ee8ab0efb8e9502a","abstract_canon_sha256":"fcb0ea604a72c031c2de8f13ac2452b0f34969a5b48c0d451ade1c27d09a870f"},"schema_version":"1.0"},"canonical_sha256":"cbe7c0f4d2d68fffb969039414e9d6e81786c447ca5601dc834f23863d7d3ece","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:39:52.004353Z","signature_b64":"93TgyKUitDdWVupKr0eXVXoSCQQQ0UDXbXH/r1QkDl4BJU1uDrGKsEStNGx03wPhiEHbTZ4Cq/TXiGeGyN/KCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"cbe7c0f4d2d68fffb969039414e9d6e81786c447ca5601dc834f23863d7d3ece","last_reissued_at":"2026-05-18T00:39:52.003642Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:39:52.003642Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1707.06677","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:39:52Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"AIF8jsnNa3r95/6FZfJp6MdH1Smpx+ghYhyaeu9DtqrQdecroeA/KKfR33lsVx7tDO8MTMLod8/9YO5oKPTPCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-26T01:32:31.805163Z"},"content_sha256":"31cd85fa57181f5cf1fb7d15ebd232bd3462876ec1db01bfb7fb3db449238bff","schema_version":"1.0","event_id":"sha256:31cd85fa57181f5cf1fb7d15ebd232bd3462876ec1db01bfb7fb3db449238bff"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:ZPT4B5GS22H77OLJAOKBJ2OW5A","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On irrationality measure of Thue-Morse constant","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Dzmitry Badziahin, Evgeniy Zorin","submitted_at":"2017-07-20T19:03:19Z","abstract_excerpt":"We provide a non-trivial measure of irrationality for a class of Mahler numbers defined with infinite products which cover the Thue-Morse constant."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1707.06677","kind":"arxiv","version":1},"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":"2026-05-18T00:39:52Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"geJNx8HmCH8ijx92g6hXEWIW6JDaqh5ZUmRT6etuaDlfL1q/bzVxjgO0gD6L2Gx3ZMHH75h3kwl1YcgH7JlNBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-26T01:32:31.805538Z"},"content_sha256":"e12cad208b807b48725545eb2f2b63aea6ce8e79304532d7962aac9efdcfef8f","schema_version":"1.0","event_id":"sha256:e12cad208b807b48725545eb2f2b63aea6ce8e79304532d7962aac9efdcfef8f"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/ZPT4B5GS22H77OLJAOKBJ2OW5A/bundle.json","state_url":"https://pith.science/pith/ZPT4B5GS22H77OLJAOKBJ2OW5A/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/ZPT4B5GS22H77OLJAOKBJ2OW5A/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":"2026-06-26T01:32:31Z","links":{"resolver":"https://pith.science/pith/ZPT4B5GS22H77OLJAOKBJ2OW5A","bundle":"https://pith.science/pith/ZPT4B5GS22H77OLJAOKBJ2OW5A/bundle.json","state":"https://pith.science/pith/ZPT4B5GS22H77OLJAOKBJ2OW5A/state.json","well_known_bundle":"https://pith.science/.well-known/pith/ZPT4B5GS22H77OLJAOKBJ2OW5A/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:ZPT4B5GS22H77OLJAOKBJ2OW5A","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":"fcb0ea604a72c031c2de8f13ac2452b0f34969a5b48c0d451ade1c27d09a870f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2017-07-20T19:03:19Z","title_canon_sha256":"39190edc6ca0aea33f994fffacc2470451420c22f0c5d611ee8ab0efb8e9502a"},"schema_version":"1.0","source":{"id":"1707.06677","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1707.06677","created_at":"2026-05-18T00:39:52Z"},{"alias_kind":"arxiv_version","alias_value":"1707.06677v1","created_at":"2026-05-18T00:39:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1707.06677","created_at":"2026-05-18T00:39:52Z"},{"alias_kind":"pith_short_12","alias_value":"ZPT4B5GS22H7","created_at":"2026-05-18T12:31:59Z"},{"alias_kind":"pith_short_16","alias_value":"ZPT4B5GS22H77OLJ","created_at":"2026-05-18T12:31:59Z"},{"alias_kind":"pith_short_8","alias_value":"ZPT4B5GS","created_at":"2026-05-18T12:31:59Z"}],"graph_snapshots":[{"event_id":"sha256:e12cad208b807b48725545eb2f2b63aea6ce8e79304532d7962aac9efdcfef8f","target":"graph","created_at":"2026-05-18T00:39:52Z","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":"We provide a non-trivial measure of irrationality for a class of Mahler numbers defined with infinite products which cover the Thue-Morse constant.","authors_text":"Dzmitry Badziahin, Evgeniy Zorin","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2017-07-20T19:03:19Z","title":"On irrationality measure of Thue-Morse constant"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1707.06677","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":"sha256:31cd85fa57181f5cf1fb7d15ebd232bd3462876ec1db01bfb7fb3db449238bff","target":"record","created_at":"2026-05-18T00:39:52Z","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":"fcb0ea604a72c031c2de8f13ac2452b0f34969a5b48c0d451ade1c27d09a870f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2017-07-20T19:03:19Z","title_canon_sha256":"39190edc6ca0aea33f994fffacc2470451420c22f0c5d611ee8ab0efb8e9502a"},"schema_version":"1.0","source":{"id":"1707.06677","kind":"arxiv","version":1}},"canonical_sha256":"cbe7c0f4d2d68fffb969039414e9d6e81786c447ca5601dc834f23863d7d3ece","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"cbe7c0f4d2d68fffb969039414e9d6e81786c447ca5601dc834f23863d7d3ece","first_computed_at":"2026-05-18T00:39:52.003642Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:39:52.003642Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"93TgyKUitDdWVupKr0eXVXoSCQQQ0UDXbXH/r1QkDl4BJU1uDrGKsEStNGx03wPhiEHbTZ4Cq/TXiGeGyN/KCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:39:52.004353Z","signed_message":"canonical_sha256_bytes"},"source_id":"1707.06677","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:31cd85fa57181f5cf1fb7d15ebd232bd3462876ec1db01bfb7fb3db449238bff","sha256:e12cad208b807b48725545eb2f2b63aea6ce8e79304532d7962aac9efdcfef8f"],"state_sha256":"45f4159178028fe14ba2c98b02499f36aaf2367ed644076b0b782243b079e9d0"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"l9S4FpFtAGhU6forju96e+aGRsmTw9gyTWpMoZ4Jvw7oGvZkYLtZxDOqHSSxD/PwMJr9MbzBw/JClEsUM8x/Cw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-26T01:32:31.807495Z","bundle_sha256":"37d63b62a29c061f8f9f2b5b37941a9e254250a2d91870629024db64f4795410"}}