{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:XWCABR2X7LI5IJIQNC74BGNRV7","short_pith_number":"pith:XWCABR2X","canonical_record":{"source":{"id":"1610.04026","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2016-10-13T11:14:37Z","cross_cats_sorted":["cs.CC","math.LO"],"title_canon_sha256":"583325f091f0ad79584779d0c119e90cafa9cd95ad04ba095772afcb590a9238","abstract_canon_sha256":"098bb72d003b12451509b4276288155334b127e40ff63e6afeeb7fbeb650d868"},"schema_version":"1.0"},"canonical_sha256":"bd8400c757fad1d4251068bfc099b1afff0ca47869cc1591de79afcbcc45db36","source":{"kind":"arxiv","id":"1610.04026","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1610.04026","created_at":"2026-05-18T01:01:37Z"},{"alias_kind":"arxiv_version","alias_value":"1610.04026v3","created_at":"2026-05-18T01:01:37Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1610.04026","created_at":"2026-05-18T01:01:37Z"},{"alias_kind":"pith_short_12","alias_value":"XWCABR2X7LI5","created_at":"2026-05-18T12:30:51Z"},{"alias_kind":"pith_short_16","alias_value":"XWCABR2X7LI5IJIQ","created_at":"2026-05-18T12:30:51Z"},{"alias_kind":"pith_short_8","alias_value":"XWCABR2X","created_at":"2026-05-18T12:30:51Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:XWCABR2X7LI5IJIQNC74BGNRV7","target":"record","payload":{"canonical_record":{"source":{"id":"1610.04026","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2016-10-13T11:14:37Z","cross_cats_sorted":["cs.CC","math.LO"],"title_canon_sha256":"583325f091f0ad79584779d0c119e90cafa9cd95ad04ba095772afcb590a9238","abstract_canon_sha256":"098bb72d003b12451509b4276288155334b127e40ff63e6afeeb7fbeb650d868"},"schema_version":"1.0"},"canonical_sha256":"bd8400c757fad1d4251068bfc099b1afff0ca47869cc1591de79afcbcc45db36","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:01:37.429045Z","signature_b64":"uqJU5ZuRsBX9Q3CtZsQuwgIYmeInZowQmDoH1dec3Ix/N3IOJ6P7eN8KQyHD0Jf6qmW2JOsuFmNTTKWot8XfCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"bd8400c757fad1d4251068bfc099b1afff0ca47869cc1591de79afcbcc45db36","last_reissued_at":"2026-05-18T01:01:37.428279Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:01:37.428279Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1610.04026","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:01:37Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"rrYzybAJzlDfjtCnJ0rX0ra+tn3Wgxqtp2C39eI9paGVBlLRkzSuX61gVOm83OmbKmdeWIPa2M5KO4WYM45VAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T23:08:30.341887Z"},"content_sha256":"16b44f7ae87f66465ccef0dc86af04c8a60a71f02274cf488e58a59ca5421eec","schema_version":"1.0","event_id":"sha256:16b44f7ae87f66465ccef0dc86af04c8a60a71f02274cf488e58a59ca5421eec"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:XWCABR2X7LI5IJIQNC74BGNRV7","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Complexities Approach to Two Problems In Number Theory","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CC","math.LO"],"primary_cat":"math.NT","authors_text":"Xiuli Wang, Yang Bai","submitted_at":"2016-10-13T11:14:37Z","abstract_excerpt":"By Kolmogorov Complexity,two number-theoretic problems are solved in different way than before,one problem is Maxim Kontsevich and Don Bernard Zagier's Problem 3 \\emph{Exhibit at least one number which does not belong to} $ \\mathcal{P}$ (period number) in their paper,another is the problem about existence of bounded coefficients of continued fraction expansion of transcendental number.Thus we show a new approach to mathematical problems in the non-logical discipline.Futhermore,we show that resource-bounded Kolmogorov Complexity and computational complexity can at least provide tips or principl"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.04026","kind":"arxiv","version":3},"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":"2026-05-18T01:01:37Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"JEw+2kXFWo/vEn6zSWLyYG+zsuyiLXxDwEsDOKsgcf8GSN5g6w1iLrGNpIA5ZnZjcYYmRWHX4yZcDbzbAcWfAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T23:08:30.342600Z"},"content_sha256":"0f819ceaf82b686b99c19cd8fda3b122cb7ec7766c03015b824c47dccc8cfb44","schema_version":"1.0","event_id":"sha256:0f819ceaf82b686b99c19cd8fda3b122cb7ec7766c03015b824c47dccc8cfb44"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/XWCABR2X7LI5IJIQNC74BGNRV7/bundle.json","state_url":"https://pith.science/pith/XWCABR2X7LI5IJIQNC74BGNRV7/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/XWCABR2X7LI5IJIQNC74BGNRV7/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":"2026-06-07T23:08:30Z","links":{"resolver":"https://pith.science/pith/XWCABR2X7LI5IJIQNC74BGNRV7","bundle":"https://pith.science/pith/XWCABR2X7LI5IJIQNC74BGNRV7/bundle.json","state":"https://pith.science/pith/XWCABR2X7LI5IJIQNC74BGNRV7/state.json","well_known_bundle":"https://pith.science/.well-known/pith/XWCABR2X7LI5IJIQNC74BGNRV7/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:XWCABR2X7LI5IJIQNC74BGNRV7","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":"098bb72d003b12451509b4276288155334b127e40ff63e6afeeb7fbeb650d868","cross_cats_sorted":["cs.CC","math.LO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2016-10-13T11:14:37Z","title_canon_sha256":"583325f091f0ad79584779d0c119e90cafa9cd95ad04ba095772afcb590a9238"},"schema_version":"1.0","source":{"id":"1610.04026","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1610.04026","created_at":"2026-05-18T01:01:37Z"},{"alias_kind":"arxiv_version","alias_value":"1610.04026v3","created_at":"2026-05-18T01:01:37Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1610.04026","created_at":"2026-05-18T01:01:37Z"},{"alias_kind":"pith_short_12","alias_value":"XWCABR2X7LI5","created_at":"2026-05-18T12:30:51Z"},{"alias_kind":"pith_short_16","alias_value":"XWCABR2X7LI5IJIQ","created_at":"2026-05-18T12:30:51Z"},{"alias_kind":"pith_short_8","alias_value":"XWCABR2X","created_at":"2026-05-18T12:30:51Z"}],"graph_snapshots":[{"event_id":"sha256:0f819ceaf82b686b99c19cd8fda3b122cb7ec7766c03015b824c47dccc8cfb44","target":"graph","created_at":"2026-05-18T01:01:37Z","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":"By Kolmogorov Complexity,two number-theoretic problems are solved in different way than before,one problem is Maxim Kontsevich and Don Bernard Zagier's Problem 3 \\emph{Exhibit at least one number which does not belong to} $ \\mathcal{P}$ (period number) in their paper,another is the problem about existence of bounded coefficients of continued fraction expansion of transcendental number.Thus we show a new approach to mathematical problems in the non-logical discipline.Futhermore,we show that resource-bounded Kolmogorov Complexity and computational complexity can at least provide tips or principl","authors_text":"Xiuli Wang, Yang Bai","cross_cats":["cs.CC","math.LO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2016-10-13T11:14:37Z","title":"Complexities Approach to Two Problems In Number Theory"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.04026","kind":"arxiv","version":3},"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":"sha256:16b44f7ae87f66465ccef0dc86af04c8a60a71f02274cf488e58a59ca5421eec","target":"record","created_at":"2026-05-18T01:01:37Z","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":"098bb72d003b12451509b4276288155334b127e40ff63e6afeeb7fbeb650d868","cross_cats_sorted":["cs.CC","math.LO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2016-10-13T11:14:37Z","title_canon_sha256":"583325f091f0ad79584779d0c119e90cafa9cd95ad04ba095772afcb590a9238"},"schema_version":"1.0","source":{"id":"1610.04026","kind":"arxiv","version":3}},"canonical_sha256":"bd8400c757fad1d4251068bfc099b1afff0ca47869cc1591de79afcbcc45db36","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"bd8400c757fad1d4251068bfc099b1afff0ca47869cc1591de79afcbcc45db36","first_computed_at":"2026-05-18T01:01:37.428279Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:01:37.428279Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"uqJU5ZuRsBX9Q3CtZsQuwgIYmeInZowQmDoH1dec3Ix/N3IOJ6P7eN8KQyHD0Jf6qmW2JOsuFmNTTKWot8XfCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:01:37.429045Z","signed_message":"canonical_sha256_bytes"},"source_id":"1610.04026","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:16b44f7ae87f66465ccef0dc86af04c8a60a71f02274cf488e58a59ca5421eec","sha256:0f819ceaf82b686b99c19cd8fda3b122cb7ec7766c03015b824c47dccc8cfb44"],"state_sha256":"8a7723eb938e86c612d4b3fe11a72384eb0eeb98df5241e553de9871de48c74a"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Y6LgnZNzqoYrZQCD5xCt+9vLwYnyH43omz/9HD9+2/o5fkWcDftyJ4tP7/jkavxbmJ36NufC3ztUwj4wM0FwDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-07T23:08:30.346160Z","bundle_sha256":"a49a02d17be16c37b097e20416f9e66129bc3baf7b28f0b3507c15a5336a1426"}}