{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:Q6RKQK7ATBNGBUJQ4D3KBQZKCU","short_pith_number":"pith:Q6RKQK7A","canonical_record":{"source":{"id":"1706.02595","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2017-06-08T14:09:24Z","cross_cats_sorted":[],"title_canon_sha256":"4a6ed4eb9de36913e266a5dcf872313a5060d7a791f4da66e0d972c4b08c6a46","abstract_canon_sha256":"bbd78bc8b642a02c278b57b2172d1c074bd032137891eeb6859d26cea9887433"},"schema_version":"1.0"},"canonical_sha256":"87a2a82be0985a60d130e0f6a0c32a1514517b03ba7dac0476a3d7decc8d352b","source":{"kind":"arxiv","id":"1706.02595","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1706.02595","created_at":"2026-05-18T00:40:23Z"},{"alias_kind":"arxiv_version","alias_value":"1706.02595v3","created_at":"2026-05-18T00:40:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1706.02595","created_at":"2026-05-18T00:40:23Z"},{"alias_kind":"pith_short_12","alias_value":"Q6RKQK7ATBNG","created_at":"2026-05-18T12:31:37Z"},{"alias_kind":"pith_short_16","alias_value":"Q6RKQK7ATBNGBUJQ","created_at":"2026-05-18T12:31:37Z"},{"alias_kind":"pith_short_8","alias_value":"Q6RKQK7A","created_at":"2026-05-18T12:31:37Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:Q6RKQK7ATBNGBUJQ4D3KBQZKCU","target":"record","payload":{"canonical_record":{"source":{"id":"1706.02595","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2017-06-08T14:09:24Z","cross_cats_sorted":[],"title_canon_sha256":"4a6ed4eb9de36913e266a5dcf872313a5060d7a791f4da66e0d972c4b08c6a46","abstract_canon_sha256":"bbd78bc8b642a02c278b57b2172d1c074bd032137891eeb6859d26cea9887433"},"schema_version":"1.0"},"canonical_sha256":"87a2a82be0985a60d130e0f6a0c32a1514517b03ba7dac0476a3d7decc8d352b","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:40:23.686064Z","signature_b64":"ewkxxbEMdPPvsgDW1c0EONEttXl8aaY+MeZeQqATKGAuOCUKNwyI9vP0+NDZtYOmix/tPlpNMa1CtC4J2oI1Cg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"87a2a82be0985a60d130e0f6a0c32a1514517b03ba7dac0476a3d7decc8d352b","last_reissued_at":"2026-05-18T00:40:23.685367Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:40:23.685367Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1706.02595","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":"2026-05-18T00:40:23Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"7OkKO/1mbdBoMtXFHZS8we/FrOe5QtDOjZZlKB7+hnJQTwoIij4W6SU8dNyMXj93UCMQ/RduZjbIHtpYeN/rDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-22T21:39:16.321632Z"},"content_sha256":"dfa2a84db18ab5c31bd0fe1b0f38f43b813438174ad0a709fa90450e38a8da7d","schema_version":"1.0","event_id":"sha256:dfa2a84db18ab5c31bd0fe1b0f38f43b813438174ad0a709fa90450e38a8da7d"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:Q6RKQK7ATBNGBUJQ4D3KBQZKCU","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Solving the Babylonian Problem of quasiperiodic rotation rates","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Evelyn Sander, James A Yorke, Suddhasattwa Das, Yoshitaka Saiki","submitted_at":"2017-06-08T14:09:24Z","abstract_excerpt":"A trajectory $u_n := F^n(u_0), n = 0,1,2, \\dots $ is quasiperiodic if the trajectory lies on and is dense in some $d$-dimensional torus, and there is a choice of coordinates on the torus $\\mathbb{T}$ for which $F$ has the form $F(\\theta) = \\theta + \\rho\\bmod1$ for all $\\theta\\in\\mathbb{T}$ and for some $\\rho\\in\\mathbb{T}$. There is an ancient literature on computing three rotation rates $\\rho$ for the Moon. %There is a literature on determining the coordinates of the vector $\\rho$, called the rotation rates of $F$. (For $d>1$ we always interpret $\\bmod1$ as being applied to each coordinate.) H"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1706.02595","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":"2026-05-18T00:40:23Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Fw9VwE+zXArX3SNqY+aMZvG4WzwEegj9PgeMSN2G7vjgOq/j0VNO4M9bjFhO/DiChl9vFWeXs/UKaE3dE1edDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-22T21:39:16.322487Z"},"content_sha256":"15611c1aec94bced0d313d116a47869471b6047a08e07da7650d6bb689413045","schema_version":"1.0","event_id":"sha256:15611c1aec94bced0d313d116a47869471b6047a08e07da7650d6bb689413045"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/Q6RKQK7ATBNGBUJQ4D3KBQZKCU/bundle.json","state_url":"https://pith.science/pith/Q6RKQK7ATBNGBUJQ4D3KBQZKCU/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/Q6RKQK7ATBNGBUJQ4D3KBQZKCU/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":"2026-06-22T21:39:16Z","links":{"resolver":"https://pith.science/pith/Q6RKQK7ATBNGBUJQ4D3KBQZKCU","bundle":"https://pith.science/pith/Q6RKQK7ATBNGBUJQ4D3KBQZKCU/bundle.json","state":"https://pith.science/pith/Q6RKQK7ATBNGBUJQ4D3KBQZKCU/state.json","well_known_bundle":"https://pith.science/.well-known/pith/Q6RKQK7ATBNGBUJQ4D3KBQZKCU/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:Q6RKQK7ATBNGBUJQ4D3KBQZKCU","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":"bbd78bc8b642a02c278b57b2172d1c074bd032137891eeb6859d26cea9887433","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2017-06-08T14:09:24Z","title_canon_sha256":"4a6ed4eb9de36913e266a5dcf872313a5060d7a791f4da66e0d972c4b08c6a46"},"schema_version":"1.0","source":{"id":"1706.02595","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1706.02595","created_at":"2026-05-18T00:40:23Z"},{"alias_kind":"arxiv_version","alias_value":"1706.02595v3","created_at":"2026-05-18T00:40:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1706.02595","created_at":"2026-05-18T00:40:23Z"},{"alias_kind":"pith_short_12","alias_value":"Q6RKQK7ATBNG","created_at":"2026-05-18T12:31:37Z"},{"alias_kind":"pith_short_16","alias_value":"Q6RKQK7ATBNGBUJQ","created_at":"2026-05-18T12:31:37Z"},{"alias_kind":"pith_short_8","alias_value":"Q6RKQK7A","created_at":"2026-05-18T12:31:37Z"}],"graph_snapshots":[{"event_id":"sha256:15611c1aec94bced0d313d116a47869471b6047a08e07da7650d6bb689413045","target":"graph","created_at":"2026-05-18T00:40:23Z","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":"A trajectory $u_n := F^n(u_0), n = 0,1,2, \\dots $ is quasiperiodic if the trajectory lies on and is dense in some $d$-dimensional torus, and there is a choice of coordinates on the torus $\\mathbb{T}$ for which $F$ has the form $F(\\theta) = \\theta + \\rho\\bmod1$ for all $\\theta\\in\\mathbb{T}$ and for some $\\rho\\in\\mathbb{T}$. There is an ancient literature on computing three rotation rates $\\rho$ for the Moon. %There is a literature on determining the coordinates of the vector $\\rho$, called the rotation rates of $F$. (For $d>1$ we always interpret $\\bmod1$ as being applied to each coordinate.) H","authors_text":"Evelyn Sander, James A Yorke, Suddhasattwa Das, Yoshitaka Saiki","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2017-06-08T14:09:24Z","title":"Solving the Babylonian Problem of quasiperiodic rotation rates"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1706.02595","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:dfa2a84db18ab5c31bd0fe1b0f38f43b813438174ad0a709fa90450e38a8da7d","target":"record","created_at":"2026-05-18T00:40:23Z","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":"bbd78bc8b642a02c278b57b2172d1c074bd032137891eeb6859d26cea9887433","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2017-06-08T14:09:24Z","title_canon_sha256":"4a6ed4eb9de36913e266a5dcf872313a5060d7a791f4da66e0d972c4b08c6a46"},"schema_version":"1.0","source":{"id":"1706.02595","kind":"arxiv","version":3}},"canonical_sha256":"87a2a82be0985a60d130e0f6a0c32a1514517b03ba7dac0476a3d7decc8d352b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"87a2a82be0985a60d130e0f6a0c32a1514517b03ba7dac0476a3d7decc8d352b","first_computed_at":"2026-05-18T00:40:23.685367Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:40:23.685367Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ewkxxbEMdPPvsgDW1c0EONEttXl8aaY+MeZeQqATKGAuOCUKNwyI9vP0+NDZtYOmix/tPlpNMa1CtC4J2oI1Cg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:40:23.686064Z","signed_message":"canonical_sha256_bytes"},"source_id":"1706.02595","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:dfa2a84db18ab5c31bd0fe1b0f38f43b813438174ad0a709fa90450e38a8da7d","sha256:15611c1aec94bced0d313d116a47869471b6047a08e07da7650d6bb689413045"],"state_sha256":"0249f936baa09db4462aef9d2fd3026d230bd623a7bf24ff6e5a71c0b8c247dd"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"GQfgAa+/jz8D/MV1YzgfuS7TlzDS+EQ2We0hzy9227gLw5tB1Oj+LSI1TPK1MFxDfzTSOFEUqmjlMXNYrLDTDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-22T21:39:16.325563Z","bundle_sha256":"4ed403dd3f580bcae4f79edafb8f09db7d7caada0fc94502af032e9c1e421e7c"}}