{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:RDQBSTK2ZJYDAU6HSDRYDHC7AJ","short_pith_number":"pith:RDQBSTK2","canonical_record":{"source":{"id":"1710.00657","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2017-09-21T23:39:20Z","cross_cats_sorted":[],"title_canon_sha256":"dd6ee2195a19f8fcc6b0a22f0cb630b675809696e449fd928e5a98c53b6f60a4","abstract_canon_sha256":"4abbc227822b95ce9dbc4fb16cc86a007bdb2a6c4d1c04542ffa54ff51647932"},"schema_version":"1.0"},"canonical_sha256":"88e0194d5aca703053c790e3819c5f02549bf3ef79ffccb2ea4d2d28ba10d217","source":{"kind":"arxiv","id":"1710.00657","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1710.00657","created_at":"2026-05-18T00:19:26Z"},{"alias_kind":"arxiv_version","alias_value":"1710.00657v1","created_at":"2026-05-18T00:19:26Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1710.00657","created_at":"2026-05-18T00:19:26Z"},{"alias_kind":"pith_short_12","alias_value":"RDQBSTK2ZJYD","created_at":"2026-05-18T12:31:39Z"},{"alias_kind":"pith_short_16","alias_value":"RDQBSTK2ZJYDAU6H","created_at":"2026-05-18T12:31:39Z"},{"alias_kind":"pith_short_8","alias_value":"RDQBSTK2","created_at":"2026-05-18T12:31:39Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:RDQBSTK2ZJYDAU6HSDRYDHC7AJ","target":"record","payload":{"canonical_record":{"source":{"id":"1710.00657","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2017-09-21T23:39:20Z","cross_cats_sorted":[],"title_canon_sha256":"dd6ee2195a19f8fcc6b0a22f0cb630b675809696e449fd928e5a98c53b6f60a4","abstract_canon_sha256":"4abbc227822b95ce9dbc4fb16cc86a007bdb2a6c4d1c04542ffa54ff51647932"},"schema_version":"1.0"},"canonical_sha256":"88e0194d5aca703053c790e3819c5f02549bf3ef79ffccb2ea4d2d28ba10d217","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:19:26.475311Z","signature_b64":"0BWkWQDMcw4pVs/dS95ptG56teayRlANilBLAalkuJdGj/PaCnP1Ul/UoepAPrjHemzboFPYwnIQS7GSR+0LCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"88e0194d5aca703053c790e3819c5f02549bf3ef79ffccb2ea4d2d28ba10d217","last_reissued_at":"2026-05-18T00:19:26.474886Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:19:26.474886Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1710.00657","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":"2026-05-18T00:19:26Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"mBWFWQEYj5JtGWcyOuip0oxL6jIqr3dygA8jogdNTx8au/uJ+75Q1A9ac/r+uyJm3n4nOsA0tBiMVnadAS3ADw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T06:49:14.558418Z"},"content_sha256":"28d24f1bc4350895c34a85827e88796a32ba3d79f0ca52d528fb219d5cccd9df","schema_version":"1.0","event_id":"sha256:28d24f1bc4350895c34a85827e88796a32ba3d79f0ca52d528fb219d5cccd9df"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:RDQBSTK2ZJYDAU6HSDRYDHC7AJ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Approximate solutions to Mathieu's equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"quant-ph","authors_text":"Dmitry S. Golubev, Jared H. Cole, Nicolas Vogt, Samuel A. Wilkinson","submitted_at":"2017-09-21T23:39:20Z","abstract_excerpt":"Mathieu's equation has many applications throughout theoretical physics. It is especially important to the theory of Josephson junctions, where it is equivalent to Schrodinger's equation. Mathieu's equation can be easily solved numerically, however there exists no closed-form analytic solution. Here we collect various approximations which appear throughout the physics and mathematics literature and examine their accuracy and regimes of applicability. Particular attention is paid to quantities relevant to the physics of Josephson junctions, but the arguments and notation are kept general so as"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1710.00657","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":"2026-05-18T00:19:26Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/RsCWAuauRADeGrA+v8HP1JrAiI9xV/SZfyzr7tsYJSMm8+aJ0tHIA+HmKfr91DvsITVA/bNA7tRS+Qz3sXRCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T06:49:14.558766Z"},"content_sha256":"8d9a3f93599366214696a57e95a6dd7240ceb76d4fa5706bda6e64ee2c69a1d5","schema_version":"1.0","event_id":"sha256:8d9a3f93599366214696a57e95a6dd7240ceb76d4fa5706bda6e64ee2c69a1d5"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/RDQBSTK2ZJYDAU6HSDRYDHC7AJ/bundle.json","state_url":"https://pith.science/pith/RDQBSTK2ZJYDAU6HSDRYDHC7AJ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/RDQBSTK2ZJYDAU6HSDRYDHC7AJ/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":"2026-06-01T06:49:14Z","links":{"resolver":"https://pith.science/pith/RDQBSTK2ZJYDAU6HSDRYDHC7AJ","bundle":"https://pith.science/pith/RDQBSTK2ZJYDAU6HSDRYDHC7AJ/bundle.json","state":"https://pith.science/pith/RDQBSTK2ZJYDAU6HSDRYDHC7AJ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/RDQBSTK2ZJYDAU6HSDRYDHC7AJ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:RDQBSTK2ZJYDAU6HSDRYDHC7AJ","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":"4abbc227822b95ce9dbc4fb16cc86a007bdb2a6c4d1c04542ffa54ff51647932","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2017-09-21T23:39:20Z","title_canon_sha256":"dd6ee2195a19f8fcc6b0a22f0cb630b675809696e449fd928e5a98c53b6f60a4"},"schema_version":"1.0","source":{"id":"1710.00657","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1710.00657","created_at":"2026-05-18T00:19:26Z"},{"alias_kind":"arxiv_version","alias_value":"1710.00657v1","created_at":"2026-05-18T00:19:26Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1710.00657","created_at":"2026-05-18T00:19:26Z"},{"alias_kind":"pith_short_12","alias_value":"RDQBSTK2ZJYD","created_at":"2026-05-18T12:31:39Z"},{"alias_kind":"pith_short_16","alias_value":"RDQBSTK2ZJYDAU6H","created_at":"2026-05-18T12:31:39Z"},{"alias_kind":"pith_short_8","alias_value":"RDQBSTK2","created_at":"2026-05-18T12:31:39Z"}],"graph_snapshots":[{"event_id":"sha256:8d9a3f93599366214696a57e95a6dd7240ceb76d4fa5706bda6e64ee2c69a1d5","target":"graph","created_at":"2026-05-18T00:19:26Z","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":"Mathieu's equation has many applications throughout theoretical physics. It is especially important to the theory of Josephson junctions, where it is equivalent to Schrodinger's equation. Mathieu's equation can be easily solved numerically, however there exists no closed-form analytic solution. Here we collect various approximations which appear throughout the physics and mathematics literature and examine their accuracy and regimes of applicability. Particular attention is paid to quantities relevant to the physics of Josephson junctions, but the arguments and notation are kept general so as","authors_text":"Dmitry S. Golubev, Jared H. Cole, Nicolas Vogt, Samuel A. Wilkinson","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2017-09-21T23:39:20Z","title":"Approximate solutions to Mathieu's equation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1710.00657","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":"sha256:28d24f1bc4350895c34a85827e88796a32ba3d79f0ca52d528fb219d5cccd9df","target":"record","created_at":"2026-05-18T00:19:26Z","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":"4abbc227822b95ce9dbc4fb16cc86a007bdb2a6c4d1c04542ffa54ff51647932","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2017-09-21T23:39:20Z","title_canon_sha256":"dd6ee2195a19f8fcc6b0a22f0cb630b675809696e449fd928e5a98c53b6f60a4"},"schema_version":"1.0","source":{"id":"1710.00657","kind":"arxiv","version":1}},"canonical_sha256":"88e0194d5aca703053c790e3819c5f02549bf3ef79ffccb2ea4d2d28ba10d217","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"88e0194d5aca703053c790e3819c5f02549bf3ef79ffccb2ea4d2d28ba10d217","first_computed_at":"2026-05-18T00:19:26.474886Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:19:26.474886Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"0BWkWQDMcw4pVs/dS95ptG56teayRlANilBLAalkuJdGj/PaCnP1Ul/UoepAPrjHemzboFPYwnIQS7GSR+0LCA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:19:26.475311Z","signed_message":"canonical_sha256_bytes"},"source_id":"1710.00657","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:28d24f1bc4350895c34a85827e88796a32ba3d79f0ca52d528fb219d5cccd9df","sha256:8d9a3f93599366214696a57e95a6dd7240ceb76d4fa5706bda6e64ee2c69a1d5"],"state_sha256":"f72bfc84d9ce3c1c1839281a6f4d6268e175e931dabe4183fbdd8fce135e9637"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ImGL1Gecsb01NqdpQY5qs+k7FKZWRubJX6xXdaLIYGNRA65yTfg1Ij87/yLAw9nqknw/59F0nntVeWPFaEklCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-01T06:49:14.560986Z","bundle_sha256":"edee29827c780cf080b8c0cb5460ee7c011083efbf22f34ab582fe833055aec5"}}