{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2008:AIIYB3TDJ4UUZ7ASEDIDHTEREX","short_pith_number":"pith:AIIYB3TD","canonical_record":{"source":{"id":"0803.1662","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2008-03-11T20:01:33Z","cross_cats_sorted":[],"title_canon_sha256":"db2ff935caa65ba35eecd7415f967f0151862a0cf5b574d4760c84df1f9e678b","abstract_canon_sha256":"00d7822cf2377cb5dc923e327a2e197e0c92cb60f6d02887ebf7f9b981b67d06"},"schema_version":"1.0"},"canonical_sha256":"021180ee634f294cfc1220d033cc9125fab00b420ec54aaf1ee52e9328a5c069","source":{"kind":"arxiv","id":"0803.1662","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0803.1662","created_at":"2026-05-18T04:34:46Z"},{"alias_kind":"arxiv_version","alias_value":"0803.1662v3","created_at":"2026-05-18T04:34:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0803.1662","created_at":"2026-05-18T04:34:46Z"},{"alias_kind":"pith_short_12","alias_value":"AIIYB3TDJ4UU","created_at":"2026-05-18T12:25:56Z"},{"alias_kind":"pith_short_16","alias_value":"AIIYB3TDJ4UUZ7AS","created_at":"2026-05-18T12:25:56Z"},{"alias_kind":"pith_short_8","alias_value":"AIIYB3TD","created_at":"2026-05-18T12:25:56Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2008:AIIYB3TDJ4UUZ7ASEDIDHTEREX","target":"record","payload":{"canonical_record":{"source":{"id":"0803.1662","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2008-03-11T20:01:33Z","cross_cats_sorted":[],"title_canon_sha256":"db2ff935caa65ba35eecd7415f967f0151862a0cf5b574d4760c84df1f9e678b","abstract_canon_sha256":"00d7822cf2377cb5dc923e327a2e197e0c92cb60f6d02887ebf7f9b981b67d06"},"schema_version":"1.0"},"canonical_sha256":"021180ee634f294cfc1220d033cc9125fab00b420ec54aaf1ee52e9328a5c069","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:34:46.443392Z","signature_b64":"PlL50yLEBcDH9qsJ6N3+UNM6bxtSUBEpgZ2/NynUh7+d1YG6uFnOivms3ANq+e+N/igktct+hNUzGm/86lnjCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"021180ee634f294cfc1220d033cc9125fab00b420ec54aaf1ee52e9328a5c069","last_reissued_at":"2026-05-18T04:34:46.442928Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:34:46.442928Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"0803.1662","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":"2026-05-18T04:34:46Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/ZI07H2SgIVnO0ZAWZHEcWh2lZFbC/o70nX6OBtyvzRmPQY9IDmZLXJczwcMzCNRFr7CkqgvHOe7acDS6tDEAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T10:58:47.102288Z"},"content_sha256":"90223807150d339b8a77a03951393f7b7b6288dd6409152eaa8cb0aa3cd95e25","schema_version":"1.0","event_id":"sha256:90223807150d339b8a77a03951393f7b7b6288dd6409152eaa8cb0aa3cd95e25"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2008:AIIYB3TDJ4UUZ7ASEDIDHTEREX","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Dynamics of the Nearly Parametric Pendulum","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"B. Horton, J. M. T. Thompson, J. Sieber, M. Wiercigroch","submitted_at":"2008-03-11T20:01:33Z","abstract_excerpt":"Dynamically stable periodic rotations of a driven pendulum provide a unique mechanism for generating a uniform rotation from bounded excitations. This paper studies the effects of a small ellipticity of the driving, perturbing the classical parametric pendulum. The first finding is that the region in the parameter plane of amplitude and frequency of excitation where rotations are possible increases with the ellipticity. Second, the resonance tongues, which are the most characteristic feature of the classical bifurcation scenario of a parametrically driven pendulum, merge into a single region o"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0803.1662","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":"2026-05-18T04:34:46Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Ft8ZTHuOJ//BN0Y1aPyPFbC47MWKcOjJ9lWqVefVVxuASQIndhKssbvG5DQS/qvR53fPAD7BFnRMCZ4Rpgx2BQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T10:58:47.102655Z"},"content_sha256":"e56d23a159e7cbd96ffdd1c1308ad80c9d70074514dabff0caaf49243c51b7ae","schema_version":"1.0","event_id":"sha256:e56d23a159e7cbd96ffdd1c1308ad80c9d70074514dabff0caaf49243c51b7ae"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/AIIYB3TDJ4UUZ7ASEDIDHTEREX/bundle.json","state_url":"https://pith.science/pith/AIIYB3TDJ4UUZ7ASEDIDHTEREX/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/AIIYB3TDJ4UUZ7ASEDIDHTEREX/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":"2026-06-24T10:58:47Z","links":{"resolver":"https://pith.science/pith/AIIYB3TDJ4UUZ7ASEDIDHTEREX","bundle":"https://pith.science/pith/AIIYB3TDJ4UUZ7ASEDIDHTEREX/bundle.json","state":"https://pith.science/pith/AIIYB3TDJ4UUZ7ASEDIDHTEREX/state.json","well_known_bundle":"https://pith.science/.well-known/pith/AIIYB3TDJ4UUZ7ASEDIDHTEREX/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2008:AIIYB3TDJ4UUZ7ASEDIDHTEREX","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":"00d7822cf2377cb5dc923e327a2e197e0c92cb60f6d02887ebf7f9b981b67d06","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2008-03-11T20:01:33Z","title_canon_sha256":"db2ff935caa65ba35eecd7415f967f0151862a0cf5b574d4760c84df1f9e678b"},"schema_version":"1.0","source":{"id":"0803.1662","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0803.1662","created_at":"2026-05-18T04:34:46Z"},{"alias_kind":"arxiv_version","alias_value":"0803.1662v3","created_at":"2026-05-18T04:34:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0803.1662","created_at":"2026-05-18T04:34:46Z"},{"alias_kind":"pith_short_12","alias_value":"AIIYB3TDJ4UU","created_at":"2026-05-18T12:25:56Z"},{"alias_kind":"pith_short_16","alias_value":"AIIYB3TDJ4UUZ7AS","created_at":"2026-05-18T12:25:56Z"},{"alias_kind":"pith_short_8","alias_value":"AIIYB3TD","created_at":"2026-05-18T12:25:56Z"}],"graph_snapshots":[{"event_id":"sha256:e56d23a159e7cbd96ffdd1c1308ad80c9d70074514dabff0caaf49243c51b7ae","target":"graph","created_at":"2026-05-18T04:34:46Z","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":"Dynamically stable periodic rotations of a driven pendulum provide a unique mechanism for generating a uniform rotation from bounded excitations. This paper studies the effects of a small ellipticity of the driving, perturbing the classical parametric pendulum. The first finding is that the region in the parameter plane of amplitude and frequency of excitation where rotations are possible increases with the ellipticity. Second, the resonance tongues, which are the most characteristic feature of the classical bifurcation scenario of a parametrically driven pendulum, merge into a single region o","authors_text":"B. Horton, J. M. T. Thompson, J. Sieber, M. Wiercigroch","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2008-03-11T20:01:33Z","title":"Dynamics of the Nearly Parametric Pendulum"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0803.1662","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":"sha256:90223807150d339b8a77a03951393f7b7b6288dd6409152eaa8cb0aa3cd95e25","target":"record","created_at":"2026-05-18T04:34:46Z","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":"00d7822cf2377cb5dc923e327a2e197e0c92cb60f6d02887ebf7f9b981b67d06","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2008-03-11T20:01:33Z","title_canon_sha256":"db2ff935caa65ba35eecd7415f967f0151862a0cf5b574d4760c84df1f9e678b"},"schema_version":"1.0","source":{"id":"0803.1662","kind":"arxiv","version":3}},"canonical_sha256":"021180ee634f294cfc1220d033cc9125fab00b420ec54aaf1ee52e9328a5c069","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"021180ee634f294cfc1220d033cc9125fab00b420ec54aaf1ee52e9328a5c069","first_computed_at":"2026-05-18T04:34:46.442928Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:34:46.442928Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"PlL50yLEBcDH9qsJ6N3+UNM6bxtSUBEpgZ2/NynUh7+d1YG6uFnOivms3ANq+e+N/igktct+hNUzGm/86lnjCA==","signature_status":"signed_v1","signed_at":"2026-05-18T04:34:46.443392Z","signed_message":"canonical_sha256_bytes"},"source_id":"0803.1662","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:90223807150d339b8a77a03951393f7b7b6288dd6409152eaa8cb0aa3cd95e25","sha256:e56d23a159e7cbd96ffdd1c1308ad80c9d70074514dabff0caaf49243c51b7ae"],"state_sha256":"84da0a6edd1bf52fb5f81ac49b00dc89dfabfad88b840942760b6e06b43dfc7e"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"fcWdlRbzaAGNL2r2pHDh274bqB3nrROallVL/o9Yu2la7oEOeR8Ftw4/zRjVTrOhMjLl6tI9e1j+nj/oTk8jBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-24T10:58:47.104535Z","bundle_sha256":"ad6adec05feb6b51fc463f7cd2c3ae7c671588f17bb8f97160fb8582a87cfd79"}}