{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:BJYWJGFOGXY4C5PD6IPSFQDXFQ","short_pith_number":"pith:BJYWJGFO","canonical_record":{"source":{"id":"1207.6022","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.SI","submitted_at":"2012-07-25T15:17:08Z","cross_cats_sorted":["nlin.CD"],"title_canon_sha256":"5260e996bb87b218de6e9dadb3544bdae7fb481b83e59dc1a164aa2162ef4849","abstract_canon_sha256":"713925f9ab9510e16c3454a5ec452c66abd0b0e64c358e72138c31e3c61ef8f6"},"schema_version":"1.0"},"canonical_sha256":"0a716498ae35f1c175e3f21f22c0772c1a22df22cc331cb1fd4ffa4a342c00cf","source":{"kind":"arxiv","id":"1207.6022","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1207.6022","created_at":"2026-05-17T23:44:05Z"},{"alias_kind":"arxiv_version","alias_value":"1207.6022v1","created_at":"2026-05-17T23:44:05Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1207.6022","created_at":"2026-05-17T23:44:05Z"},{"alias_kind":"pith_short_12","alias_value":"BJYWJGFOGXY4","created_at":"2026-05-18T12:27:01Z"},{"alias_kind":"pith_short_16","alias_value":"BJYWJGFOGXY4C5PD","created_at":"2026-05-18T12:27:01Z"},{"alias_kind":"pith_short_8","alias_value":"BJYWJGFO","created_at":"2026-05-18T12:27:01Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:BJYWJGFOGXY4C5PD6IPSFQDXFQ","target":"record","payload":{"canonical_record":{"source":{"id":"1207.6022","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.SI","submitted_at":"2012-07-25T15:17:08Z","cross_cats_sorted":["nlin.CD"],"title_canon_sha256":"5260e996bb87b218de6e9dadb3544bdae7fb481b83e59dc1a164aa2162ef4849","abstract_canon_sha256":"713925f9ab9510e16c3454a5ec452c66abd0b0e64c358e72138c31e3c61ef8f6"},"schema_version":"1.0"},"canonical_sha256":"0a716498ae35f1c175e3f21f22c0772c1a22df22cc331cb1fd4ffa4a342c00cf","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:44:05.058086Z","signature_b64":"Gs8Yzku/qQVA3lMPaayPLk6I9MBVnba0Ojm0yr4CjLwA1PTRzdcEIGkDoYgIIuJAuCgdY71sfqQ8+OhTaW4sCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0a716498ae35f1c175e3f21f22c0772c1a22df22cc331cb1fd4ffa4a342c00cf","last_reissued_at":"2026-05-17T23:44:05.057638Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:44:05.057638Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1207.6022","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":"2026-05-17T23:44:05Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"NqKI5OzEz6oaKShPSKD+J1EyPZx8BtIlMv2lheUFQWWaLxuvonQKflMWjvtfEawm7IN2hWiFkIaJWl/GjJC9BQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-19T10:20:02.880690Z"},"content_sha256":"9557ea5b7cf56abc8ca75cd853a1f42e25f09995bbe9658f88e5a051f9e5e6b7","schema_version":"1.0","event_id":"sha256:9557ea5b7cf56abc8ca75cd853a1f42e25f09995bbe9658f88e5a051f9e5e6b7"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:BJYWJGFOGXY4C5PD6IPSFQDXFQ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Quaternion Solution for the Rock'n'roller: Box Orbits, Loop Orbits and Recession","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["nlin.CD"],"primary_cat":"nlin.SI","authors_text":"Miguel D Bustamante, Peter Lynch","submitted_at":"2012-07-25T15:17:08Z","abstract_excerpt":"We consider two types of trajectories found in a wide range of mechanical systems, viz. box orbits and loop orbits. We elucidate the dynamics of these orbits in the simple context of a perturbed harmonic oscillator in two dimensions. We then examine the small-amplitude motion of a rigid body, the rock'n'roller, a sphere with eccentric distribution of mass. The equations of motion are expressed in quaternionic form and a complete analytical solution is obtained. Both types of orbit, boxes and loops, are found, the particular form depending on the initial conditions. We interpret the motion in t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1207.6022","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":"2026-05-17T23:44:05Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"2RXkS6v9rK9uIwElTgUD4Mir2n0qJs7MjUUH3in03tCutbSHl7G1AanioxLAYYPioobtmH0WQbOlly9yuNK1AQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-19T10:20:02.881040Z"},"content_sha256":"e9be2ee9a9364861cccb92b6e2b6a349bc919a21d65cfb4959e2c60ab37c8185","schema_version":"1.0","event_id":"sha256:e9be2ee9a9364861cccb92b6e2b6a349bc919a21d65cfb4959e2c60ab37c8185"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/BJYWJGFOGXY4C5PD6IPSFQDXFQ/bundle.json","state_url":"https://pith.science/pith/BJYWJGFOGXY4C5PD6IPSFQDXFQ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/BJYWJGFOGXY4C5PD6IPSFQDXFQ/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":"2026-05-19T10:20:02Z","links":{"resolver":"https://pith.science/pith/BJYWJGFOGXY4C5PD6IPSFQDXFQ","bundle":"https://pith.science/pith/BJYWJGFOGXY4C5PD6IPSFQDXFQ/bundle.json","state":"https://pith.science/pith/BJYWJGFOGXY4C5PD6IPSFQDXFQ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/BJYWJGFOGXY4C5PD6IPSFQDXFQ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:BJYWJGFOGXY4C5PD6IPSFQDXFQ","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":"713925f9ab9510e16c3454a5ec452c66abd0b0e64c358e72138c31e3c61ef8f6","cross_cats_sorted":["nlin.CD"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.SI","submitted_at":"2012-07-25T15:17:08Z","title_canon_sha256":"5260e996bb87b218de6e9dadb3544bdae7fb481b83e59dc1a164aa2162ef4849"},"schema_version":"1.0","source":{"id":"1207.6022","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1207.6022","created_at":"2026-05-17T23:44:05Z"},{"alias_kind":"arxiv_version","alias_value":"1207.6022v1","created_at":"2026-05-17T23:44:05Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1207.6022","created_at":"2026-05-17T23:44:05Z"},{"alias_kind":"pith_short_12","alias_value":"BJYWJGFOGXY4","created_at":"2026-05-18T12:27:01Z"},{"alias_kind":"pith_short_16","alias_value":"BJYWJGFOGXY4C5PD","created_at":"2026-05-18T12:27:01Z"},{"alias_kind":"pith_short_8","alias_value":"BJYWJGFO","created_at":"2026-05-18T12:27:01Z"}],"graph_snapshots":[{"event_id":"sha256:e9be2ee9a9364861cccb92b6e2b6a349bc919a21d65cfb4959e2c60ab37c8185","target":"graph","created_at":"2026-05-17T23:44:05Z","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 consider two types of trajectories found in a wide range of mechanical systems, viz. box orbits and loop orbits. We elucidate the dynamics of these orbits in the simple context of a perturbed harmonic oscillator in two dimensions. We then examine the small-amplitude motion of a rigid body, the rock'n'roller, a sphere with eccentric distribution of mass. The equations of motion are expressed in quaternionic form and a complete analytical solution is obtained. Both types of orbit, boxes and loops, are found, the particular form depending on the initial conditions. We interpret the motion in t","authors_text":"Miguel D Bustamante, Peter Lynch","cross_cats":["nlin.CD"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.SI","submitted_at":"2012-07-25T15:17:08Z","title":"Quaternion Solution for the Rock'n'roller: Box Orbits, Loop Orbits and Recession"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1207.6022","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":"sha256:9557ea5b7cf56abc8ca75cd853a1f42e25f09995bbe9658f88e5a051f9e5e6b7","target":"record","created_at":"2026-05-17T23:44:05Z","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":"713925f9ab9510e16c3454a5ec452c66abd0b0e64c358e72138c31e3c61ef8f6","cross_cats_sorted":["nlin.CD"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.SI","submitted_at":"2012-07-25T15:17:08Z","title_canon_sha256":"5260e996bb87b218de6e9dadb3544bdae7fb481b83e59dc1a164aa2162ef4849"},"schema_version":"1.0","source":{"id":"1207.6022","kind":"arxiv","version":1}},"canonical_sha256":"0a716498ae35f1c175e3f21f22c0772c1a22df22cc331cb1fd4ffa4a342c00cf","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0a716498ae35f1c175e3f21f22c0772c1a22df22cc331cb1fd4ffa4a342c00cf","first_computed_at":"2026-05-17T23:44:05.057638Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:44:05.057638Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Gs8Yzku/qQVA3lMPaayPLk6I9MBVnba0Ojm0yr4CjLwA1PTRzdcEIGkDoYgIIuJAuCgdY71sfqQ8+OhTaW4sCA==","signature_status":"signed_v1","signed_at":"2026-05-17T23:44:05.058086Z","signed_message":"canonical_sha256_bytes"},"source_id":"1207.6022","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9557ea5b7cf56abc8ca75cd853a1f42e25f09995bbe9658f88e5a051f9e5e6b7","sha256:e9be2ee9a9364861cccb92b6e2b6a349bc919a21d65cfb4959e2c60ab37c8185"],"state_sha256":"2a339b9ca9760ce6f26f412315d5370d9a72314c16ccbb2ee573eff39b101e56"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/A52HQNB7o22005Pmygra30L/3jH2cLFJihP5GV0k3hYwspBULgjwo1AND9bIRf3tUpgyaAY+/mAVcCqSBdpDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-19T10:20:02.882741Z","bundle_sha256":"ab52d41e92603ab23972231f26954d949bf8a6971f3f5e5626cf296302d9cc37"}}