{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:7IJUR57PJKC5SQX45HVOANJ53J","short_pith_number":"pith:7IJUR57P","canonical_record":{"source":{"id":"1209.1342","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"astro-ph.GA","submitted_at":"2012-09-06T16:51:56Z","cross_cats_sorted":[],"title_canon_sha256":"a7795c61669e42cb9bd33f0496aa0bb28a7697ebfe39a79b5839dcef13bdbd8e","abstract_canon_sha256":"44308715afb96834d43e3eb73f46a4bae3bdf7420dda83f380ae4a7ef7196ec5"},"schema_version":"1.0"},"canonical_sha256":"fa1348f7ef4a85d942fce9eae0353dda64444372dfc14e7d7bffd85258890c4c","source":{"kind":"arxiv","id":"1209.1342","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1209.1342","created_at":"2026-05-18T01:54:39Z"},{"alias_kind":"arxiv_version","alias_value":"1209.1342v1","created_at":"2026-05-18T01:54:39Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1209.1342","created_at":"2026-05-18T01:54:39Z"},{"alias_kind":"pith_short_12","alias_value":"7IJUR57PJKC5","created_at":"2026-05-18T12:26:56Z"},{"alias_kind":"pith_short_16","alias_value":"7IJUR57PJKC5SQX4","created_at":"2026-05-18T12:26:56Z"},{"alias_kind":"pith_short_8","alias_value":"7IJUR57P","created_at":"2026-05-18T12:26:56Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:7IJUR57PJKC5SQX45HVOANJ53J","target":"record","payload":{"canonical_record":{"source":{"id":"1209.1342","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"astro-ph.GA","submitted_at":"2012-09-06T16:51:56Z","cross_cats_sorted":[],"title_canon_sha256":"a7795c61669e42cb9bd33f0496aa0bb28a7697ebfe39a79b5839dcef13bdbd8e","abstract_canon_sha256":"44308715afb96834d43e3eb73f46a4bae3bdf7420dda83f380ae4a7ef7196ec5"},"schema_version":"1.0"},"canonical_sha256":"fa1348f7ef4a85d942fce9eae0353dda64444372dfc14e7d7bffd85258890c4c","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:54:39.210982Z","signature_b64":"PMsJudO9+/gZjEACKiLoZNgrE4wPdAirvqjSfsXdrnrFMRFgp+Pd+041bmu2HMxdaE/LqOEePcXExm55pSTPAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"fa1348f7ef4a85d942fce9eae0353dda64444372dfc14e7d7bffd85258890c4c","last_reissued_at":"2026-05-18T01:54:39.210277Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:54:39.210277Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1209.1342","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":"2026-05-18T01:54:39Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"2zO85iMxyU5TXsVyG5cLURfoMkmsVq5mw/sRRcbddVWuDwCwBJYDOaJd8Y1kTKcahPqF4rYX/cT23fTLgT1PDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T04:16:07.691662Z"},"content_sha256":"1d0ca381a5d26873bcc9d16c277fdd46343a95c26fd14805b6b580c5bcc21d92","schema_version":"1.0","event_id":"sha256:1d0ca381a5d26873bcc9d16c277fdd46343a95c26fd14805b6b580c5bcc21d92"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:7IJUR57PJKC5SQX45HVOANJ53J","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A Study of the Orbits of the Logarithmic Potential for Galaxies","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"astro-ph.GA","authors_text":"J. Drozd, M. DaSilva, P. A. Wiegert, S. R. Valluri","submitted_at":"2012-09-06T16:51:56Z","abstract_excerpt":"The logarithmic potential is of great interest and relevance in the study of the dynamics of galaxies. Some small corrections to the work of Contopoulos & Seimenis (1990) who used the method of Prendergast (1982) to find periodic orbits and bifurcations within such a potential are presented. The solution of the orbital radial equation for the purely radial logarithmic potential is then considered using the p-ellipse (precessing ellipse) method pioneered by Struck (2006). This differential orbital equation is a special case of the generalized Burgers equation. The apsidal angle is also determin"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1209.1342","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":"2026-05-18T01:54:39Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"jyQn3diBrwUIsrCzdPF63+gcXSriRJfbbOu5AhALQYhLCIJR+S1b4LG0LpHjI7+R01s3BtDQ19hAIO9n5N8nAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T04:16:07.692342Z"},"content_sha256":"8de8e35f44f80f4e4628774884e7d6c400a5f691ee39b461aeff3abb3a11a812","schema_version":"1.0","event_id":"sha256:8de8e35f44f80f4e4628774884e7d6c400a5f691ee39b461aeff3abb3a11a812"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/7IJUR57PJKC5SQX45HVOANJ53J/bundle.json","state_url":"https://pith.science/pith/7IJUR57PJKC5SQX45HVOANJ53J/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/7IJUR57PJKC5SQX45HVOANJ53J/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":"2026-06-05T04:16:07Z","links":{"resolver":"https://pith.science/pith/7IJUR57PJKC5SQX45HVOANJ53J","bundle":"https://pith.science/pith/7IJUR57PJKC5SQX45HVOANJ53J/bundle.json","state":"https://pith.science/pith/7IJUR57PJKC5SQX45HVOANJ53J/state.json","well_known_bundle":"https://pith.science/.well-known/pith/7IJUR57PJKC5SQX45HVOANJ53J/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:7IJUR57PJKC5SQX45HVOANJ53J","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":"44308715afb96834d43e3eb73f46a4bae3bdf7420dda83f380ae4a7ef7196ec5","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"astro-ph.GA","submitted_at":"2012-09-06T16:51:56Z","title_canon_sha256":"a7795c61669e42cb9bd33f0496aa0bb28a7697ebfe39a79b5839dcef13bdbd8e"},"schema_version":"1.0","source":{"id":"1209.1342","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1209.1342","created_at":"2026-05-18T01:54:39Z"},{"alias_kind":"arxiv_version","alias_value":"1209.1342v1","created_at":"2026-05-18T01:54:39Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1209.1342","created_at":"2026-05-18T01:54:39Z"},{"alias_kind":"pith_short_12","alias_value":"7IJUR57PJKC5","created_at":"2026-05-18T12:26:56Z"},{"alias_kind":"pith_short_16","alias_value":"7IJUR57PJKC5SQX4","created_at":"2026-05-18T12:26:56Z"},{"alias_kind":"pith_short_8","alias_value":"7IJUR57P","created_at":"2026-05-18T12:26:56Z"}],"graph_snapshots":[{"event_id":"sha256:8de8e35f44f80f4e4628774884e7d6c400a5f691ee39b461aeff3abb3a11a812","target":"graph","created_at":"2026-05-18T01:54:39Z","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":"The logarithmic potential is of great interest and relevance in the study of the dynamics of galaxies. Some small corrections to the work of Contopoulos & Seimenis (1990) who used the method of Prendergast (1982) to find periodic orbits and bifurcations within such a potential are presented. The solution of the orbital radial equation for the purely radial logarithmic potential is then considered using the p-ellipse (precessing ellipse) method pioneered by Struck (2006). This differential orbital equation is a special case of the generalized Burgers equation. The apsidal angle is also determin","authors_text":"J. Drozd, M. DaSilva, P. A. Wiegert, S. R. Valluri","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"astro-ph.GA","submitted_at":"2012-09-06T16:51:56Z","title":"A Study of the Orbits of the Logarithmic Potential for Galaxies"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1209.1342","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":"sha256:1d0ca381a5d26873bcc9d16c277fdd46343a95c26fd14805b6b580c5bcc21d92","target":"record","created_at":"2026-05-18T01:54:39Z","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":"44308715afb96834d43e3eb73f46a4bae3bdf7420dda83f380ae4a7ef7196ec5","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"astro-ph.GA","submitted_at":"2012-09-06T16:51:56Z","title_canon_sha256":"a7795c61669e42cb9bd33f0496aa0bb28a7697ebfe39a79b5839dcef13bdbd8e"},"schema_version":"1.0","source":{"id":"1209.1342","kind":"arxiv","version":1}},"canonical_sha256":"fa1348f7ef4a85d942fce9eae0353dda64444372dfc14e7d7bffd85258890c4c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"fa1348f7ef4a85d942fce9eae0353dda64444372dfc14e7d7bffd85258890c4c","first_computed_at":"2026-05-18T01:54:39.210277Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:54:39.210277Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"PMsJudO9+/gZjEACKiLoZNgrE4wPdAirvqjSfsXdrnrFMRFgp+Pd+041bmu2HMxdaE/LqOEePcXExm55pSTPAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:54:39.210982Z","signed_message":"canonical_sha256_bytes"},"source_id":"1209.1342","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1d0ca381a5d26873bcc9d16c277fdd46343a95c26fd14805b6b580c5bcc21d92","sha256:8de8e35f44f80f4e4628774884e7d6c400a5f691ee39b461aeff3abb3a11a812"],"state_sha256":"4b6f218e114c0cd2ce574235dc651c8e9fc94ce7dad3cb50f151d709cc355f5e"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ehychcSL3DotPw17Wga4L1ccM9Tzi6nu9PJDWQEiaBdrcHkJuH8tSjR+JsBsopXYuWMdm8aBHHKBkeAOP/fgCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-05T04:16:07.696193Z","bundle_sha256":"89f2e8dc8bf384165a1a1fd2c0d046f632f512b019fb88a9c1b396548318c2a2"}}