{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2010:HKCV7RDKAD4ETNV2JDTGRNR34I","short_pith_number":"pith:HKCV7RDK","canonical_record":{"source":{"id":"1008.2424","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"astro-ph.GA","submitted_at":"2010-08-14T09:51:32Z","cross_cats_sorted":[],"title_canon_sha256":"ac013fbf765279a9dc9b779ef757eeb5d36932d899d1a3308e56e231087f792b","abstract_canon_sha256":"dfd8ba7b0c0316ee89069793a372017cba76bb2c28337a4f685fe89d8f26bdf7"},"schema_version":"1.0"},"canonical_sha256":"3a855fc46a00f849b6ba48e668b63be20fe60cdfa84c8da34ecd2f21496ee6a6","source":{"kind":"arxiv","id":"1008.2424","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1008.2424","created_at":"2026-05-18T04:38:16Z"},{"alias_kind":"arxiv_version","alias_value":"1008.2424v1","created_at":"2026-05-18T04:38:16Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1008.2424","created_at":"2026-05-18T04:38:16Z"},{"alias_kind":"pith_short_12","alias_value":"HKCV7RDKAD4E","created_at":"2026-05-18T12:26:07Z"},{"alias_kind":"pith_short_16","alias_value":"HKCV7RDKAD4ETNV2","created_at":"2026-05-18T12:26:07Z"},{"alias_kind":"pith_short_8","alias_value":"HKCV7RDK","created_at":"2026-05-18T12:26:07Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2010:HKCV7RDKAD4ETNV2JDTGRNR34I","target":"record","payload":{"canonical_record":{"source":{"id":"1008.2424","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"astro-ph.GA","submitted_at":"2010-08-14T09:51:32Z","cross_cats_sorted":[],"title_canon_sha256":"ac013fbf765279a9dc9b779ef757eeb5d36932d899d1a3308e56e231087f792b","abstract_canon_sha256":"dfd8ba7b0c0316ee89069793a372017cba76bb2c28337a4f685fe89d8f26bdf7"},"schema_version":"1.0"},"canonical_sha256":"3a855fc46a00f849b6ba48e668b63be20fe60cdfa84c8da34ecd2f21496ee6a6","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:38:16.750173Z","signature_b64":"NqlIU2FD9So7tGetM8VrBjsb38Y4v2bEtkYyUIlg72zRAj2bVgYnb5EStiiQ3uZG1wOOB8WvzcFbziFMKz4CDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3a855fc46a00f849b6ba48e668b63be20fe60cdfa84c8da34ecd2f21496ee6a6","last_reissued_at":"2026-05-18T04:38:16.749688Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:38:16.749688Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1008.2424","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":"2026-05-18T04:38:16Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"JduJSuoN8uqQnTeU/VMQY/FI0j1lCzZJPhZeKg9pwk8GSS6rZ+yd1ZExI6t7B02uzSZuWNegthw+75yWh+ZoCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T02:06:51.338299Z"},"content_sha256":"a12d6772d9811e7213e5a44c3c50959fc6b0d041520c3768b093a3981e4eb2b2","schema_version":"1.0","event_id":"sha256:a12d6772d9811e7213e5a44c3c50959fc6b0d041520c3768b093a3981e4eb2b2"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2010:HKCV7RDKAD4ETNV2JDTGRNR34I","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Analytical potential-density pairs for bars","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"astro-ph.GA","authors_text":"D. Vogt, P. S. Letelier","submitted_at":"2010-08-14T09:51:32Z","abstract_excerpt":"An identity that relates multipolar solutions of the Einstein equations to Newtonian potentials of bars with linear densities proportional to Legendre polynomials is used to construct analytical potential-density pairs of infinitesimally thin bars with a given linear density profile. By means of a suitable transformation, softened bars that are free of singularities are also obtained. As an application we study the equilibrium points and stability for the motion of test particles in the gravitational field for three models of rotating bars."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1008.2424","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":"2026-05-18T04:38:16Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"1EIZjKY5JMealFM1aqv6U6owl/tTv8Hd6DIVgJXeArbI4/lFR14aio74Ei8j7+SsAZTNX+uDCIEQk6qgOXH5CQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T02:06:51.338668Z"},"content_sha256":"84664496176f0cb310b7a837d86662eb1962551b3a2a4cab9aa073e96cec3531","schema_version":"1.0","event_id":"sha256:84664496176f0cb310b7a837d86662eb1962551b3a2a4cab9aa073e96cec3531"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/HKCV7RDKAD4ETNV2JDTGRNR34I/bundle.json","state_url":"https://pith.science/pith/HKCV7RDKAD4ETNV2JDTGRNR34I/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/HKCV7RDKAD4ETNV2JDTGRNR34I/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":"2026-06-24T02:06:51Z","links":{"resolver":"https://pith.science/pith/HKCV7RDKAD4ETNV2JDTGRNR34I","bundle":"https://pith.science/pith/HKCV7RDKAD4ETNV2JDTGRNR34I/bundle.json","state":"https://pith.science/pith/HKCV7RDKAD4ETNV2JDTGRNR34I/state.json","well_known_bundle":"https://pith.science/.well-known/pith/HKCV7RDKAD4ETNV2JDTGRNR34I/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:HKCV7RDKAD4ETNV2JDTGRNR34I","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":"dfd8ba7b0c0316ee89069793a372017cba76bb2c28337a4f685fe89d8f26bdf7","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"astro-ph.GA","submitted_at":"2010-08-14T09:51:32Z","title_canon_sha256":"ac013fbf765279a9dc9b779ef757eeb5d36932d899d1a3308e56e231087f792b"},"schema_version":"1.0","source":{"id":"1008.2424","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1008.2424","created_at":"2026-05-18T04:38:16Z"},{"alias_kind":"arxiv_version","alias_value":"1008.2424v1","created_at":"2026-05-18T04:38:16Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1008.2424","created_at":"2026-05-18T04:38:16Z"},{"alias_kind":"pith_short_12","alias_value":"HKCV7RDKAD4E","created_at":"2026-05-18T12:26:07Z"},{"alias_kind":"pith_short_16","alias_value":"HKCV7RDKAD4ETNV2","created_at":"2026-05-18T12:26:07Z"},{"alias_kind":"pith_short_8","alias_value":"HKCV7RDK","created_at":"2026-05-18T12:26:07Z"}],"graph_snapshots":[{"event_id":"sha256:84664496176f0cb310b7a837d86662eb1962551b3a2a4cab9aa073e96cec3531","target":"graph","created_at":"2026-05-18T04:38:16Z","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":"An identity that relates multipolar solutions of the Einstein equations to Newtonian potentials of bars with linear densities proportional to Legendre polynomials is used to construct analytical potential-density pairs of infinitesimally thin bars with a given linear density profile. By means of a suitable transformation, softened bars that are free of singularities are also obtained. As an application we study the equilibrium points and stability for the motion of test particles in the gravitational field for three models of rotating bars.","authors_text":"D. Vogt, P. S. Letelier","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"astro-ph.GA","submitted_at":"2010-08-14T09:51:32Z","title":"Analytical potential-density pairs for bars"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1008.2424","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:a12d6772d9811e7213e5a44c3c50959fc6b0d041520c3768b093a3981e4eb2b2","target":"record","created_at":"2026-05-18T04:38:16Z","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":"dfd8ba7b0c0316ee89069793a372017cba76bb2c28337a4f685fe89d8f26bdf7","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"astro-ph.GA","submitted_at":"2010-08-14T09:51:32Z","title_canon_sha256":"ac013fbf765279a9dc9b779ef757eeb5d36932d899d1a3308e56e231087f792b"},"schema_version":"1.0","source":{"id":"1008.2424","kind":"arxiv","version":1}},"canonical_sha256":"3a855fc46a00f849b6ba48e668b63be20fe60cdfa84c8da34ecd2f21496ee6a6","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3a855fc46a00f849b6ba48e668b63be20fe60cdfa84c8da34ecd2f21496ee6a6","first_computed_at":"2026-05-18T04:38:16.749688Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:38:16.749688Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"NqlIU2FD9So7tGetM8VrBjsb38Y4v2bEtkYyUIlg72zRAj2bVgYnb5EStiiQ3uZG1wOOB8WvzcFbziFMKz4CDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T04:38:16.750173Z","signed_message":"canonical_sha256_bytes"},"source_id":"1008.2424","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a12d6772d9811e7213e5a44c3c50959fc6b0d041520c3768b093a3981e4eb2b2","sha256:84664496176f0cb310b7a837d86662eb1962551b3a2a4cab9aa073e96cec3531"],"state_sha256":"6674d5acad4bf2f24f34c8932514cdcf50ba3fac4470a28f84660387eee8ca88"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"G52V+U3ooieqAr3v76fbpl4P4QfROK6xdwC4zxRq4I5NHnPd+3/Nt4aSa/9RN14R1ihRHCbovR9tjBhJXNevDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-24T02:06:51.340783Z","bundle_sha256":"ddcfa5e8568e5e657bfe15eac114052edf8feb83338f90fffc3975b9a4b8e777"}}