{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:ID4R6GEV7L3GVP7Y22BWYMDZEK","short_pith_number":"pith:ID4R6GEV","schema_version":"1.0","canonical_sha256":"40f91f1895faf66abff8d6836c3079229b980206bbd141fc08e8f6815d7def6a","source":{"kind":"arxiv","id":"1411.0805","version":1},"attestation_state":"computed","paper":{"title":"Trajectories of point particles in cosmology and the Zel'dovich approximation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["astro-ph.CO","physics.class-ph"],"primary_cat":"gr-qc","authors_text":"Matthias Bartelmann","submitted_at":"2014-11-04T07:07:42Z","abstract_excerpt":"Using a Green's function approach, we compare the trajectories of classical Hamiltonian point particles in an expanding space-time to the effectively inertial trajectories in the Zel'dovich approximation. It is shown that the effective gravitational potential accelerating the particles relative to the Zel'dovich trajectories vanishes exactly initially as a consequence of the continuity equation, and acts only during a short, early period. The Green's function approach suggests an iterative scheme for improving the Zel'dovich trajectories, which can be analytically solved. We construct these tr"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1411.0805","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2014-11-04T07:07:42Z","cross_cats_sorted":["astro-ph.CO","physics.class-ph"],"title_canon_sha256":"0254e33c0b5f88c428e3921c2ae274f4d47d45d687b1c4cd118741e113e084b1","abstract_canon_sha256":"739368c9350ff94c26dcace6fced611db5c9d1e233bae2b979f57165f792d805"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:41:35.451284Z","signature_b64":"aGFHEaeqzayb3SZ991GCpjKYP+Qs3Px4jbG9tXI6c6DmwPIRClijeTn5tgJU9cPgRQkThl3JfPhNnHeJZf0qDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"40f91f1895faf66abff8d6836c3079229b980206bbd141fc08e8f6815d7def6a","last_reissued_at":"2026-05-18T01:41:35.450666Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:41:35.450666Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Trajectories of point particles in cosmology and the Zel'dovich approximation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["astro-ph.CO","physics.class-ph"],"primary_cat":"gr-qc","authors_text":"Matthias Bartelmann","submitted_at":"2014-11-04T07:07:42Z","abstract_excerpt":"Using a Green's function approach, we compare the trajectories of classical Hamiltonian point particles in an expanding space-time to the effectively inertial trajectories in the Zel'dovich approximation. It is shown that the effective gravitational potential accelerating the particles relative to the Zel'dovich trajectories vanishes exactly initially as a consequence of the continuity equation, and acts only during a short, early period. The Green's function approach suggests an iterative scheme for improving the Zel'dovich trajectories, which can be analytically solved. We construct these tr"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1411.0805","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1411.0805","created_at":"2026-05-18T01:41:35.450753+00:00"},{"alias_kind":"arxiv_version","alias_value":"1411.0805v1","created_at":"2026-05-18T01:41:35.450753+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1411.0805","created_at":"2026-05-18T01:41:35.450753+00:00"},{"alias_kind":"pith_short_12","alias_value":"ID4R6GEV7L3G","created_at":"2026-05-18T12:28:33.132498+00:00"},{"alias_kind":"pith_short_16","alias_value":"ID4R6GEV7L3GVP7Y","created_at":"2026-05-18T12:28:33.132498+00:00"},{"alias_kind":"pith_short_8","alias_value":"ID4R6GEV","created_at":"2026-05-18T12:28:33.132498+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/ID4R6GEV7L3GVP7Y22BWYMDZEK","json":"https://pith.science/pith/ID4R6GEV7L3GVP7Y22BWYMDZEK.json","graph_json":"https://pith.science/api/pith-number/ID4R6GEV7L3GVP7Y22BWYMDZEK/graph.json","events_json":"https://pith.science/api/pith-number/ID4R6GEV7L3GVP7Y22BWYMDZEK/events.json","paper":"https://pith.science/paper/ID4R6GEV"},"agent_actions":{"view_html":"https://pith.science/pith/ID4R6GEV7L3GVP7Y22BWYMDZEK","download_json":"https://pith.science/pith/ID4R6GEV7L3GVP7Y22BWYMDZEK.json","view_paper":"https://pith.science/paper/ID4R6GEV","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1411.0805&json=true","fetch_graph":"https://pith.science/api/pith-number/ID4R6GEV7L3GVP7Y22BWYMDZEK/graph.json","fetch_events":"https://pith.science/api/pith-number/ID4R6GEV7L3GVP7Y22BWYMDZEK/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/ID4R6GEV7L3GVP7Y22BWYMDZEK/action/timestamp_anchor","attest_storage":"https://pith.science/pith/ID4R6GEV7L3GVP7Y22BWYMDZEK/action/storage_attestation","attest_author":"https://pith.science/pith/ID4R6GEV7L3GVP7Y22BWYMDZEK/action/author_attestation","sign_citation":"https://pith.science/pith/ID4R6GEV7L3GVP7Y22BWYMDZEK/action/citation_signature","submit_replication":"https://pith.science/pith/ID4R6GEV7L3GVP7Y22BWYMDZEK/action/replication_record"}},"created_at":"2026-05-18T01:41:35.450753+00:00","updated_at":"2026-05-18T01:41:35.450753+00:00"}