{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2004:O2C5IC4BLSV7KUEKJ7YFVVO7AO","short_pith_number":"pith:O2C5IC4B","schema_version":"1.0","canonical_sha256":"7685d40b815cabf5508a4ff05ad5df03ae1768078300f2e3e02e87e01889d033","source":{"kind":"arxiv","id":"gr-qc/0407062","version":1},"attestation_state":"computed","paper":{"title":"Structure of solutions near the initial singularity for the surface-symmetric Einstein-Vlasov system","license":"","headline":"","cross_cats":[],"primary_cat":"gr-qc","authors_text":"Sophonie Blaise Tchapnda","submitted_at":"2004-07-16T08:00:07Z","abstract_excerpt":"Results on the behaviour in the past time direction of cosmological models with collisionless matter and a cosmological constant $\\Lambda$ are presented. It is shown that under the assumption of non-positive $\\Lambda$ and spherical or plane symmetry the area radius goes to zero at the initial singularity. Under a smallness assumption on the initial data, these properties hold in the case of hyperbolic symmetry and negative $\\Lambda$ as well as in the positive $\\Lambda$ case. Furthermore in the latter cases past global existence of spatially homogeneous solutions is proved for generic initial d"},"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":"gr-qc/0407062","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"gr-qc","submitted_at":"2004-07-16T08:00:07Z","cross_cats_sorted":[],"title_canon_sha256":"88658651abe8ec8a01684e2382391e700443d94320b4e5d6dfb51676ec7e7a22","abstract_canon_sha256":"6dc96dd245c344070498909be6507be42ce42e5da96aa04b7847acdb205449e1"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:37:30.017536Z","signature_b64":"Vxm/3oQWgdg79u+Vf1uozT74udTAJZJviikSe2iHpElLGply1OWgrEooWm9/AFn479dfTMqZLG7AWVAqGxl6AQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7685d40b815cabf5508a4ff05ad5df03ae1768078300f2e3e02e87e01889d033","last_reissued_at":"2026-05-18T02:37:30.017144Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:37:30.017144Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Structure of solutions near the initial singularity for the surface-symmetric Einstein-Vlasov system","license":"","headline":"","cross_cats":[],"primary_cat":"gr-qc","authors_text":"Sophonie Blaise Tchapnda","submitted_at":"2004-07-16T08:00:07Z","abstract_excerpt":"Results on the behaviour in the past time direction of cosmological models with collisionless matter and a cosmological constant $\\Lambda$ are presented. It is shown that under the assumption of non-positive $\\Lambda$ and spherical or plane symmetry the area radius goes to zero at the initial singularity. Under a smallness assumption on the initial data, these properties hold in the case of hyperbolic symmetry and negative $\\Lambda$ as well as in the positive $\\Lambda$ case. Furthermore in the latter cases past global existence of spatially homogeneous solutions is proved for generic initial d"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"gr-qc/0407062","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":"gr-qc/0407062","created_at":"2026-05-18T02:37:30.017201+00:00"},{"alias_kind":"arxiv_version","alias_value":"gr-qc/0407062v1","created_at":"2026-05-18T02:37:30.017201+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.gr-qc/0407062","created_at":"2026-05-18T02:37:30.017201+00:00"},{"alias_kind":"pith_short_12","alias_value":"O2C5IC4BLSV7","created_at":"2026-05-18T12:25:52.687210+00:00"},{"alias_kind":"pith_short_16","alias_value":"O2C5IC4BLSV7KUEK","created_at":"2026-05-18T12:25:52.687210+00:00"},{"alias_kind":"pith_short_8","alias_value":"O2C5IC4B","created_at":"2026-05-18T12:25:52.687210+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/O2C5IC4BLSV7KUEKJ7YFVVO7AO","json":"https://pith.science/pith/O2C5IC4BLSV7KUEKJ7YFVVO7AO.json","graph_json":"https://pith.science/api/pith-number/O2C5IC4BLSV7KUEKJ7YFVVO7AO/graph.json","events_json":"https://pith.science/api/pith-number/O2C5IC4BLSV7KUEKJ7YFVVO7AO/events.json","paper":"https://pith.science/paper/O2C5IC4B"},"agent_actions":{"view_html":"https://pith.science/pith/O2C5IC4BLSV7KUEKJ7YFVVO7AO","download_json":"https://pith.science/pith/O2C5IC4BLSV7KUEKJ7YFVVO7AO.json","view_paper":"https://pith.science/paper/O2C5IC4B","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=gr-qc/0407062&json=true","fetch_graph":"https://pith.science/api/pith-number/O2C5IC4BLSV7KUEKJ7YFVVO7AO/graph.json","fetch_events":"https://pith.science/api/pith-number/O2C5IC4BLSV7KUEKJ7YFVVO7AO/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/O2C5IC4BLSV7KUEKJ7YFVVO7AO/action/timestamp_anchor","attest_storage":"https://pith.science/pith/O2C5IC4BLSV7KUEKJ7YFVVO7AO/action/storage_attestation","attest_author":"https://pith.science/pith/O2C5IC4BLSV7KUEKJ7YFVVO7AO/action/author_attestation","sign_citation":"https://pith.science/pith/O2C5IC4BLSV7KUEKJ7YFVVO7AO/action/citation_signature","submit_replication":"https://pith.science/pith/O2C5IC4BLSV7KUEKJ7YFVVO7AO/action/replication_record"}},"created_at":"2026-05-18T02:37:30.017201+00:00","updated_at":"2026-05-18T02:37:30.017201+00:00"}