{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:SSOHOZGZOBBQNOGVMEXLGHKWIM","short_pith_number":"pith:SSOHOZGZ","schema_version":"1.0","canonical_sha256":"949c7764d9704306b8d5612eb31d56433f733a0610fd573014d37376ede4c608","source":{"kind":"arxiv","id":"1411.1791","version":2},"attestation_state":"computed","paper":{"title":"Critical thresholds in 1D Euler equations with nonlocal forces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Changhui Tan, Eitan Tadmor, Jos\\'e A. Carrillo, Young-Pil Choi","submitted_at":"2014-11-06T23:05:20Z","abstract_excerpt":"We study the critical thresholds for the compressible pressureless Euler equations with pairwise attractive or repulsive interaction forces and non-local alignment forces in velocity in one dimension. We provide a complete description for the critical threshold to the system without interaction forces leading to a sharp dichotomy condition between global in time existence or finite-time blow-up of strong solutions. When the interaction forces are considered, we also give a classification of the critical thresholds according to the different type of interaction forces. We also analyze condition"},"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":"1411.1791","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-11-06T23:05:20Z","cross_cats_sorted":[],"title_canon_sha256":"d91f10e7b2afa96f6022fc14265d7ac1b512557e1faa9a7877b12f952202a219","abstract_canon_sha256":"a2cb1c5ec474fa541b28e348965cf87cbe44ff6ebadfa2827b0176deb2749e06"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:03:48.183648Z","signature_b64":"I3WIHYQB2dQsOCml5wdEqKc3F6GZH7oSeFELKWWKZvel/I68AaVeft5HtRNOBB2mIOygU871/ukk3NjMeJzrBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"949c7764d9704306b8d5612eb31d56433f733a0610fd573014d37376ede4c608","last_reissued_at":"2026-05-18T02:03:48.182910Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:03:48.182910Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Critical thresholds in 1D Euler equations with nonlocal forces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Changhui Tan, Eitan Tadmor, Jos\\'e A. Carrillo, Young-Pil Choi","submitted_at":"2014-11-06T23:05:20Z","abstract_excerpt":"We study the critical thresholds for the compressible pressureless Euler equations with pairwise attractive or repulsive interaction forces and non-local alignment forces in velocity in one dimension. We provide a complete description for the critical threshold to the system without interaction forces leading to a sharp dichotomy condition between global in time existence or finite-time blow-up of strong solutions. When the interaction forces are considered, we also give a classification of the critical thresholds according to the different type of interaction forces. We also analyze condition"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1411.1791","kind":"arxiv","version":2},"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":"1411.1791","created_at":"2026-05-18T02:03:48.183019+00:00"},{"alias_kind":"arxiv_version","alias_value":"1411.1791v2","created_at":"2026-05-18T02:03:48.183019+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1411.1791","created_at":"2026-05-18T02:03:48.183019+00:00"},{"alias_kind":"pith_short_12","alias_value":"SSOHOZGZOBBQ","created_at":"2026-05-18T12:28:49.207871+00:00"},{"alias_kind":"pith_short_16","alias_value":"SSOHOZGZOBBQNOGV","created_at":"2026-05-18T12:28:49.207871+00:00"},{"alias_kind":"pith_short_8","alias_value":"SSOHOZGZ","created_at":"2026-05-18T12:28:49.207871+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/SSOHOZGZOBBQNOGVMEXLGHKWIM","json":"https://pith.science/pith/SSOHOZGZOBBQNOGVMEXLGHKWIM.json","graph_json":"https://pith.science/api/pith-number/SSOHOZGZOBBQNOGVMEXLGHKWIM/graph.json","events_json":"https://pith.science/api/pith-number/SSOHOZGZOBBQNOGVMEXLGHKWIM/events.json","paper":"https://pith.science/paper/SSOHOZGZ"},"agent_actions":{"view_html":"https://pith.science/pith/SSOHOZGZOBBQNOGVMEXLGHKWIM","download_json":"https://pith.science/pith/SSOHOZGZOBBQNOGVMEXLGHKWIM.json","view_paper":"https://pith.science/paper/SSOHOZGZ","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1411.1791&json=true","fetch_graph":"https://pith.science/api/pith-number/SSOHOZGZOBBQNOGVMEXLGHKWIM/graph.json","fetch_events":"https://pith.science/api/pith-number/SSOHOZGZOBBQNOGVMEXLGHKWIM/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/SSOHOZGZOBBQNOGVMEXLGHKWIM/action/timestamp_anchor","attest_storage":"https://pith.science/pith/SSOHOZGZOBBQNOGVMEXLGHKWIM/action/storage_attestation","attest_author":"https://pith.science/pith/SSOHOZGZOBBQNOGVMEXLGHKWIM/action/author_attestation","sign_citation":"https://pith.science/pith/SSOHOZGZOBBQNOGVMEXLGHKWIM/action/citation_signature","submit_replication":"https://pith.science/pith/SSOHOZGZOBBQNOGVMEXLGHKWIM/action/replication_record"}},"created_at":"2026-05-18T02:03:48.183019+00:00","updated_at":"2026-05-18T02:03:48.183019+00:00"}