{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:SSOHOZGZOBBQNOGVMEXLGHKWIM","short_pith_number":"pith:SSOHOZGZ","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"},"canonical_sha256":"949c7764d9704306b8d5612eb31d56433f733a0610fd573014d37376ede4c608","source":{"kind":"arxiv","id":"1411.1791","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1411.1791","created_at":"2026-05-18T02:03:48Z"},{"alias_kind":"arxiv_version","alias_value":"1411.1791v2","created_at":"2026-05-18T02:03:48Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1411.1791","created_at":"2026-05-18T02:03:48Z"},{"alias_kind":"pith_short_12","alias_value":"SSOHOZGZOBBQ","created_at":"2026-05-18T12:28:49Z"},{"alias_kind":"pith_short_16","alias_value":"SSOHOZGZOBBQNOGV","created_at":"2026-05-18T12:28:49Z"},{"alias_kind":"pith_short_8","alias_value":"SSOHOZGZ","created_at":"2026-05-18T12:28:49Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:SSOHOZGZOBBQNOGVMEXLGHKWIM","target":"record","payload":{"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"},"canonical_sha256":"949c7764d9704306b8d5612eb31d56433f733a0610fd573014d37376ede4c608","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"},"source_kind":"arxiv","source_id":"1411.1791","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:03:48Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ipghv4huFs9iUmHIelNgp8hOPMMHZlNXIcUacq+FznLeO7fiHnPuOeamFsHlsxkf3QetFLqZXrJe2G+pP8jiDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-27T09:18:43.852310Z"},"content_sha256":"10e3fc01b528491d3d78e1dc9bac1e3bdb183517ac8ce29606938fb2c261ab15","schema_version":"1.0","event_id":"sha256:10e3fc01b528491d3d78e1dc9bac1e3bdb183517ac8ce29606938fb2c261ab15"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:SSOHOZGZOBBQNOGVMEXLGHKWIM","target":"graph","payload":{"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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:03:48Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"OTkgf2v3F+febzyFGZ6rJFG/f+fv9dMEMjdtYUu1Ztt62tylGIHexG17lsOda3YhYsJYygx3uARdlpl7KMXBBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-27T09:18:43.852662Z"},"content_sha256":"4e638073fa5e57134c95bec7ee564dad072f90f0f0c0b8bdbf8d4fe3bb236626","schema_version":"1.0","event_id":"sha256:4e638073fa5e57134c95bec7ee564dad072f90f0f0c0b8bdbf8d4fe3bb236626"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/SSOHOZGZOBBQNOGVMEXLGHKWIM/bundle.json","state_url":"https://pith.science/pith/SSOHOZGZOBBQNOGVMEXLGHKWIM/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/SSOHOZGZOBBQNOGVMEXLGHKWIM/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":"2026-06-27T09:18:43Z","links":{"resolver":"https://pith.science/pith/SSOHOZGZOBBQNOGVMEXLGHKWIM","bundle":"https://pith.science/pith/SSOHOZGZOBBQNOGVMEXLGHKWIM/bundle.json","state":"https://pith.science/pith/SSOHOZGZOBBQNOGVMEXLGHKWIM/state.json","well_known_bundle":"https://pith.science/.well-known/pith/SSOHOZGZOBBQNOGVMEXLGHKWIM/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:SSOHOZGZOBBQNOGVMEXLGHKWIM","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":"a2cb1c5ec474fa541b28e348965cf87cbe44ff6ebadfa2827b0176deb2749e06","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-11-06T23:05:20Z","title_canon_sha256":"d91f10e7b2afa96f6022fc14265d7ac1b512557e1faa9a7877b12f952202a219"},"schema_version":"1.0","source":{"id":"1411.1791","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1411.1791","created_at":"2026-05-18T02:03:48Z"},{"alias_kind":"arxiv_version","alias_value":"1411.1791v2","created_at":"2026-05-18T02:03:48Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1411.1791","created_at":"2026-05-18T02:03:48Z"},{"alias_kind":"pith_short_12","alias_value":"SSOHOZGZOBBQ","created_at":"2026-05-18T12:28:49Z"},{"alias_kind":"pith_short_16","alias_value":"SSOHOZGZOBBQNOGV","created_at":"2026-05-18T12:28:49Z"},{"alias_kind":"pith_short_8","alias_value":"SSOHOZGZ","created_at":"2026-05-18T12:28:49Z"}],"graph_snapshots":[{"event_id":"sha256:4e638073fa5e57134c95bec7ee564dad072f90f0f0c0b8bdbf8d4fe3bb236626","target":"graph","created_at":"2026-05-18T02:03:48Z","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":"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","authors_text":"Changhui Tan, Eitan Tadmor, Jos\\'e A. Carrillo, Young-Pil Choi","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-11-06T23:05:20Z","title":"Critical thresholds in 1D Euler equations with nonlocal forces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1411.1791","kind":"arxiv","version":2},"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":"sha256:10e3fc01b528491d3d78e1dc9bac1e3bdb183517ac8ce29606938fb2c261ab15","target":"record","created_at":"2026-05-18T02:03:48Z","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":"a2cb1c5ec474fa541b28e348965cf87cbe44ff6ebadfa2827b0176deb2749e06","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-11-06T23:05:20Z","title_canon_sha256":"d91f10e7b2afa96f6022fc14265d7ac1b512557e1faa9a7877b12f952202a219"},"schema_version":"1.0","source":{"id":"1411.1791","kind":"arxiv","version":2}},"canonical_sha256":"949c7764d9704306b8d5612eb31d56433f733a0610fd573014d37376ede4c608","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"949c7764d9704306b8d5612eb31d56433f733a0610fd573014d37376ede4c608","first_computed_at":"2026-05-18T02:03:48.182910Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:03:48.182910Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"I3WIHYQB2dQsOCml5wdEqKc3F6GZH7oSeFELKWWKZvel/I68AaVeft5HtRNOBB2mIOygU871/ukk3NjMeJzrBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:03:48.183648Z","signed_message":"canonical_sha256_bytes"},"source_id":"1411.1791","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:10e3fc01b528491d3d78e1dc9bac1e3bdb183517ac8ce29606938fb2c261ab15","sha256:4e638073fa5e57134c95bec7ee564dad072f90f0f0c0b8bdbf8d4fe3bb236626"],"state_sha256":"1b81a20749d03fd37cea255304ccf8e1c9e3702b2be95bf62f586102652f7a3a"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"B7S5x2F8ysyZPf5MQQjUyRXQNs+t0Pavv0m5de4vdD3bYm0HJwITu/nIpz6dJriN1/m80Rc82HvOmxhZLyYcCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-27T09:18:43.854492Z","bundle_sha256":"e83029b41dab63bf3af3917140a1f3e9e0859c222e28e3b9a22295bc0aaf5448"}}