{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2009:6UT2PO3CM7CBBZHXWRJWXRRVD2","short_pith_number":"pith:6UT2PO3C","canonical_record":{"source":{"id":"0912.0661","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.soft","submitted_at":"2009-12-03T14:12:27Z","cross_cats_sorted":["physics.flu-dyn"],"title_canon_sha256":"44bd21ae41bdd5e49c6db061f57757832777f4091b3ac44ffa313a96081ff843","abstract_canon_sha256":"aa3902524a5d3504159d56e330a811081bc532aedf06a43508fc1cc0d669cbd7"},"schema_version":"1.0"},"canonical_sha256":"f527a7bb6267c410e4f7b4536bc6351e8c8b4e666bd14dcf83571fbf21d22db6","source":{"kind":"arxiv","id":"0912.0661","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0912.0661","created_at":"2026-05-18T02:10:34Z"},{"alias_kind":"arxiv_version","alias_value":"0912.0661v2","created_at":"2026-05-18T02:10:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0912.0661","created_at":"2026-05-18T02:10:34Z"},{"alias_kind":"pith_short_12","alias_value":"6UT2PO3CM7CB","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_16","alias_value":"6UT2PO3CM7CBBZHX","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_8","alias_value":"6UT2PO3C","created_at":"2026-05-18T12:25:58Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2009:6UT2PO3CM7CBBZHXWRJWXRRVD2","target":"record","payload":{"canonical_record":{"source":{"id":"0912.0661","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.soft","submitted_at":"2009-12-03T14:12:27Z","cross_cats_sorted":["physics.flu-dyn"],"title_canon_sha256":"44bd21ae41bdd5e49c6db061f57757832777f4091b3ac44ffa313a96081ff843","abstract_canon_sha256":"aa3902524a5d3504159d56e330a811081bc532aedf06a43508fc1cc0d669cbd7"},"schema_version":"1.0"},"canonical_sha256":"f527a7bb6267c410e4f7b4536bc6351e8c8b4e666bd14dcf83571fbf21d22db6","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:10:34.259639Z","signature_b64":"Vn8RY6tBfyFK/6lW6RIc8h9LfN9lXDNhIHrobI4EX8t7KnfNDYIRtL/4HbQ5zDPNSy11OCEjELhoLmH0z5RBDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f527a7bb6267c410e4f7b4536bc6351e8c8b4e666bd14dcf83571fbf21d22db6","last_reissued_at":"2026-05-18T02:10:34.259041Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:10:34.259041Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"0912.0661","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":"2026-05-18T02:10:34Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"IkFuODK+fAYZ89gxFN3ijdWLC0+zW1iwrl7GIqI52EoL8th4wSi1Fw5TsnqAJ5o7uCN/uBK/VgakzqUroJBSAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T21:06:33.151916Z"},"content_sha256":"185df82ea3a1209ca38c4083da4def29b6245c8e0745048afa48ffae0f1d7e28","schema_version":"1.0","event_id":"sha256:185df82ea3a1209ca38c4083da4def29b6245c8e0745048afa48ffae0f1d7e28"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2009:6UT2PO3CM7CBBZHXWRJWXRRVD2","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Navier-Stokes hydrodynamics of thermal collapse in a freely cooling granular gas","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["physics.flu-dyn"],"primary_cat":"cond-mat.soft","authors_text":"Baruch Meerson, Eli Livne, Itamar Kolvin","submitted_at":"2009-12-03T14:12:27Z","abstract_excerpt":"We employ Navier-Stokes granular hydrodynamics to investigate the long-time behavior of clustering instability in a freely cooling dilute granular gas in two dimensions. We find that, in circular containers, the homogeneous cooling state (HCS) of the gas loses its stability via a sub-critical pitchfork bifurcation. There are no time-independent solutions for the gas density in the supercritical region, and we present analytical and numerical evidence that the gas develops thermal collapse unarrested by heat diffusion. To get more insight, we switch to a simpler geometry of a narrow-sector-shap"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0912.0661","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":"2026-05-18T02:10:34Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"iDzW7PvKJwU6TN/bK94lug9LWFCWPnPKpe1H6kzmYODtZqknvYeUGoVo3JlgJ0bVni5eZXHtyrk4o9ioBlmmDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T21:06:33.152754Z"},"content_sha256":"e7bc895d51c2bf7455973bd2c09c68f9272ac7be760ba44f36c1b27e887248ab","schema_version":"1.0","event_id":"sha256:e7bc895d51c2bf7455973bd2c09c68f9272ac7be760ba44f36c1b27e887248ab"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/6UT2PO3CM7CBBZHXWRJWXRRVD2/bundle.json","state_url":"https://pith.science/pith/6UT2PO3CM7CBBZHXWRJWXRRVD2/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/6UT2PO3CM7CBBZHXWRJWXRRVD2/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":"2026-05-31T21:06:33Z","links":{"resolver":"https://pith.science/pith/6UT2PO3CM7CBBZHXWRJWXRRVD2","bundle":"https://pith.science/pith/6UT2PO3CM7CBBZHXWRJWXRRVD2/bundle.json","state":"https://pith.science/pith/6UT2PO3CM7CBBZHXWRJWXRRVD2/state.json","well_known_bundle":"https://pith.science/.well-known/pith/6UT2PO3CM7CBBZHXWRJWXRRVD2/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2009:6UT2PO3CM7CBBZHXWRJWXRRVD2","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":"aa3902524a5d3504159d56e330a811081bc532aedf06a43508fc1cc0d669cbd7","cross_cats_sorted":["physics.flu-dyn"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.soft","submitted_at":"2009-12-03T14:12:27Z","title_canon_sha256":"44bd21ae41bdd5e49c6db061f57757832777f4091b3ac44ffa313a96081ff843"},"schema_version":"1.0","source":{"id":"0912.0661","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0912.0661","created_at":"2026-05-18T02:10:34Z"},{"alias_kind":"arxiv_version","alias_value":"0912.0661v2","created_at":"2026-05-18T02:10:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0912.0661","created_at":"2026-05-18T02:10:34Z"},{"alias_kind":"pith_short_12","alias_value":"6UT2PO3CM7CB","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_16","alias_value":"6UT2PO3CM7CBBZHX","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_8","alias_value":"6UT2PO3C","created_at":"2026-05-18T12:25:58Z"}],"graph_snapshots":[{"event_id":"sha256:e7bc895d51c2bf7455973bd2c09c68f9272ac7be760ba44f36c1b27e887248ab","target":"graph","created_at":"2026-05-18T02:10:34Z","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 employ Navier-Stokes granular hydrodynamics to investigate the long-time behavior of clustering instability in a freely cooling dilute granular gas in two dimensions. We find that, in circular containers, the homogeneous cooling state (HCS) of the gas loses its stability via a sub-critical pitchfork bifurcation. There are no time-independent solutions for the gas density in the supercritical region, and we present analytical and numerical evidence that the gas develops thermal collapse unarrested by heat diffusion. To get more insight, we switch to a simpler geometry of a narrow-sector-shap","authors_text":"Baruch Meerson, Eli Livne, Itamar Kolvin","cross_cats":["physics.flu-dyn"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.soft","submitted_at":"2009-12-03T14:12:27Z","title":"Navier-Stokes hydrodynamics of thermal collapse in a freely cooling granular gas"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0912.0661","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":"sha256:185df82ea3a1209ca38c4083da4def29b6245c8e0745048afa48ffae0f1d7e28","target":"record","created_at":"2026-05-18T02:10:34Z","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":"aa3902524a5d3504159d56e330a811081bc532aedf06a43508fc1cc0d669cbd7","cross_cats_sorted":["physics.flu-dyn"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.soft","submitted_at":"2009-12-03T14:12:27Z","title_canon_sha256":"44bd21ae41bdd5e49c6db061f57757832777f4091b3ac44ffa313a96081ff843"},"schema_version":"1.0","source":{"id":"0912.0661","kind":"arxiv","version":2}},"canonical_sha256":"f527a7bb6267c410e4f7b4536bc6351e8c8b4e666bd14dcf83571fbf21d22db6","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f527a7bb6267c410e4f7b4536bc6351e8c8b4e666bd14dcf83571fbf21d22db6","first_computed_at":"2026-05-18T02:10:34.259041Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:10:34.259041Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Vn8RY6tBfyFK/6lW6RIc8h9LfN9lXDNhIHrobI4EX8t7KnfNDYIRtL/4HbQ5zDPNSy11OCEjELhoLmH0z5RBDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:10:34.259639Z","signed_message":"canonical_sha256_bytes"},"source_id":"0912.0661","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:185df82ea3a1209ca38c4083da4def29b6245c8e0745048afa48ffae0f1d7e28","sha256:e7bc895d51c2bf7455973bd2c09c68f9272ac7be760ba44f36c1b27e887248ab"],"state_sha256":"b1178281658f564a19d244dc80ae128c1e3b850e222d8d8a39612ccd676f7486"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"fhyQ6lo0IW52exi0Wsi0Lh3F6Ivgp/IF7WsszYHbQtpvkw2sbGajiHrKhBFSuyRmeBm8nJjqKH685QuDt63sDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-31T21:06:33.158112Z","bundle_sha256":"ef4c05a6d132f86b962e0a26bd016ffee20a9af3a32e89faef6fb80c731b15a0"}}