{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:MWUPY5SZ3KBTEE2YPMWGXWSVEO","short_pith_number":"pith:MWUPY5SZ","canonical_record":{"source":{"id":"1306.1379","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-06-06T11:33:57Z","cross_cats_sorted":[],"title_canon_sha256":"bf0610e522221637ab78d0e68ecbee33daca86e9dcec384c339cf2f53f586705","abstract_canon_sha256":"5209f4fa4d2df251d7459b0956c8cea8203ea26e7463ce9311baaa68ffdd3505"},"schema_version":"1.0"},"canonical_sha256":"65a8fc7659da833213587b2c6bda552391f2e96b74d656eb3a1aa8266cf320d8","source":{"kind":"arxiv","id":"1306.1379","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1306.1379","created_at":"2026-05-18T01:49:32Z"},{"alias_kind":"arxiv_version","alias_value":"1306.1379v2","created_at":"2026-05-18T01:49:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1306.1379","created_at":"2026-05-18T01:49:32Z"},{"alias_kind":"pith_short_12","alias_value":"MWUPY5SZ3KBT","created_at":"2026-05-18T12:27:52Z"},{"alias_kind":"pith_short_16","alias_value":"MWUPY5SZ3KBTEE2Y","created_at":"2026-05-18T12:27:52Z"},{"alias_kind":"pith_short_8","alias_value":"MWUPY5SZ","created_at":"2026-05-18T12:27:52Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:MWUPY5SZ3KBTEE2YPMWGXWSVEO","target":"record","payload":{"canonical_record":{"source":{"id":"1306.1379","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-06-06T11:33:57Z","cross_cats_sorted":[],"title_canon_sha256":"bf0610e522221637ab78d0e68ecbee33daca86e9dcec384c339cf2f53f586705","abstract_canon_sha256":"5209f4fa4d2df251d7459b0956c8cea8203ea26e7463ce9311baaa68ffdd3505"},"schema_version":"1.0"},"canonical_sha256":"65a8fc7659da833213587b2c6bda552391f2e96b74d656eb3a1aa8266cf320d8","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:49:32.043779Z","signature_b64":"tElMfeVKRsC27FrRKrKek4KzU7Xv3aEXLme1xal41bnMws3vwlaJTbBEYsMQ8CbgT23GkEEGhqlk40xKeweCBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"65a8fc7659da833213587b2c6bda552391f2e96b74d656eb3a1aa8266cf320d8","last_reissued_at":"2026-05-18T01:49:32.043334Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:49:32.043334Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1306.1379","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":"2026-05-18T01:49:32Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"tSFeOMMavIR6QbH5PI2OA8BBFECxwEuPX/UaU+BIQx5FpMJiIXsXoNbw9R+rgjeWzu1Pkh2WtFN09N5ToqrpDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-20T10:48:46.834821Z"},"content_sha256":"8fccb0862042885fd2a2281caf076a59a8f840a36aa853367e739e7e44de57b2","schema_version":"1.0","event_id":"sha256:8fccb0862042885fd2a2281caf076a59a8f840a36aa853367e739e7e44de57b2"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:MWUPY5SZ3KBTEE2YPMWGXWSVEO","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Boltzmann Model for viscoelastic particles: asymptotic behavior, pointwise lower bounds and regularity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Bertrand Lods, Ricardo J. Alonso","submitted_at":"2013-06-06T11:33:57Z","abstract_excerpt":"We investigate the long time behavior of a system of viscoelastic particles modeled with the homogeneous Boltzmann equation. We prove the existence of a universal Maxwellian intermediate asymptotic state and explicit the rate of convergence towards it. Exponential lower pointwise bounds and propagation of regularity are also studied. These results can be seen as the generalization of several classical facts holding for the pseudo-Maxwellian and constant normal restitution models."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1306.1379","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":"2026-05-18T01:49:32Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"0yi3zipVoxCpPirOBPcNFG/RmHYwgzEswUtMBVcEQrEMkod95UxF4wrftPIx3g45OeendLPVMc5QzIR05lwhBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-20T10:48:46.835142Z"},"content_sha256":"54bf88bef5002b0f34bee63c8d790c824eee944d1d87cea7c10ea2b3d3aadb15","schema_version":"1.0","event_id":"sha256:54bf88bef5002b0f34bee63c8d790c824eee944d1d87cea7c10ea2b3d3aadb15"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/MWUPY5SZ3KBTEE2YPMWGXWSVEO/bundle.json","state_url":"https://pith.science/pith/MWUPY5SZ3KBTEE2YPMWGXWSVEO/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/MWUPY5SZ3KBTEE2YPMWGXWSVEO/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":"2026-06-20T10:48:46Z","links":{"resolver":"https://pith.science/pith/MWUPY5SZ3KBTEE2YPMWGXWSVEO","bundle":"https://pith.science/pith/MWUPY5SZ3KBTEE2YPMWGXWSVEO/bundle.json","state":"https://pith.science/pith/MWUPY5SZ3KBTEE2YPMWGXWSVEO/state.json","well_known_bundle":"https://pith.science/.well-known/pith/MWUPY5SZ3KBTEE2YPMWGXWSVEO/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:MWUPY5SZ3KBTEE2YPMWGXWSVEO","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":"5209f4fa4d2df251d7459b0956c8cea8203ea26e7463ce9311baaa68ffdd3505","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-06-06T11:33:57Z","title_canon_sha256":"bf0610e522221637ab78d0e68ecbee33daca86e9dcec384c339cf2f53f586705"},"schema_version":"1.0","source":{"id":"1306.1379","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1306.1379","created_at":"2026-05-18T01:49:32Z"},{"alias_kind":"arxiv_version","alias_value":"1306.1379v2","created_at":"2026-05-18T01:49:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1306.1379","created_at":"2026-05-18T01:49:32Z"},{"alias_kind":"pith_short_12","alias_value":"MWUPY5SZ3KBT","created_at":"2026-05-18T12:27:52Z"},{"alias_kind":"pith_short_16","alias_value":"MWUPY5SZ3KBTEE2Y","created_at":"2026-05-18T12:27:52Z"},{"alias_kind":"pith_short_8","alias_value":"MWUPY5SZ","created_at":"2026-05-18T12:27:52Z"}],"graph_snapshots":[{"event_id":"sha256:54bf88bef5002b0f34bee63c8d790c824eee944d1d87cea7c10ea2b3d3aadb15","target":"graph","created_at":"2026-05-18T01:49:32Z","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 investigate the long time behavior of a system of viscoelastic particles modeled with the homogeneous Boltzmann equation. We prove the existence of a universal Maxwellian intermediate asymptotic state and explicit the rate of convergence towards it. Exponential lower pointwise bounds and propagation of regularity are also studied. These results can be seen as the generalization of several classical facts holding for the pseudo-Maxwellian and constant normal restitution models.","authors_text":"Bertrand Lods, Ricardo J. Alonso","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-06-06T11:33:57Z","title":"Boltzmann Model for viscoelastic particles: asymptotic behavior, pointwise lower bounds and regularity"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1306.1379","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":"sha256:8fccb0862042885fd2a2281caf076a59a8f840a36aa853367e739e7e44de57b2","target":"record","created_at":"2026-05-18T01:49:32Z","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":"5209f4fa4d2df251d7459b0956c8cea8203ea26e7463ce9311baaa68ffdd3505","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-06-06T11:33:57Z","title_canon_sha256":"bf0610e522221637ab78d0e68ecbee33daca86e9dcec384c339cf2f53f586705"},"schema_version":"1.0","source":{"id":"1306.1379","kind":"arxiv","version":2}},"canonical_sha256":"65a8fc7659da833213587b2c6bda552391f2e96b74d656eb3a1aa8266cf320d8","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"65a8fc7659da833213587b2c6bda552391f2e96b74d656eb3a1aa8266cf320d8","first_computed_at":"2026-05-18T01:49:32.043334Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:49:32.043334Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"tElMfeVKRsC27FrRKrKek4KzU7Xv3aEXLme1xal41bnMws3vwlaJTbBEYsMQ8CbgT23GkEEGhqlk40xKeweCBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:49:32.043779Z","signed_message":"canonical_sha256_bytes"},"source_id":"1306.1379","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8fccb0862042885fd2a2281caf076a59a8f840a36aa853367e739e7e44de57b2","sha256:54bf88bef5002b0f34bee63c8d790c824eee944d1d87cea7c10ea2b3d3aadb15"],"state_sha256":"84d0bf789ee22781a59d8ff80504530f512028b11db6132b6992b3a847bb057c"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"8kWnmMApxhfV7pj9GrpS0VBOLQ4QcLD9R8wpcQRh9+Rb3oTNfD3Yhk/f9tR+mwU4mkemySY340wKGwt3TsRYAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-20T10:48:46.836916Z","bundle_sha256":"c595eb526ee12543d6922bc7e9d81eaf9501ede66f367f5fe4b3178ae16e008f"}}