{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:IIPFQ4LYENC4YXOSETYMNHOMKF","short_pith_number":"pith:IIPFQ4LY","canonical_record":{"source":{"id":"1205.3690","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2012-05-16T14:43:48Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"2507184e6adb359fc7459a094f768c4eff7d685b2212074e4946f1dfc1f44ecb","abstract_canon_sha256":"87e7a36442e77d25adf07e08f38644ebe814eeb065c320b0a382c74a539c0287"},"schema_version":"1.0"},"canonical_sha256":"421e5871782345cc5dd224f0c69dcc51703217cbf5f925b2f2a3fa6faeb59138","source":{"kind":"arxiv","id":"1205.3690","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1205.3690","created_at":"2026-05-18T03:42:44Z"},{"alias_kind":"arxiv_version","alias_value":"1205.3690v2","created_at":"2026-05-18T03:42:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1205.3690","created_at":"2026-05-18T03:42:44Z"},{"alias_kind":"pith_short_12","alias_value":"IIPFQ4LYENC4","created_at":"2026-05-18T12:27:09Z"},{"alias_kind":"pith_short_16","alias_value":"IIPFQ4LYENC4YXOS","created_at":"2026-05-18T12:27:09Z"},{"alias_kind":"pith_short_8","alias_value":"IIPFQ4LY","created_at":"2026-05-18T12:27:09Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:IIPFQ4LYENC4YXOSETYMNHOMKF","target":"record","payload":{"canonical_record":{"source":{"id":"1205.3690","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2012-05-16T14:43:48Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"2507184e6adb359fc7459a094f768c4eff7d685b2212074e4946f1dfc1f44ecb","abstract_canon_sha256":"87e7a36442e77d25adf07e08f38644ebe814eeb065c320b0a382c74a539c0287"},"schema_version":"1.0"},"canonical_sha256":"421e5871782345cc5dd224f0c69dcc51703217cbf5f925b2f2a3fa6faeb59138","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:42:44.333056Z","signature_b64":"fL7IxfYAqOFICRutPVp3CTB4J4dgp2S5pzMSVkSz3yohUz42oWYNeVPOUoPCNljmsH/0tHj3DVscgHrkEkOqBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"421e5871782345cc5dd224f0c69dcc51703217cbf5f925b2f2a3fa6faeb59138","last_reissued_at":"2026-05-18T03:42:44.332486Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:42:44.332486Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1205.3690","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":"2026-05-18T03:42:44Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"CfbsebhQhZHMSo90fcxG4Ve3qBHKcX8v96e6Pa6p30SMgT8QpYEiPMgmo/lSz3MGTXaTLqk9uH1R9zTZ5kF2AQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-27T07:18:14.964915Z"},"content_sha256":"9c28a22f2e1d749b4bc2d07fc06055658c8d3887ad88dc165ba575a91973d152","schema_version":"1.0","event_id":"sha256:9c28a22f2e1d749b4bc2d07fc06055658c8d3887ad88dc165ba575a91973d152"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:IIPFQ4LYENC4YXOSETYMNHOMKF","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Speed of convergence to equilibrium in Wasserstein metrics for Kac-s like kinetic equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.PR","authors_text":"Eleonora Perversi, Federico Bassetti","submitted_at":"2012-05-16T14:43:48Z","abstract_excerpt":"This work deals with a class of one-dimensional measure-valued kinetic equations, which constitute extensions of the Kac caricature. It is known that if the initial datum belongs to the domain of normal attraction of an \\alpha-stable law, the solution of the equation converges weakly to a suitable scale mixture of centered \\alpha-stable laws. In this paper we present explicit exponential rates for the convergence to equilibrium in Kantorovich-Wasserstein distances of order p>\\alpha, under the natural assumption that the distance between the initial datum and the limit distribution is finite. F"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1205.3690","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":"2026-05-18T03:42:44Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"gEZjds6A/OkYFMGRyyLytDy9hFAsarNE/X7i/Uac/573JZDzot7QrWZrjDiW8gqqBMr3SgxRmDrjIYlisMmGDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-27T07:18:14.965263Z"},"content_sha256":"f2327fb49d5cd645ecd9f4e4d40748206d2c72dc92096d878c33a42439850b72","schema_version":"1.0","event_id":"sha256:f2327fb49d5cd645ecd9f4e4d40748206d2c72dc92096d878c33a42439850b72"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/IIPFQ4LYENC4YXOSETYMNHOMKF/bundle.json","state_url":"https://pith.science/pith/IIPFQ4LYENC4YXOSETYMNHOMKF/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/IIPFQ4LYENC4YXOSETYMNHOMKF/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":"2026-06-27T07:18:14Z","links":{"resolver":"https://pith.science/pith/IIPFQ4LYENC4YXOSETYMNHOMKF","bundle":"https://pith.science/pith/IIPFQ4LYENC4YXOSETYMNHOMKF/bundle.json","state":"https://pith.science/pith/IIPFQ4LYENC4YXOSETYMNHOMKF/state.json","well_known_bundle":"https://pith.science/.well-known/pith/IIPFQ4LYENC4YXOSETYMNHOMKF/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:IIPFQ4LYENC4YXOSETYMNHOMKF","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":"87e7a36442e77d25adf07e08f38644ebe814eeb065c320b0a382c74a539c0287","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2012-05-16T14:43:48Z","title_canon_sha256":"2507184e6adb359fc7459a094f768c4eff7d685b2212074e4946f1dfc1f44ecb"},"schema_version":"1.0","source":{"id":"1205.3690","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1205.3690","created_at":"2026-05-18T03:42:44Z"},{"alias_kind":"arxiv_version","alias_value":"1205.3690v2","created_at":"2026-05-18T03:42:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1205.3690","created_at":"2026-05-18T03:42:44Z"},{"alias_kind":"pith_short_12","alias_value":"IIPFQ4LYENC4","created_at":"2026-05-18T12:27:09Z"},{"alias_kind":"pith_short_16","alias_value":"IIPFQ4LYENC4YXOS","created_at":"2026-05-18T12:27:09Z"},{"alias_kind":"pith_short_8","alias_value":"IIPFQ4LY","created_at":"2026-05-18T12:27:09Z"}],"graph_snapshots":[{"event_id":"sha256:f2327fb49d5cd645ecd9f4e4d40748206d2c72dc92096d878c33a42439850b72","target":"graph","created_at":"2026-05-18T03:42:44Z","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":"This work deals with a class of one-dimensional measure-valued kinetic equations, which constitute extensions of the Kac caricature. It is known that if the initial datum belongs to the domain of normal attraction of an \\alpha-stable law, the solution of the equation converges weakly to a suitable scale mixture of centered \\alpha-stable laws. In this paper we present explicit exponential rates for the convergence to equilibrium in Kantorovich-Wasserstein distances of order p>\\alpha, under the natural assumption that the distance between the initial datum and the limit distribution is finite. F","authors_text":"Eleonora Perversi, Federico Bassetti","cross_cats":["math-ph","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2012-05-16T14:43:48Z","title":"Speed of convergence to equilibrium in Wasserstein metrics for Kac-s like kinetic equations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1205.3690","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":"sha256:9c28a22f2e1d749b4bc2d07fc06055658c8d3887ad88dc165ba575a91973d152","target":"record","created_at":"2026-05-18T03:42:44Z","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":"87e7a36442e77d25adf07e08f38644ebe814eeb065c320b0a382c74a539c0287","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2012-05-16T14:43:48Z","title_canon_sha256":"2507184e6adb359fc7459a094f768c4eff7d685b2212074e4946f1dfc1f44ecb"},"schema_version":"1.0","source":{"id":"1205.3690","kind":"arxiv","version":2}},"canonical_sha256":"421e5871782345cc5dd224f0c69dcc51703217cbf5f925b2f2a3fa6faeb59138","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"421e5871782345cc5dd224f0c69dcc51703217cbf5f925b2f2a3fa6faeb59138","first_computed_at":"2026-05-18T03:42:44.332486Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:42:44.332486Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"fL7IxfYAqOFICRutPVp3CTB4J4dgp2S5pzMSVkSz3yohUz42oWYNeVPOUoPCNljmsH/0tHj3DVscgHrkEkOqBg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:42:44.333056Z","signed_message":"canonical_sha256_bytes"},"source_id":"1205.3690","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9c28a22f2e1d749b4bc2d07fc06055658c8d3887ad88dc165ba575a91973d152","sha256:f2327fb49d5cd645ecd9f4e4d40748206d2c72dc92096d878c33a42439850b72"],"state_sha256":"cc56b3722aa3da75282c1710b9b7d8c2aae0fcd7dbacc4407ebd71150d4a6ec2"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"szQpIAdkDIGxDGzj3GidXTWARhcl3UEe0UBsMbWJGEI0/OlEd4iZ5WCqW6JYZTJe0CY+Y9zC6Cf5xvhiZ2m1Dw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-27T07:18:14.971668Z","bundle_sha256":"5bb8c2f02800ca622197cf4a7c7662761e9c8b0e9d5b6a811536eb88d49d49a4"}}