{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:ELTEPYSA6624BR5LOOZBW62C5T","short_pith_number":"pith:ELTEPYSA","canonical_record":{"source":{"id":"1212.4971","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2012-12-20T10:40:58Z","cross_cats_sorted":["math.MP","math.PR"],"title_canon_sha256":"6087e8cea4d1e6abe14938af4d4b25b163f2c946701dc13b1bf7fc899a1544fe","abstract_canon_sha256":"897d356e5fcfbdf5936ab648be9c81ffaf37653f7e594b2aed46e4fa3cc0be90"},"schema_version":"1.0"},"canonical_sha256":"22e647e240f7b5c0c7ab73b21b7b42ecc1c9e5b8389d40c9051d82adc93f99e8","source":{"kind":"arxiv","id":"1212.4971","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1212.4971","created_at":"2026-05-18T03:38:04Z"},{"alias_kind":"arxiv_version","alias_value":"1212.4971v1","created_at":"2026-05-18T03:38:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1212.4971","created_at":"2026-05-18T03:38:04Z"},{"alias_kind":"pith_short_12","alias_value":"ELTEPYSA6624","created_at":"2026-05-18T12:27:04Z"},{"alias_kind":"pith_short_16","alias_value":"ELTEPYSA6624BR5L","created_at":"2026-05-18T12:27:04Z"},{"alias_kind":"pith_short_8","alias_value":"ELTEPYSA","created_at":"2026-05-18T12:27:04Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:ELTEPYSA6624BR5LOOZBW62C5T","target":"record","payload":{"canonical_record":{"source":{"id":"1212.4971","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2012-12-20T10:40:58Z","cross_cats_sorted":["math.MP","math.PR"],"title_canon_sha256":"6087e8cea4d1e6abe14938af4d4b25b163f2c946701dc13b1bf7fc899a1544fe","abstract_canon_sha256":"897d356e5fcfbdf5936ab648be9c81ffaf37653f7e594b2aed46e4fa3cc0be90"},"schema_version":"1.0"},"canonical_sha256":"22e647e240f7b5c0c7ab73b21b7b42ecc1c9e5b8389d40c9051d82adc93f99e8","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:38:04.197797Z","signature_b64":"ChwZtwrqPoQvLlhfYd13QEzH8iYEI9hEBSgPGHixngggp+ETpmHq0dT/WhaJsBhjzdbaBdNDId0BadPY6j38Dg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"22e647e240f7b5c0c7ab73b21b7b42ecc1c9e5b8389d40c9051d82adc93f99e8","last_reissued_at":"2026-05-18T03:38:04.197211Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:38:04.197211Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1212.4971","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:38:04Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"yXgvD8y9T8jwLjVlvwMtkchY+6JCXYOfjxDMV4QxaOpUfbAf2ET4ORlgU4sDaHoYXBYMrge6+UatbNhoaAA+Cg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T23:46:30.307595Z"},"content_sha256":"dc9efa13778b3e6347d40ba56b275f8a3e4080b9106c993b970ba3120417eefe","schema_version":"1.0","event_id":"sha256:dc9efa13778b3e6347d40ba56b275f8a3e4080b9106c993b970ba3120417eefe"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:ELTEPYSA6624BR5LOOZBW62C5T","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Asymptotic of grazing collisions for the spatially homogeneous Boltzmann equation for soft and Coulomb potentials","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP","math.PR"],"primary_cat":"math-ph","authors_text":"David Godinho","submitted_at":"2012-12-20T10:40:58Z","abstract_excerpt":"We give an explicit bound for the Wasserstein distance with quadratic cost between the solutions of Boltzmann's and Landau's equations in the case of soft and Coulomb potentials. This gives an explicit rate of convergence for the grazing collisions limit. Our result is local in time for very soft and Coulomb potentials and global in time for moderately soft potentials."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1212.4971","kind":"arxiv","version":1},"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":"2026-05-18T03:38:04Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+zBnKqD0Ze869sMyarLzzJMgOef8mOS/Xm9gTejEFA5fvXGsSYu8KE9spIKJIXtxZXZ7MXQTEMogV2L13J7eAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T23:46:30.307954Z"},"content_sha256":"3c790d11844047de4a9c917ddda6aaf0947268b9938d77762ed3aa55ca754efb","schema_version":"1.0","event_id":"sha256:3c790d11844047de4a9c917ddda6aaf0947268b9938d77762ed3aa55ca754efb"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/ELTEPYSA6624BR5LOOZBW62C5T/bundle.json","state_url":"https://pith.science/pith/ELTEPYSA6624BR5LOOZBW62C5T/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/ELTEPYSA6624BR5LOOZBW62C5T/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":"2026-05-27T23:46:30Z","links":{"resolver":"https://pith.science/pith/ELTEPYSA6624BR5LOOZBW62C5T","bundle":"https://pith.science/pith/ELTEPYSA6624BR5LOOZBW62C5T/bundle.json","state":"https://pith.science/pith/ELTEPYSA6624BR5LOOZBW62C5T/state.json","well_known_bundle":"https://pith.science/.well-known/pith/ELTEPYSA6624BR5LOOZBW62C5T/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:ELTEPYSA6624BR5LOOZBW62C5T","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":"897d356e5fcfbdf5936ab648be9c81ffaf37653f7e594b2aed46e4fa3cc0be90","cross_cats_sorted":["math.MP","math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2012-12-20T10:40:58Z","title_canon_sha256":"6087e8cea4d1e6abe14938af4d4b25b163f2c946701dc13b1bf7fc899a1544fe"},"schema_version":"1.0","source":{"id":"1212.4971","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1212.4971","created_at":"2026-05-18T03:38:04Z"},{"alias_kind":"arxiv_version","alias_value":"1212.4971v1","created_at":"2026-05-18T03:38:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1212.4971","created_at":"2026-05-18T03:38:04Z"},{"alias_kind":"pith_short_12","alias_value":"ELTEPYSA6624","created_at":"2026-05-18T12:27:04Z"},{"alias_kind":"pith_short_16","alias_value":"ELTEPYSA6624BR5L","created_at":"2026-05-18T12:27:04Z"},{"alias_kind":"pith_short_8","alias_value":"ELTEPYSA","created_at":"2026-05-18T12:27:04Z"}],"graph_snapshots":[{"event_id":"sha256:3c790d11844047de4a9c917ddda6aaf0947268b9938d77762ed3aa55ca754efb","target":"graph","created_at":"2026-05-18T03:38:04Z","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 give an explicit bound for the Wasserstein distance with quadratic cost between the solutions of Boltzmann's and Landau's equations in the case of soft and Coulomb potentials. This gives an explicit rate of convergence for the grazing collisions limit. Our result is local in time for very soft and Coulomb potentials and global in time for moderately soft potentials.","authors_text":"David Godinho","cross_cats":["math.MP","math.PR"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2012-12-20T10:40:58Z","title":"Asymptotic of grazing collisions for the spatially homogeneous Boltzmann equation for soft and Coulomb potentials"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1212.4971","kind":"arxiv","version":1},"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:dc9efa13778b3e6347d40ba56b275f8a3e4080b9106c993b970ba3120417eefe","target":"record","created_at":"2026-05-18T03:38:04Z","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":"897d356e5fcfbdf5936ab648be9c81ffaf37653f7e594b2aed46e4fa3cc0be90","cross_cats_sorted":["math.MP","math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2012-12-20T10:40:58Z","title_canon_sha256":"6087e8cea4d1e6abe14938af4d4b25b163f2c946701dc13b1bf7fc899a1544fe"},"schema_version":"1.0","source":{"id":"1212.4971","kind":"arxiv","version":1}},"canonical_sha256":"22e647e240f7b5c0c7ab73b21b7b42ecc1c9e5b8389d40c9051d82adc93f99e8","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"22e647e240f7b5c0c7ab73b21b7b42ecc1c9e5b8389d40c9051d82adc93f99e8","first_computed_at":"2026-05-18T03:38:04.197211Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:38:04.197211Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ChwZtwrqPoQvLlhfYd13QEzH8iYEI9hEBSgPGHixngggp+ETpmHq0dT/WhaJsBhjzdbaBdNDId0BadPY6j38Dg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:38:04.197797Z","signed_message":"canonical_sha256_bytes"},"source_id":"1212.4971","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:dc9efa13778b3e6347d40ba56b275f8a3e4080b9106c993b970ba3120417eefe","sha256:3c790d11844047de4a9c917ddda6aaf0947268b9938d77762ed3aa55ca754efb"],"state_sha256":"8b051cd67e44dbacaacc296955310cbe4d4af06c1a17eb875b156a09df3bebb1"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"J68THjVsG0uvhKyCg/jThyejzHWkoi+ty2b5icjZCbf2+2OR25S9sUgA3Mq9uhudQ83uq1R+gCurEJOLXDO5Bg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-27T23:46:30.310265Z","bundle_sha256":"485bdef8f0940095f331d7ba64fa9d02be43b523acfa48001d6927486c21df09"}}