{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:VQUGQAWNCXIBTVHYQUDCOSNAKV","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":"7a9e72d53f69a694c630bcb6e00dfae7e6e16e77d37285115208b1f0c334759c","cross_cats_sorted":["math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2017-05-15T14:58:17Z","title_canon_sha256":"00b0bc263d8d7a5dc02856cf3c55a1de687150448b538e4942eb04f532ed651b"},"schema_version":"1.0","source":{"id":"1705.05277","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1705.05277","created_at":"2026-05-18T00:44:30Z"},{"alias_kind":"arxiv_version","alias_value":"1705.05277v1","created_at":"2026-05-18T00:44:30Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1705.05277","created_at":"2026-05-18T00:44:30Z"},{"alias_kind":"pith_short_12","alias_value":"VQUGQAWNCXIB","created_at":"2026-05-18T12:31:49Z"},{"alias_kind":"pith_short_16","alias_value":"VQUGQAWNCXIBTVHY","created_at":"2026-05-18T12:31:49Z"},{"alias_kind":"pith_short_8","alias_value":"VQUGQAWN","created_at":"2026-05-18T12:31:49Z"}],"graph_snapshots":[{"event_id":"sha256:99676a68fafced3d1dc783cd21834917f066ec4e2be73427beb5597d55a3bdf1","target":"graph","created_at":"2026-05-18T00:44:30Z","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":"In this paper the problem is posed of the prescription of the so-called Boltzmann-Grad (BG) limit ($\\mathcal{L}_{BG}$) for the $N-$body system of smooth hard-spheres which undergo unary, binary as well as multiple elastic instantaneous collisions. The statistical description is couched in terms of the Master kinetic equation, i.e., the kinetic equation which realizes the axiomatic \"\\textit{ab initio}\" approach to the classical statistical mechanics of finite hard-sphere systems recently developed (Tessarotto \\textit{et al.}, 2013-2017). The issue addressed here concerns the prescription of the","authors_text":"A. Soranzo, C. Asci, C. Cremaschini, G. Tironi, M. Mond, M. Tessarotto","cross_cats":["math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2017-05-15T14:58:17Z","title":"On the Boltzmann-Grad limit of the Master Kinetic Equation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1705.05277","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:e382cbcff8fb4ba979c8bae5000d59b9b1e7e1fa3fedf53ef0915f4eea59f399","target":"record","created_at":"2026-05-18T00:44:30Z","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":"7a9e72d53f69a694c630bcb6e00dfae7e6e16e77d37285115208b1f0c334759c","cross_cats_sorted":["math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2017-05-15T14:58:17Z","title_canon_sha256":"00b0bc263d8d7a5dc02856cf3c55a1de687150448b538e4942eb04f532ed651b"},"schema_version":"1.0","source":{"id":"1705.05277","kind":"arxiv","version":1}},"canonical_sha256":"ac286802cd15d019d4f885062749a0555c8cc27fcd28ac6965bdc8139fc41cbc","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ac286802cd15d019d4f885062749a0555c8cc27fcd28ac6965bdc8139fc41cbc","first_computed_at":"2026-05-18T00:44:30.922675Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:44:30.922675Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"uab4CAPm1EjL2v/w6pTngDSFCmxMhIbB7Lw3W+juKgncrANUhFKU3C+dwCEanc9LFOAKi8gxpI9kwETyhq4EBw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:44:30.923196Z","signed_message":"canonical_sha256_bytes"},"source_id":"1705.05277","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e382cbcff8fb4ba979c8bae5000d59b9b1e7e1fa3fedf53ef0915f4eea59f399","sha256:99676a68fafced3d1dc783cd21834917f066ec4e2be73427beb5597d55a3bdf1"],"state_sha256":"db39fd40866e9535180d6093ab452fa6ae14e67165f1d269f9f6777ed60a3f69"}