{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2012:UO7SG2BVJZIJXBJXWAYFPVFMXS","short_pith_number":"pith:UO7SG2BV","schema_version":"1.0","canonical_sha256":"a3bf2368354e509b8537b03057d4acbcb27a0984ef016b0f547487ca056f9a16","source":{"kind":"arxiv","id":"1209.3379","version":2},"attestation_state":"computed","paper":{"title":"Existence of self-similar profile for a kinetic annihilation model","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Bertrand Lods, V\\'eronique Bagland","submitted_at":"2012-09-15T09:19:42Z","abstract_excerpt":"We show the existence of a self-similar solution for a modified Boltzmann equation describing probabilistic ballistic annihilation. Such a model describes a system of hard-spheres such that, whenever two particles meet, they either annihilate with probability $\\alpha \\in (0,1)$ or they undergo an elastic collision with probability $1 - \\alpha$. For such a model, the number of particles, the linear momentum and the kinetic energy are not conserved. We show that, for $\\alpha$ smaller than some explicit threshold value $ \\alpha_*$, a self-similar solution exists."},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1209.3379","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2012-09-15T09:19:42Z","cross_cats_sorted":[],"title_canon_sha256":"8907e2041c15c38e10b110020ae3fe8c52afa3939546e9caaf0c2c51c86b4c40","abstract_canon_sha256":"547d386d20615b3b7db308e319614528df43f7b7abf22cda08befa8c593c6004"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:40:45.920669Z","signature_b64":"tz7mWdhuPlaK2Jcx9b1Nc7PvuVjMD+/ffXbrUMHuulgKLQuC//5yKUm3D7wJi55wO77rx9pIuRzgN3GbS0c4BQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a3bf2368354e509b8537b03057d4acbcb27a0984ef016b0f547487ca056f9a16","last_reissued_at":"2026-05-18T02:40:45.920180Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:40:45.920180Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Existence of self-similar profile for a kinetic annihilation model","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Bertrand Lods, V\\'eronique Bagland","submitted_at":"2012-09-15T09:19:42Z","abstract_excerpt":"We show the existence of a self-similar solution for a modified Boltzmann equation describing probabilistic ballistic annihilation. Such a model describes a system of hard-spheres such that, whenever two particles meet, they either annihilate with probability $\\alpha \\in (0,1)$ or they undergo an elastic collision with probability $1 - \\alpha$. For such a model, the number of particles, the linear momentum and the kinetic energy are not conserved. We show that, for $\\alpha$ smaller than some explicit threshold value $ \\alpha_*$, a self-similar solution exists."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1209.3379","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1209.3379","created_at":"2026-05-18T02:40:45.920253+00:00"},{"alias_kind":"arxiv_version","alias_value":"1209.3379v2","created_at":"2026-05-18T02:40:45.920253+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1209.3379","created_at":"2026-05-18T02:40:45.920253+00:00"},{"alias_kind":"pith_short_12","alias_value":"UO7SG2BVJZIJ","created_at":"2026-05-18T12:27:23.164592+00:00"},{"alias_kind":"pith_short_16","alias_value":"UO7SG2BVJZIJXBJX","created_at":"2026-05-18T12:27:23.164592+00:00"},{"alias_kind":"pith_short_8","alias_value":"UO7SG2BV","created_at":"2026-05-18T12:27:23.164592+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/UO7SG2BVJZIJXBJXWAYFPVFMXS","json":"https://pith.science/pith/UO7SG2BVJZIJXBJXWAYFPVFMXS.json","graph_json":"https://pith.science/api/pith-number/UO7SG2BVJZIJXBJXWAYFPVFMXS/graph.json","events_json":"https://pith.science/api/pith-number/UO7SG2BVJZIJXBJXWAYFPVFMXS/events.json","paper":"https://pith.science/paper/UO7SG2BV"},"agent_actions":{"view_html":"https://pith.science/pith/UO7SG2BVJZIJXBJXWAYFPVFMXS","download_json":"https://pith.science/pith/UO7SG2BVJZIJXBJXWAYFPVFMXS.json","view_paper":"https://pith.science/paper/UO7SG2BV","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1209.3379&json=true","fetch_graph":"https://pith.science/api/pith-number/UO7SG2BVJZIJXBJXWAYFPVFMXS/graph.json","fetch_events":"https://pith.science/api/pith-number/UO7SG2BVJZIJXBJXWAYFPVFMXS/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/UO7SG2BVJZIJXBJXWAYFPVFMXS/action/timestamp_anchor","attest_storage":"https://pith.science/pith/UO7SG2BVJZIJXBJXWAYFPVFMXS/action/storage_attestation","attest_author":"https://pith.science/pith/UO7SG2BVJZIJXBJXWAYFPVFMXS/action/author_attestation","sign_citation":"https://pith.science/pith/UO7SG2BVJZIJXBJXWAYFPVFMXS/action/citation_signature","submit_replication":"https://pith.science/pith/UO7SG2BVJZIJXBJXWAYFPVFMXS/action/replication_record"}},"created_at":"2026-05-18T02:40:45.920253+00:00","updated_at":"2026-05-18T02:40:45.920253+00:00"}