{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:N5Y554CBHFSD5SOFHDEPLHMAEK","short_pith_number":"pith:N5Y554CB","schema_version":"1.0","canonical_sha256":"6f71def04139643ec9c538c8f59d8022a11f14648783de87ada4aad1a28e3397","source":{"kind":"arxiv","id":"1811.08350","version":1},"attestation_state":"computed","paper":{"title":"Stability of the spectral gap for the Boltzmann multi-species operator linearized around non-equilibrium Maxwell distributions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP","math.MP"],"primary_cat":"math-ph","authors_text":"Andrea Bondesan, B\\'er\\'enice Grec, Laurent Boudin, Marc Briant","submitted_at":"2018-11-20T16:24:19Z","abstract_excerpt":"We consider the Boltzmann operator for mixtures with cutoff Maxwellian, hard potentials, or hard spheres collision kernels. In a perturbative regime around the global Maxwellian equilibrium, the linearized Boltzmann multi-species operator $\\mathbf{L}$ is known to possess an explicit spectral gap $\\lambda_{\\mathbf{L}}$, in the global equilibrium weighted $L^2$ space. We study a new operator $\\mathbf{L^\\varepsilon}$ obtained by linearizing the Boltzmann operator for mixtures around local Maxwellian distributions, where all the species evolve with different small macroscopic velocities of order $"},"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":"1811.08350","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2018-11-20T16:24:19Z","cross_cats_sorted":["math.AP","math.MP"],"title_canon_sha256":"ca36362918080678b843500f8feeb36623837b5c8260ffd3c99cafcddf74ae17","abstract_canon_sha256":"3f5dce4adc0b2e31df73895f821fd7636da1331f13672a6f0424046f87fd1850"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:00:14.291642Z","signature_b64":"zNz5rqpWr5n02PV7kK+7t7C2HBYTxaAGLpHJTvA3sde69JuCYq2KjLmyHN3ezdtlpHYM1P3ppye9IENKSi19DA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6f71def04139643ec9c538c8f59d8022a11f14648783de87ada4aad1a28e3397","last_reissued_at":"2026-05-18T00:00:14.290975Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:00:14.290975Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Stability of the spectral gap for the Boltzmann multi-species operator linearized around non-equilibrium Maxwell distributions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP","math.MP"],"primary_cat":"math-ph","authors_text":"Andrea Bondesan, B\\'er\\'enice Grec, Laurent Boudin, Marc Briant","submitted_at":"2018-11-20T16:24:19Z","abstract_excerpt":"We consider the Boltzmann operator for mixtures with cutoff Maxwellian, hard potentials, or hard spheres collision kernels. In a perturbative regime around the global Maxwellian equilibrium, the linearized Boltzmann multi-species operator $\\mathbf{L}$ is known to possess an explicit spectral gap $\\lambda_{\\mathbf{L}}$, in the global equilibrium weighted $L^2$ space. We study a new operator $\\mathbf{L^\\varepsilon}$ obtained by linearizing the Boltzmann operator for mixtures around local Maxwellian distributions, where all the species evolve with different small macroscopic velocities of order $"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1811.08350","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1811.08350","created_at":"2026-05-18T00:00:14.291072+00:00"},{"alias_kind":"arxiv_version","alias_value":"1811.08350v1","created_at":"2026-05-18T00:00:14.291072+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1811.08350","created_at":"2026-05-18T00:00:14.291072+00:00"},{"alias_kind":"pith_short_12","alias_value":"N5Y554CBHFSD","created_at":"2026-05-18T12:32:40.477152+00:00"},{"alias_kind":"pith_short_16","alias_value":"N5Y554CBHFSD5SOF","created_at":"2026-05-18T12:32:40.477152+00:00"},{"alias_kind":"pith_short_8","alias_value":"N5Y554CB","created_at":"2026-05-18T12:32:40.477152+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/N5Y554CBHFSD5SOFHDEPLHMAEK","json":"https://pith.science/pith/N5Y554CBHFSD5SOFHDEPLHMAEK.json","graph_json":"https://pith.science/api/pith-number/N5Y554CBHFSD5SOFHDEPLHMAEK/graph.json","events_json":"https://pith.science/api/pith-number/N5Y554CBHFSD5SOFHDEPLHMAEK/events.json","paper":"https://pith.science/paper/N5Y554CB"},"agent_actions":{"view_html":"https://pith.science/pith/N5Y554CBHFSD5SOFHDEPLHMAEK","download_json":"https://pith.science/pith/N5Y554CBHFSD5SOFHDEPLHMAEK.json","view_paper":"https://pith.science/paper/N5Y554CB","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1811.08350&json=true","fetch_graph":"https://pith.science/api/pith-number/N5Y554CBHFSD5SOFHDEPLHMAEK/graph.json","fetch_events":"https://pith.science/api/pith-number/N5Y554CBHFSD5SOFHDEPLHMAEK/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/N5Y554CBHFSD5SOFHDEPLHMAEK/action/timestamp_anchor","attest_storage":"https://pith.science/pith/N5Y554CBHFSD5SOFHDEPLHMAEK/action/storage_attestation","attest_author":"https://pith.science/pith/N5Y554CBHFSD5SOFHDEPLHMAEK/action/author_attestation","sign_citation":"https://pith.science/pith/N5Y554CBHFSD5SOFHDEPLHMAEK/action/citation_signature","submit_replication":"https://pith.science/pith/N5Y554CBHFSD5SOFHDEPLHMAEK/action/replication_record"}},"created_at":"2026-05-18T00:00:14.291072+00:00","updated_at":"2026-05-18T00:00:14.291072+00:00"}