{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:AL4AH7UQ2BTMWQMB7PC7UBNO6W","short_pith_number":"pith:AL4AH7UQ","schema_version":"1.0","canonical_sha256":"02f803fe90d066cb4181fbc5fa05aef585aef35e43c8c7081a5b9ba2da0c2ca3","source":{"kind":"arxiv","id":"1703.02807","version":1},"attestation_state":"computed","paper":{"title":"From Gaussian estimates for nonlinear evolution equations to the long time behavior of branching processes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.PR"],"primary_cat":"math.AP","authors_text":"J. D. Rossi, L. Beznea, L. I. Ignat","submitted_at":"2017-03-08T12:20:07Z","abstract_excerpt":"We study solutions to the evolution equation $u_t=\\Delta u-u +\\sum_{k\\geqslant 1}q_ku^k$, $t>0$, in $\\mathbf{R}^d$. Here the coefficients $q_k\\geqslant 0$ verify $ \\sum_{k\\geqslant 1}q_k=1< \\sum_{k\\geqslant 1}kq_k<\\infty$. First, we deal with existence, uniqueness, and the asymptotic behavior of the solutions as $t\\to +\\infty$. We then deduce results on the long time behavior of the associated branching process, with state space the set of all finite configurations of $\\mathbf{R}^d$, under the assumption that $\\sum_{k\\geq 1} k^2q_k<\\infty$. It turns out that the distribution of the branching p"},"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":"1703.02807","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-03-08T12:20:07Z","cross_cats_sorted":["math.PR"],"title_canon_sha256":"11ed43f39f95706b87a658b324fbbf74cf96f52d6247d97f2cfc49649f12c048","abstract_canon_sha256":"636c7fb66adbfc53bfe899783b3dcc70b493f597b3dc495a4690eff619d3d0bf"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:49:05.571886Z","signature_b64":"32ZSdL+1nqBfbDI8Vo+933FN3g+pQN/xmfMgA4zZh+3EQZEhjYop4WzCv3YV6KEY4g0N1Og1iYC8PXI+xBrkAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"02f803fe90d066cb4181fbc5fa05aef585aef35e43c8c7081a5b9ba2da0c2ca3","last_reissued_at":"2026-05-18T00:49:05.571415Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:49:05.571415Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"From Gaussian estimates for nonlinear evolution equations to the long time behavior of branching processes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.PR"],"primary_cat":"math.AP","authors_text":"J. D. Rossi, L. Beznea, L. I. Ignat","submitted_at":"2017-03-08T12:20:07Z","abstract_excerpt":"We study solutions to the evolution equation $u_t=\\Delta u-u +\\sum_{k\\geqslant 1}q_ku^k$, $t>0$, in $\\mathbf{R}^d$. Here the coefficients $q_k\\geqslant 0$ verify $ \\sum_{k\\geqslant 1}q_k=1< \\sum_{k\\geqslant 1}kq_k<\\infty$. First, we deal with existence, uniqueness, and the asymptotic behavior of the solutions as $t\\to +\\infty$. We then deduce results on the long time behavior of the associated branching process, with state space the set of all finite configurations of $\\mathbf{R}^d$, under the assumption that $\\sum_{k\\geq 1} k^2q_k<\\infty$. It turns out that the distribution of the branching p"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1703.02807","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":"1703.02807","created_at":"2026-05-18T00:49:05.571485+00:00"},{"alias_kind":"arxiv_version","alias_value":"1703.02807v1","created_at":"2026-05-18T00:49:05.571485+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1703.02807","created_at":"2026-05-18T00:49:05.571485+00:00"},{"alias_kind":"pith_short_12","alias_value":"AL4AH7UQ2BTM","created_at":"2026-05-18T12:31:05.417338+00:00"},{"alias_kind":"pith_short_16","alias_value":"AL4AH7UQ2BTMWQMB","created_at":"2026-05-18T12:31:05.417338+00:00"},{"alias_kind":"pith_short_8","alias_value":"AL4AH7UQ","created_at":"2026-05-18T12:31:05.417338+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/AL4AH7UQ2BTMWQMB7PC7UBNO6W","json":"https://pith.science/pith/AL4AH7UQ2BTMWQMB7PC7UBNO6W.json","graph_json":"https://pith.science/api/pith-number/AL4AH7UQ2BTMWQMB7PC7UBNO6W/graph.json","events_json":"https://pith.science/api/pith-number/AL4AH7UQ2BTMWQMB7PC7UBNO6W/events.json","paper":"https://pith.science/paper/AL4AH7UQ"},"agent_actions":{"view_html":"https://pith.science/pith/AL4AH7UQ2BTMWQMB7PC7UBNO6W","download_json":"https://pith.science/pith/AL4AH7UQ2BTMWQMB7PC7UBNO6W.json","view_paper":"https://pith.science/paper/AL4AH7UQ","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1703.02807&json=true","fetch_graph":"https://pith.science/api/pith-number/AL4AH7UQ2BTMWQMB7PC7UBNO6W/graph.json","fetch_events":"https://pith.science/api/pith-number/AL4AH7UQ2BTMWQMB7PC7UBNO6W/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/AL4AH7UQ2BTMWQMB7PC7UBNO6W/action/timestamp_anchor","attest_storage":"https://pith.science/pith/AL4AH7UQ2BTMWQMB7PC7UBNO6W/action/storage_attestation","attest_author":"https://pith.science/pith/AL4AH7UQ2BTMWQMB7PC7UBNO6W/action/author_attestation","sign_citation":"https://pith.science/pith/AL4AH7UQ2BTMWQMB7PC7UBNO6W/action/citation_signature","submit_replication":"https://pith.science/pith/AL4AH7UQ2BTMWQMB7PC7UBNO6W/action/replication_record"}},"created_at":"2026-05-18T00:49:05.571485+00:00","updated_at":"2026-05-18T00:49:05.571485+00:00"}