{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:QC33IQKERP3SDZMQNOP5RSLFM2","short_pith_number":"pith:QC33IQKE","schema_version":"1.0","canonical_sha256":"80b7b441448bf721e5906b9fd8c96566b7c9de6fc170a603ee1b60357e16033c","source":{"kind":"arxiv","id":"1707.00553","version":1},"attestation_state":"computed","paper":{"title":"Stochastic homogenization for functionals with anisotropic rescaling and non-coercive Hamilton-Jacobi equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Claudio Marchi, Federica Dragoni, Nicolas Dirr, Paola Mannucci","submitted_at":"2017-07-03T14:01:12Z","abstract_excerpt":"We study the stochastic homogenization for a Cauchy problem for a first-order Hamilton-Jacobi equation whose operator is not coercive w.r.t. the gradient variable. We look at Hamiltonians like $H(x,\\sigma(x)p,\\omega)$ where $\\sigma(x)$ is a matrix associated to a Carnot group. The rescaling considered is consistent with the underlying Carnot group structure, thus anisotropic. We will prove that under suitable assumptions for the Hamiltonian, the solutions of the $\\varepsilon$-problem converge to a deterministic function which can be characterized as the unique (viscosity) solution of a suitabl"},"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":"1707.00553","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-07-03T14:01:12Z","cross_cats_sorted":[],"title_canon_sha256":"225c135281c371a1b8a709c861ea3ec4ad9d05f0a8996a31b86e63ce710a7026","abstract_canon_sha256":"32fb196266a3d5a8b8f0d2f0f51dcbb12fb579c88b2628e39c9fc0f9c8ddff12"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:41:03.031362Z","signature_b64":"Giu0/DN0IAEf+U4QmXYj15bIzaiug/brLuiPuW2nOOPkDvdZGd2VIJQF7APfLfsigBR6Vknk/Td8zN0kx/5SCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"80b7b441448bf721e5906b9fd8c96566b7c9de6fc170a603ee1b60357e16033c","last_reissued_at":"2026-05-18T00:41:03.030666Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:41:03.030666Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Stochastic homogenization for functionals with anisotropic rescaling and non-coercive Hamilton-Jacobi equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Claudio Marchi, Federica Dragoni, Nicolas Dirr, Paola Mannucci","submitted_at":"2017-07-03T14:01:12Z","abstract_excerpt":"We study the stochastic homogenization for a Cauchy problem for a first-order Hamilton-Jacobi equation whose operator is not coercive w.r.t. the gradient variable. We look at Hamiltonians like $H(x,\\sigma(x)p,\\omega)$ where $\\sigma(x)$ is a matrix associated to a Carnot group. The rescaling considered is consistent with the underlying Carnot group structure, thus anisotropic. We will prove that under suitable assumptions for the Hamiltonian, the solutions of the $\\varepsilon$-problem converge to a deterministic function which can be characterized as the unique (viscosity) solution of a suitabl"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1707.00553","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":"1707.00553","created_at":"2026-05-18T00:41:03.030779+00:00"},{"alias_kind":"arxiv_version","alias_value":"1707.00553v1","created_at":"2026-05-18T00:41:03.030779+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1707.00553","created_at":"2026-05-18T00:41:03.030779+00:00"},{"alias_kind":"pith_short_12","alias_value":"QC33IQKERP3S","created_at":"2026-05-18T12:31:37.085036+00:00"},{"alias_kind":"pith_short_16","alias_value":"QC33IQKERP3SDZMQ","created_at":"2026-05-18T12:31:37.085036+00:00"},{"alias_kind":"pith_short_8","alias_value":"QC33IQKE","created_at":"2026-05-18T12:31:37.085036+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/QC33IQKERP3SDZMQNOP5RSLFM2","json":"https://pith.science/pith/QC33IQKERP3SDZMQNOP5RSLFM2.json","graph_json":"https://pith.science/api/pith-number/QC33IQKERP3SDZMQNOP5RSLFM2/graph.json","events_json":"https://pith.science/api/pith-number/QC33IQKERP3SDZMQNOP5RSLFM2/events.json","paper":"https://pith.science/paper/QC33IQKE"},"agent_actions":{"view_html":"https://pith.science/pith/QC33IQKERP3SDZMQNOP5RSLFM2","download_json":"https://pith.science/pith/QC33IQKERP3SDZMQNOP5RSLFM2.json","view_paper":"https://pith.science/paper/QC33IQKE","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1707.00553&json=true","fetch_graph":"https://pith.science/api/pith-number/QC33IQKERP3SDZMQNOP5RSLFM2/graph.json","fetch_events":"https://pith.science/api/pith-number/QC33IQKERP3SDZMQNOP5RSLFM2/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/QC33IQKERP3SDZMQNOP5RSLFM2/action/timestamp_anchor","attest_storage":"https://pith.science/pith/QC33IQKERP3SDZMQNOP5RSLFM2/action/storage_attestation","attest_author":"https://pith.science/pith/QC33IQKERP3SDZMQNOP5RSLFM2/action/author_attestation","sign_citation":"https://pith.science/pith/QC33IQKERP3SDZMQNOP5RSLFM2/action/citation_signature","submit_replication":"https://pith.science/pith/QC33IQKERP3SDZMQNOP5RSLFM2/action/replication_record"}},"created_at":"2026-05-18T00:41:03.030779+00:00","updated_at":"2026-05-18T00:41:03.030779+00:00"}