{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2022:72S4BLBJWEWDIYW5FQTJWICATS","short_pith_number":"pith:72S4BLBJ","canonical_record":{"source":{"id":"2209.06342","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/publicdomain/zero/1.0/","primary_cat":"math.AP","submitted_at":"2022-09-13T23:10:26Z","cross_cats_sorted":[],"title_canon_sha256":"77b780bb08245e947b4c4f23460d15849f9aec16eb68da35b2414ac8b256d409","abstract_canon_sha256":"bb243f225af74c534a026362d13b8f282cde22a5d574ad44ee2a42028b29a31c"},"schema_version":"1.0"},"canonical_sha256":"fea5c0ac29b12c3462dd2c269b20409c8cccaa4f9dcdfbbbe929243fe5c8420c","source":{"kind":"arxiv","id":"2209.06342","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2209.06342","created_at":"2026-07-05T04:57:29Z"},{"alias_kind":"arxiv_version","alias_value":"2209.06342v1","created_at":"2026-07-05T04:57:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2209.06342","created_at":"2026-07-05T04:57:29Z"},{"alias_kind":"pith_short_12","alias_value":"72S4BLBJWEWD","created_at":"2026-07-05T04:57:29Z"},{"alias_kind":"pith_short_16","alias_value":"72S4BLBJWEWDIYW5","created_at":"2026-07-05T04:57:29Z"},{"alias_kind":"pith_short_8","alias_value":"72S4BLBJ","created_at":"2026-07-05T04:57:29Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2022:72S4BLBJWEWDIYW5FQTJWICATS","target":"record","payload":{"canonical_record":{"source":{"id":"2209.06342","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/publicdomain/zero/1.0/","primary_cat":"math.AP","submitted_at":"2022-09-13T23:10:26Z","cross_cats_sorted":[],"title_canon_sha256":"77b780bb08245e947b4c4f23460d15849f9aec16eb68da35b2414ac8b256d409","abstract_canon_sha256":"bb243f225af74c534a026362d13b8f282cde22a5d574ad44ee2a42028b29a31c"},"schema_version":"1.0"},"canonical_sha256":"fea5c0ac29b12c3462dd2c269b20409c8cccaa4f9dcdfbbbe929243fe5c8420c","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T04:57:29.540282Z","signature_b64":"Q3YANzUmct/l/1hIX5W5aYlBiqUwG8OkV6ynTgjx8tvnTPbyZseSmqWnyWbHKE0QXOZ2BLUI7BAgQyNqywAGAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"fea5c0ac29b12c3462dd2c269b20409c8cccaa4f9dcdfbbbe929243fe5c8420c","last_reissued_at":"2026-07-05T04:57:29.539906Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T04:57:29.539906Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2209.06342","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T04:57:29Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+Xnw/1E3OsacCjVEJgFzgS5anKe+aWJhwXw4M07Gsw3lEQmXeSCrSe8fjltcZxW6Ao+xTVa5v6gVkpf5NBy0Dw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-16T22:24:15.723731Z"},"content_sha256":"fbecd1e438525abec0207a7d3474130e2f5ce4ac5060d2cc8937347077a2404c","schema_version":"1.0","event_id":"sha256:fbecd1e438525abec0207a7d3474130e2f5ce4ac5060d2cc8937347077a2404c"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2022:72S4BLBJWEWDIYW5FQTJWICATS","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Stochastic homogenization of a porous-medium type equation","license":"http://creativecommons.org/publicdomain/zero/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Stefania Patrizi","submitted_at":"2022-09-13T23:10:26Z","abstract_excerpt":"We consider the homogenization problem for the stochastic porous-medium type equation $\\p_{t} u^\\epsilon =\\Delta f\\left(T\\left(\\frac{x}{\\ep}\\right)\\om,u^\\ep\\right)$, with a well-prepared initial datum, where $f(T(y)\\om,u)$ is a stationary process, increasing in $u$, on a given probability space $(\\Om, \\mathcal{F}, \\mu)$ endowed with an ergodic dynamical system $\\{T(y)\\,:\\,y\\in\\R^N\\}$. Differently from the previous literature \\cite{afs,fs}, here we do not assume $\\Om$ compact. We first show that the weak solution $u^\\ep$ satisfies a kinetic formulation of the equation, then we exploit the theor"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2209.06342","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2209.06342/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T04:57:29Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"m0i1HM2r71MT3EWTBumHubjvxudRZAhN1qV2y5NKBQ6JskGdZp63JicQB6jcnJxkT/Q14gcmuc/58KY5skk6Aw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-16T22:24:15.724229Z"},"content_sha256":"cea34e04f7bc47c453b5aba8513a5b6988d0e70ec544950236e839361aae0348","schema_version":"1.0","event_id":"sha256:cea34e04f7bc47c453b5aba8513a5b6988d0e70ec544950236e839361aae0348"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/72S4BLBJWEWDIYW5FQTJWICATS/bundle.json","state_url":"https://pith.science/pith/72S4BLBJWEWDIYW5FQTJWICATS/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/72S4BLBJWEWDIYW5FQTJWICATS/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-08-16T22:24:15Z","links":{"resolver":"https://pith.science/pith/72S4BLBJWEWDIYW5FQTJWICATS","bundle":"https://pith.science/pith/72S4BLBJWEWDIYW5FQTJWICATS/bundle.json","state":"https://pith.science/pith/72S4BLBJWEWDIYW5FQTJWICATS/state.json","well_known_bundle":"https://pith.science/.well-known/pith/72S4BLBJWEWDIYW5FQTJWICATS/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2022:72S4BLBJWEWDIYW5FQTJWICATS","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":"bb243f225af74c534a026362d13b8f282cde22a5d574ad44ee2a42028b29a31c","cross_cats_sorted":[],"license":"http://creativecommons.org/publicdomain/zero/1.0/","primary_cat":"math.AP","submitted_at":"2022-09-13T23:10:26Z","title_canon_sha256":"77b780bb08245e947b4c4f23460d15849f9aec16eb68da35b2414ac8b256d409"},"schema_version":"1.0","source":{"id":"2209.06342","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2209.06342","created_at":"2026-07-05T04:57:29Z"},{"alias_kind":"arxiv_version","alias_value":"2209.06342v1","created_at":"2026-07-05T04:57:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2209.06342","created_at":"2026-07-05T04:57:29Z"},{"alias_kind":"pith_short_12","alias_value":"72S4BLBJWEWD","created_at":"2026-07-05T04:57:29Z"},{"alias_kind":"pith_short_16","alias_value":"72S4BLBJWEWDIYW5","created_at":"2026-07-05T04:57:29Z"},{"alias_kind":"pith_short_8","alias_value":"72S4BLBJ","created_at":"2026-07-05T04:57:29Z"}],"graph_snapshots":[{"event_id":"sha256:cea34e04f7bc47c453b5aba8513a5b6988d0e70ec544950236e839361aae0348","target":"graph","created_at":"2026-07-05T04:57:29Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2209.06342/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We consider the homogenization problem for the stochastic porous-medium type equation $\\p_{t} u^\\epsilon =\\Delta f\\left(T\\left(\\frac{x}{\\ep}\\right)\\om,u^\\ep\\right)$, with a well-prepared initial datum, where $f(T(y)\\om,u)$ is a stationary process, increasing in $u$, on a given probability space $(\\Om, \\mathcal{F}, \\mu)$ endowed with an ergodic dynamical system $\\{T(y)\\,:\\,y\\in\\R^N\\}$. Differently from the previous literature \\cite{afs,fs}, here we do not assume $\\Om$ compact. We first show that the weak solution $u^\\ep$ satisfies a kinetic formulation of the equation, then we exploit the theor","authors_text":"Stefania Patrizi","cross_cats":[],"headline":"","license":"http://creativecommons.org/publicdomain/zero/1.0/","primary_cat":"math.AP","submitted_at":"2022-09-13T23:10:26Z","title":"Stochastic homogenization of a porous-medium type equation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2209.06342","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:fbecd1e438525abec0207a7d3474130e2f5ce4ac5060d2cc8937347077a2404c","target":"record","created_at":"2026-07-05T04:57:29Z","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":"bb243f225af74c534a026362d13b8f282cde22a5d574ad44ee2a42028b29a31c","cross_cats_sorted":[],"license":"http://creativecommons.org/publicdomain/zero/1.0/","primary_cat":"math.AP","submitted_at":"2022-09-13T23:10:26Z","title_canon_sha256":"77b780bb08245e947b4c4f23460d15849f9aec16eb68da35b2414ac8b256d409"},"schema_version":"1.0","source":{"id":"2209.06342","kind":"arxiv","version":1}},"canonical_sha256":"fea5c0ac29b12c3462dd2c269b20409c8cccaa4f9dcdfbbbe929243fe5c8420c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"fea5c0ac29b12c3462dd2c269b20409c8cccaa4f9dcdfbbbe929243fe5c8420c","first_computed_at":"2026-07-05T04:57:29.539906Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T04:57:29.539906Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Q3YANzUmct/l/1hIX5W5aYlBiqUwG8OkV6ynTgjx8tvnTPbyZseSmqWnyWbHKE0QXOZ2BLUI7BAgQyNqywAGAg==","signature_status":"signed_v1","signed_at":"2026-07-05T04:57:29.540282Z","signed_message":"canonical_sha256_bytes"},"source_id":"2209.06342","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:fbecd1e438525abec0207a7d3474130e2f5ce4ac5060d2cc8937347077a2404c","sha256:cea34e04f7bc47c453b5aba8513a5b6988d0e70ec544950236e839361aae0348"],"state_sha256":"ae49ee3adfa1c21c6ade19e9466ef94a8b7000e8edf54675843145c833f59b13"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"9EJRQGNP51ss+Ai+oFYrJvPdIvrtBW+bfADGf0UIfDmnZIUWaIOtXsnS+0i4Ue7MDqJ92V5QwEcot54G9CsiCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-16T22:24:15.729414Z","bundle_sha256":"75111e2b9ebfebbd8f6e18dedbc7ffe04719fbaf121941d1726c830e9bed201e"}}