{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:OHSGEX745RY73Y7U5DHQJVXRFF","short_pith_number":"pith:OHSGEX74","canonical_record":{"source":{"id":"1405.0040","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-04-30T21:32:20Z","cross_cats_sorted":[],"title_canon_sha256":"17139fb3b982b9db31005c5851287f28f1c1fb79ac913f58dd3c7758caef4bc7","abstract_canon_sha256":"960ea5f95ca5bcb87c694138ee8dec2a26cf4b9efd954d46c78a3fb8b51a07f5"},"schema_version":"1.0"},"canonical_sha256":"71e4625ffcec71fde3f4e8cf04d6f129533d884faffed74d6866e769fb969625","source":{"kind":"arxiv","id":"1405.0040","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1405.0040","created_at":"2026-05-18T02:39:31Z"},{"alias_kind":"arxiv_version","alias_value":"1405.0040v3","created_at":"2026-05-18T02:39:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1405.0040","created_at":"2026-05-18T02:39:31Z"},{"alias_kind":"pith_short_12","alias_value":"OHSGEX745RY7","created_at":"2026-05-18T12:28:41Z"},{"alias_kind":"pith_short_16","alias_value":"OHSGEX745RY73Y7U","created_at":"2026-05-18T12:28:41Z"},{"alias_kind":"pith_short_8","alias_value":"OHSGEX74","created_at":"2026-05-18T12:28:41Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:OHSGEX745RY73Y7U5DHQJVXRFF","target":"record","payload":{"canonical_record":{"source":{"id":"1405.0040","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-04-30T21:32:20Z","cross_cats_sorted":[],"title_canon_sha256":"17139fb3b982b9db31005c5851287f28f1c1fb79ac913f58dd3c7758caef4bc7","abstract_canon_sha256":"960ea5f95ca5bcb87c694138ee8dec2a26cf4b9efd954d46c78a3fb8b51a07f5"},"schema_version":"1.0"},"canonical_sha256":"71e4625ffcec71fde3f4e8cf04d6f129533d884faffed74d6866e769fb969625","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:39:31.823560Z","signature_b64":"RRSWf9LWCFnyifrYw5cyeNDtqic3cjoA+Nd66fEXvfd3E42K0ZDVEKaehYTyFUSq5jH2p20UjmsIVgcawDpZAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"71e4625ffcec71fde3f4e8cf04d6f129533d884faffed74d6866e769fb969625","last_reissued_at":"2026-05-18T02:39:31.823003Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:39:31.823003Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1405.0040","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:39:31Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"6oljY5lQcGtIKEDQcpPC/ycsZpLBamjf/Ww+rdAZbm2tURZaLuX+GDVrBpEk5VLmMMr27FtVFdde/UR0iqMfCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T14:58:36.262298Z"},"content_sha256":"e3c898d5e0ab7fb4cce681622a321a13eba7e488dea528162217560afdddbd1e","schema_version":"1.0","event_id":"sha256:e3c898d5e0ab7fb4cce681622a321a13eba7e488dea528162217560afdddbd1e"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:OHSGEX745RY73Y7U5DHQJVXRFF","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A note on the stochastic weakly* almost periodic homogenization of fully nonlinear elliptic equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Hermano Frid","submitted_at":"2014-04-30T21:32:20Z","abstract_excerpt":"A function $f\\in \\BUC(\\R^d)$ is said to be weakly* almost periodic, denoted $f\\in\\APs(\\R^d)$, if there is $g\\in\\AP(\\R^d)$, such that, $\\oM(|f-g|)=0$, where $\\BUC(\\R^d)$ and $\\AP(\\R^d)$ are, respectively, the space of bounded uniformly continuous functions and the space of almost periodic functions, in $\\R^d$, and $\\oM(h)$ denotes the mean value of $h$, if it exists. We give a very simple direct proof of the stochastic homogenization property of the Dirichlet problem for fully nonlinear uniformly elliptic equations of the form $F(\\om,\\frac{x}{\\ve},D^2u)=0$, $x\\in U$, in a bounded domain $U\\subs"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1405.0040","kind":"arxiv","version":3},"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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:39:31Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"IYB00RW4PFk3CUVVUQm/vDUJ2oPCR8DhN35kVeceAGnvJwd+GhQHTzXuQzl0YYyU2X///S6pDCxj8akcPooODw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T14:58:36.262656Z"},"content_sha256":"7f7d02384fc4fd620b45a510708d370c0199830cbfd689fba7eeed53d50871b6","schema_version":"1.0","event_id":"sha256:7f7d02384fc4fd620b45a510708d370c0199830cbfd689fba7eeed53d50871b6"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/OHSGEX745RY73Y7U5DHQJVXRFF/bundle.json","state_url":"https://pith.science/pith/OHSGEX745RY73Y7U5DHQJVXRFF/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/OHSGEX745RY73Y7U5DHQJVXRFF/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":"2026-05-28T14:58:36Z","links":{"resolver":"https://pith.science/pith/OHSGEX745RY73Y7U5DHQJVXRFF","bundle":"https://pith.science/pith/OHSGEX745RY73Y7U5DHQJVXRFF/bundle.json","state":"https://pith.science/pith/OHSGEX745RY73Y7U5DHQJVXRFF/state.json","well_known_bundle":"https://pith.science/.well-known/pith/OHSGEX745RY73Y7U5DHQJVXRFF/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:OHSGEX745RY73Y7U5DHQJVXRFF","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":"960ea5f95ca5bcb87c694138ee8dec2a26cf4b9efd954d46c78a3fb8b51a07f5","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-04-30T21:32:20Z","title_canon_sha256":"17139fb3b982b9db31005c5851287f28f1c1fb79ac913f58dd3c7758caef4bc7"},"schema_version":"1.0","source":{"id":"1405.0040","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1405.0040","created_at":"2026-05-18T02:39:31Z"},{"alias_kind":"arxiv_version","alias_value":"1405.0040v3","created_at":"2026-05-18T02:39:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1405.0040","created_at":"2026-05-18T02:39:31Z"},{"alias_kind":"pith_short_12","alias_value":"OHSGEX745RY7","created_at":"2026-05-18T12:28:41Z"},{"alias_kind":"pith_short_16","alias_value":"OHSGEX745RY73Y7U","created_at":"2026-05-18T12:28:41Z"},{"alias_kind":"pith_short_8","alias_value":"OHSGEX74","created_at":"2026-05-18T12:28:41Z"}],"graph_snapshots":[{"event_id":"sha256:7f7d02384fc4fd620b45a510708d370c0199830cbfd689fba7eeed53d50871b6","target":"graph","created_at":"2026-05-18T02:39:31Z","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"},"paper":{"abstract_excerpt":"A function $f\\in \\BUC(\\R^d)$ is said to be weakly* almost periodic, denoted $f\\in\\APs(\\R^d)$, if there is $g\\in\\AP(\\R^d)$, such that, $\\oM(|f-g|)=0$, where $\\BUC(\\R^d)$ and $\\AP(\\R^d)$ are, respectively, the space of bounded uniformly continuous functions and the space of almost periodic functions, in $\\R^d$, and $\\oM(h)$ denotes the mean value of $h$, if it exists. We give a very simple direct proof of the stochastic homogenization property of the Dirichlet problem for fully nonlinear uniformly elliptic equations of the form $F(\\om,\\frac{x}{\\ve},D^2u)=0$, $x\\in U$, in a bounded domain $U\\subs","authors_text":"Hermano Frid","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-04-30T21:32:20Z","title":"A note on the stochastic weakly* almost periodic homogenization of fully nonlinear elliptic equations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1405.0040","kind":"arxiv","version":3},"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:e3c898d5e0ab7fb4cce681622a321a13eba7e488dea528162217560afdddbd1e","target":"record","created_at":"2026-05-18T02:39:31Z","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":"960ea5f95ca5bcb87c694138ee8dec2a26cf4b9efd954d46c78a3fb8b51a07f5","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-04-30T21:32:20Z","title_canon_sha256":"17139fb3b982b9db31005c5851287f28f1c1fb79ac913f58dd3c7758caef4bc7"},"schema_version":"1.0","source":{"id":"1405.0040","kind":"arxiv","version":3}},"canonical_sha256":"71e4625ffcec71fde3f4e8cf04d6f129533d884faffed74d6866e769fb969625","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"71e4625ffcec71fde3f4e8cf04d6f129533d884faffed74d6866e769fb969625","first_computed_at":"2026-05-18T02:39:31.823003Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:39:31.823003Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"RRSWf9LWCFnyifrYw5cyeNDtqic3cjoA+Nd66fEXvfd3E42K0ZDVEKaehYTyFUSq5jH2p20UjmsIVgcawDpZAA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:39:31.823560Z","signed_message":"canonical_sha256_bytes"},"source_id":"1405.0040","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e3c898d5e0ab7fb4cce681622a321a13eba7e488dea528162217560afdddbd1e","sha256:7f7d02384fc4fd620b45a510708d370c0199830cbfd689fba7eeed53d50871b6"],"state_sha256":"d77582a4ed5e4f7da8741c7bec7b0c0479d0230435fccad8eae52a6f5ed9f89e"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"CVxjgDRO0DVFKiI1G4v3XHOqLnuILvWH5eVj9AiBXcJISATscxPQtNaoV82k3UcUxS295htZGrEmMADyrZbCBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-28T14:58:36.264570Z","bundle_sha256":"6b8a68e03cad4d870f2be825b61f66f702fbd43b76c7641af847d29acd52be15"}}