{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2021:GAHJXRKWJH4M43YTQLZ2BXKDEO","short_pith_number":"pith:GAHJXRKW","canonical_record":{"source":{"id":"2105.12447","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2021-05-26T10:08:34Z","cross_cats_sorted":["math.AP"],"title_canon_sha256":"01544c3d92ef7ca2d74c0471c5a9ba1d6b4622e712aa5a8bbf3efa75649866d3","abstract_canon_sha256":"caa856db21a9fab5c90eb1930d129f52cd46d972670182a6c7d88c9bceec81cf"},"schema_version":"1.0"},"canonical_sha256":"300e9bc55649f8ce6f1382f3a0dd4323890d790cd22b0cdc68d6708de4bc3dbc","source":{"kind":"arxiv","id":"2105.12447","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2105.12447","created_at":"2026-07-05T02:43:39Z"},{"alias_kind":"arxiv_version","alias_value":"2105.12447v1","created_at":"2026-07-05T02:43:39Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2105.12447","created_at":"2026-07-05T02:43:39Z"},{"alias_kind":"pith_short_12","alias_value":"GAHJXRKWJH4M","created_at":"2026-07-05T02:43:39Z"},{"alias_kind":"pith_short_16","alias_value":"GAHJXRKWJH4M43YT","created_at":"2026-07-05T02:43:39Z"},{"alias_kind":"pith_short_8","alias_value":"GAHJXRKW","created_at":"2026-07-05T02:43:39Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2021:GAHJXRKWJH4M43YTQLZ2BXKDEO","target":"record","payload":{"canonical_record":{"source":{"id":"2105.12447","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2021-05-26T10:08:34Z","cross_cats_sorted":["math.AP"],"title_canon_sha256":"01544c3d92ef7ca2d74c0471c5a9ba1d6b4622e712aa5a8bbf3efa75649866d3","abstract_canon_sha256":"caa856db21a9fab5c90eb1930d129f52cd46d972670182a6c7d88c9bceec81cf"},"schema_version":"1.0"},"canonical_sha256":"300e9bc55649f8ce6f1382f3a0dd4323890d790cd22b0cdc68d6708de4bc3dbc","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T02:43:39.007283Z","signature_b64":"Cueicb0BgQ6WUtBsCgfC6rRdOFmiOPvBn0bzxYnica5dxo0KrWS7jf54c9xI35IuqJicYxFLEPMRt7tZUEbJAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"300e9bc55649f8ce6f1382f3a0dd4323890d790cd22b0cdc68d6708de4bc3dbc","last_reissued_at":"2026-07-05T02:43:39.006851Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T02:43:39.006851Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2105.12447","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":"2026-07-05T02:43:39Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"3nqI77x1fiR+FQ9ojdT+FoOT5BxcsUKMfPM/J9TPCtEWy71e5ulIAaJvgPgRYlzs3FgxKuGd66Ujoce6nf6xBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-19T07:21:07.068691Z"},"content_sha256":"6358a2b011f6c9dfa7bee24ea1808c783c25f8eee482747fbb6555bb0d1a6db0","schema_version":"1.0","event_id":"sha256:6358a2b011f6c9dfa7bee24ea1808c783c25f8eee482747fbb6555bb0d1a6db0"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2021:GAHJXRKWJH4M43YTQLZ2BXKDEO","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Stochastic two-scale convergence and Young measures","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP"],"primary_cat":"math.PR","authors_text":"Mario Varga, Martin Heida, Stefan Neukamm","submitted_at":"2021-05-26T10:08:34Z","abstract_excerpt":"In this paper we compare the notion of stochastic two-scale convergence in the mean (by Bourgeat, Mikeli\\'c and Wright), the notion of stochastic unfolding (recently introduced by the authors), and the quenched notion of stochastic two-scale convergence (by Zhikov and Pyatnitskii). In particular, we introduce stochastic two-scale Young measures as a tool to compare mean and quenched limits. Moreover, we discuss two examples, which can be naturally analyzed via stochastic unfolding, but which cannot be treated via quenched stochastic two-scale convergence."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2105.12447","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/2105.12447/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":"2026-07-05T02:43:39Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"opT7bb4gkXu7ctd9WqFWiWziVYNtxlsv+CMrHJ0revgpmoxiYdXUYCpYigNeQ7pYh9DyoDh96BaEUW7w5gv5Cg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-19T07:21:07.069060Z"},"content_sha256":"a38e2a04433c2f56aaa0d9dc47cc9f6d316d2882656e2779f9065f64caa159c9","schema_version":"1.0","event_id":"sha256:a38e2a04433c2f56aaa0d9dc47cc9f6d316d2882656e2779f9065f64caa159c9"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/GAHJXRKWJH4M43YTQLZ2BXKDEO/bundle.json","state_url":"https://pith.science/pith/GAHJXRKWJH4M43YTQLZ2BXKDEO/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/GAHJXRKWJH4M43YTQLZ2BXKDEO/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":"2026-07-19T07:21:07Z","links":{"resolver":"https://pith.science/pith/GAHJXRKWJH4M43YTQLZ2BXKDEO","bundle":"https://pith.science/pith/GAHJXRKWJH4M43YTQLZ2BXKDEO/bundle.json","state":"https://pith.science/pith/GAHJXRKWJH4M43YTQLZ2BXKDEO/state.json","well_known_bundle":"https://pith.science/.well-known/pith/GAHJXRKWJH4M43YTQLZ2BXKDEO/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2021:GAHJXRKWJH4M43YTQLZ2BXKDEO","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":"caa856db21a9fab5c90eb1930d129f52cd46d972670182a6c7d88c9bceec81cf","cross_cats_sorted":["math.AP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2021-05-26T10:08:34Z","title_canon_sha256":"01544c3d92ef7ca2d74c0471c5a9ba1d6b4622e712aa5a8bbf3efa75649866d3"},"schema_version":"1.0","source":{"id":"2105.12447","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2105.12447","created_at":"2026-07-05T02:43:39Z"},{"alias_kind":"arxiv_version","alias_value":"2105.12447v1","created_at":"2026-07-05T02:43:39Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2105.12447","created_at":"2026-07-05T02:43:39Z"},{"alias_kind":"pith_short_12","alias_value":"GAHJXRKWJH4M","created_at":"2026-07-05T02:43:39Z"},{"alias_kind":"pith_short_16","alias_value":"GAHJXRKWJH4M43YT","created_at":"2026-07-05T02:43:39Z"},{"alias_kind":"pith_short_8","alias_value":"GAHJXRKW","created_at":"2026-07-05T02:43:39Z"}],"graph_snapshots":[{"event_id":"sha256:a38e2a04433c2f56aaa0d9dc47cc9f6d316d2882656e2779f9065f64caa159c9","target":"graph","created_at":"2026-07-05T02:43:39Z","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/2105.12447/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In this paper we compare the notion of stochastic two-scale convergence in the mean (by Bourgeat, Mikeli\\'c and Wright), the notion of stochastic unfolding (recently introduced by the authors), and the quenched notion of stochastic two-scale convergence (by Zhikov and Pyatnitskii). In particular, we introduce stochastic two-scale Young measures as a tool to compare mean and quenched limits. Moreover, we discuss two examples, which can be naturally analyzed via stochastic unfolding, but which cannot be treated via quenched stochastic two-scale convergence.","authors_text":"Mario Varga, Martin Heida, Stefan Neukamm","cross_cats":["math.AP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2021-05-26T10:08:34Z","title":"Stochastic two-scale convergence and Young measures"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2105.12447","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":"sha256:6358a2b011f6c9dfa7bee24ea1808c783c25f8eee482747fbb6555bb0d1a6db0","target":"record","created_at":"2026-07-05T02:43:39Z","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":"caa856db21a9fab5c90eb1930d129f52cd46d972670182a6c7d88c9bceec81cf","cross_cats_sorted":["math.AP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2021-05-26T10:08:34Z","title_canon_sha256":"01544c3d92ef7ca2d74c0471c5a9ba1d6b4622e712aa5a8bbf3efa75649866d3"},"schema_version":"1.0","source":{"id":"2105.12447","kind":"arxiv","version":1}},"canonical_sha256":"300e9bc55649f8ce6f1382f3a0dd4323890d790cd22b0cdc68d6708de4bc3dbc","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"300e9bc55649f8ce6f1382f3a0dd4323890d790cd22b0cdc68d6708de4bc3dbc","first_computed_at":"2026-07-05T02:43:39.006851Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T02:43:39.006851Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Cueicb0BgQ6WUtBsCgfC6rRdOFmiOPvBn0bzxYnica5dxo0KrWS7jf54c9xI35IuqJicYxFLEPMRt7tZUEbJAA==","signature_status":"signed_v1","signed_at":"2026-07-05T02:43:39.007283Z","signed_message":"canonical_sha256_bytes"},"source_id":"2105.12447","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6358a2b011f6c9dfa7bee24ea1808c783c25f8eee482747fbb6555bb0d1a6db0","sha256:a38e2a04433c2f56aaa0d9dc47cc9f6d316d2882656e2779f9065f64caa159c9"],"state_sha256":"5887155c8b2005f244c7fcda6ad437f67d3b00d9d72bde2d97a6ec3b57a22680"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Xd5VHEY0mWhEF6/rXAroVuFziZmDleOJF9D5sYu74Jkb4EmliZMEMeIEn11cOaPR+vWEFoH6NfX0uDsJRkp/AA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-19T07:21:07.071136Z","bundle_sha256":"30fa9d6ddfb111eededd6f41aa59325577cc0d3998418c6005db7344c6eade4f"}}