{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2022:5PGBNVSCHQEUTSHO43LHE2C4TL","short_pith_number":"pith:5PGBNVSC","canonical_record":{"source":{"id":"2210.06488","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2022-10-12T18:00:00Z","cross_cats_sorted":["math.PR"],"title_canon_sha256":"71371cbd7c64685454071cfa58c44b1cf3f4a2ff71bf331a6c20057903e6153a","abstract_canon_sha256":"bfadd9297344d5d237304df042db728c7a68bf656f85e734dc1f8956cfe6054c"},"schema_version":"1.0"},"canonical_sha256":"ebcc16d6423c0949c8eee6d672685c9ac9311c6985d815b0c1ed0c2c90816b11","source":{"kind":"arxiv","id":"2210.06488","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2210.06488","created_at":"2026-07-05T09:08:18Z"},{"alias_kind":"arxiv_version","alias_value":"2210.06488v2","created_at":"2026-07-05T09:08:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2210.06488","created_at":"2026-07-05T09:08:18Z"},{"alias_kind":"pith_short_12","alias_value":"5PGBNVSCHQEU","created_at":"2026-07-05T09:08:18Z"},{"alias_kind":"pith_short_16","alias_value":"5PGBNVSCHQEUTSHO","created_at":"2026-07-05T09:08:18Z"},{"alias_kind":"pith_short_8","alias_value":"5PGBNVSC","created_at":"2026-07-05T09:08:18Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2022:5PGBNVSCHQEUTSHO43LHE2C4TL","target":"record","payload":{"canonical_record":{"source":{"id":"2210.06488","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2022-10-12T18:00:00Z","cross_cats_sorted":["math.PR"],"title_canon_sha256":"71371cbd7c64685454071cfa58c44b1cf3f4a2ff71bf331a6c20057903e6153a","abstract_canon_sha256":"bfadd9297344d5d237304df042db728c7a68bf656f85e734dc1f8956cfe6054c"},"schema_version":"1.0"},"canonical_sha256":"ebcc16d6423c0949c8eee6d672685c9ac9311c6985d815b0c1ed0c2c90816b11","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T09:08:18.750886Z","signature_b64":"821rsD9roeTbf5tRS01ObBLrUApGFBXiBeI5uaBGPywRHE33GXArFBGhnZUtpxQUPGOksNqvD3riS6IoB3mVDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ebcc16d6423c0949c8eee6d672685c9ac9311c6985d815b0c1ed0c2c90816b11","last_reissued_at":"2026-07-05T09:08:18.750354Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T09:08:18.750354Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2210.06488","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T09:08:18Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"eadHDaT6EgSRLIQr8etkkit68rPTfhiltwiwrW9lfqDkGBhe+uaOQprW1KuYATc2ytvSNKkqwKGu2AQLbTOeBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-08T09:41:58.256719Z"},"content_sha256":"a387dfd91278bb9e87be36c69c0c96ab6fbf2fce64abf2b1ea1950c9ece1e2e5","schema_version":"1.0","event_id":"sha256:a387dfd91278bb9e87be36c69c0c96ab6fbf2fce64abf2b1ea1950c9ece1e2e5"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2022:5PGBNVSCHQEUTSHO43LHE2C4TL","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Elliptic homogenization from qualitative to quantitative","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.PR"],"primary_cat":"math.AP","authors_text":"Scott Armstrong, Tuomo Kuusi","submitted_at":"2022-10-12T18:00:00Z","abstract_excerpt":"We give a self-contained introduction to the theory of elliptic homogenization for random coefficient fields, starting from classical qualitative homogenization. The presentation also contains new results, such as optimal estimates (both in terms of stochastic moments and scaling of the error) for coefficient fields which are local functions of Gaussian random fields."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2210.06488","kind":"arxiv","version":2},"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/2210.06488/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":"2026-07-05T09:08:18Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"e4A5cxisfkPHQm++Ml7UvaJp2v0bmmZb7odOc7OXRUFtBn9Z1fW0Vaozo4NarEEFKnCY/fE8GDfyQkMwGuuHAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-08T09:41:58.257633Z"},"content_sha256":"5cc8d6b83bbb2a742558880563bd2e23e4bf85e12ffae697f102cc6395fa1d6f","schema_version":"1.0","event_id":"sha256:5cc8d6b83bbb2a742558880563bd2e23e4bf85e12ffae697f102cc6395fa1d6f"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/5PGBNVSCHQEUTSHO43LHE2C4TL/bundle.json","state_url":"https://pith.science/pith/5PGBNVSCHQEUTSHO43LHE2C4TL/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/5PGBNVSCHQEUTSHO43LHE2C4TL/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":"2026-08-08T09:41:58Z","links":{"resolver":"https://pith.science/pith/5PGBNVSCHQEUTSHO43LHE2C4TL","bundle":"https://pith.science/pith/5PGBNVSCHQEUTSHO43LHE2C4TL/bundle.json","state":"https://pith.science/pith/5PGBNVSCHQEUTSHO43LHE2C4TL/state.json","well_known_bundle":"https://pith.science/.well-known/pith/5PGBNVSCHQEUTSHO43LHE2C4TL/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2022:5PGBNVSCHQEUTSHO43LHE2C4TL","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":"bfadd9297344d5d237304df042db728c7a68bf656f85e734dc1f8956cfe6054c","cross_cats_sorted":["math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2022-10-12T18:00:00Z","title_canon_sha256":"71371cbd7c64685454071cfa58c44b1cf3f4a2ff71bf331a6c20057903e6153a"},"schema_version":"1.0","source":{"id":"2210.06488","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2210.06488","created_at":"2026-07-05T09:08:18Z"},{"alias_kind":"arxiv_version","alias_value":"2210.06488v2","created_at":"2026-07-05T09:08:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2210.06488","created_at":"2026-07-05T09:08:18Z"},{"alias_kind":"pith_short_12","alias_value":"5PGBNVSCHQEU","created_at":"2026-07-05T09:08:18Z"},{"alias_kind":"pith_short_16","alias_value":"5PGBNVSCHQEUTSHO","created_at":"2026-07-05T09:08:18Z"},{"alias_kind":"pith_short_8","alias_value":"5PGBNVSC","created_at":"2026-07-05T09:08:18Z"}],"graph_snapshots":[{"event_id":"sha256:5cc8d6b83bbb2a742558880563bd2e23e4bf85e12ffae697f102cc6395fa1d6f","target":"graph","created_at":"2026-07-05T09:08:18Z","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/2210.06488/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We give a self-contained introduction to the theory of elliptic homogenization for random coefficient fields, starting from classical qualitative homogenization. The presentation also contains new results, such as optimal estimates (both in terms of stochastic moments and scaling of the error) for coefficient fields which are local functions of Gaussian random fields.","authors_text":"Scott Armstrong, Tuomo Kuusi","cross_cats":["math.PR"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2022-10-12T18:00:00Z","title":"Elliptic homogenization from qualitative to quantitative"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2210.06488","kind":"arxiv","version":2},"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:a387dfd91278bb9e87be36c69c0c96ab6fbf2fce64abf2b1ea1950c9ece1e2e5","target":"record","created_at":"2026-07-05T09:08:18Z","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":"bfadd9297344d5d237304df042db728c7a68bf656f85e734dc1f8956cfe6054c","cross_cats_sorted":["math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2022-10-12T18:00:00Z","title_canon_sha256":"71371cbd7c64685454071cfa58c44b1cf3f4a2ff71bf331a6c20057903e6153a"},"schema_version":"1.0","source":{"id":"2210.06488","kind":"arxiv","version":2}},"canonical_sha256":"ebcc16d6423c0949c8eee6d672685c9ac9311c6985d815b0c1ed0c2c90816b11","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ebcc16d6423c0949c8eee6d672685c9ac9311c6985d815b0c1ed0c2c90816b11","first_computed_at":"2026-07-05T09:08:18.750354Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T09:08:18.750354Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"821rsD9roeTbf5tRS01ObBLrUApGFBXiBeI5uaBGPywRHE33GXArFBGhnZUtpxQUPGOksNqvD3riS6IoB3mVDw==","signature_status":"signed_v1","signed_at":"2026-07-05T09:08:18.750886Z","signed_message":"canonical_sha256_bytes"},"source_id":"2210.06488","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a387dfd91278bb9e87be36c69c0c96ab6fbf2fce64abf2b1ea1950c9ece1e2e5","sha256:5cc8d6b83bbb2a742558880563bd2e23e4bf85e12ffae697f102cc6395fa1d6f"],"state_sha256":"46db13860237fb1b5aa69932a29243daf3e47c4f9592d3523c97a09b80e98a03"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"J3d+hXqqxFxr+x5jL5584AxBqPAveJGBPEd/b3LcjCRScpyN/ndUoyyZDFI7/djkco35TMWFM89UkUSN++PNAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-08T09:41:58.263102Z","bundle_sha256":"7b7a3a581b6876d01e1fb28566b937f44974115aee4eacc591efb310b787a60e"}}