{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:NMXNMJAPFUW3SLTI2DTPM7VVHV","short_pith_number":"pith:NMXNMJAP","canonical_record":{"source":{"id":"1602.04467","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2016-02-14T15:38:14Z","cross_cats_sorted":[],"title_canon_sha256":"c742e1c2e74793b72ef1f47ee398c4e63617a1c93b2ddc6405b2570d73109861","abstract_canon_sha256":"84410a1a7341fab5486560324ce69ee5b9bc38f420b7b85d1ed2efedda82fcf9"},"schema_version":"1.0"},"canonical_sha256":"6b2ed6240f2d2db92e68d0e6f67eb53d4b2990806a36436a2c00e43f050971a1","source":{"kind":"arxiv","id":"1602.04467","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1602.04467","created_at":"2026-05-18T00:51:05Z"},{"alias_kind":"arxiv_version","alias_value":"1602.04467v3","created_at":"2026-05-18T00:51:05Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1602.04467","created_at":"2026-05-18T00:51:05Z"},{"alias_kind":"pith_short_12","alias_value":"NMXNMJAPFUW3","created_at":"2026-05-18T12:30:32Z"},{"alias_kind":"pith_short_16","alias_value":"NMXNMJAPFUW3SLTI","created_at":"2026-05-18T12:30:32Z"},{"alias_kind":"pith_short_8","alias_value":"NMXNMJAP","created_at":"2026-05-18T12:30:32Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:NMXNMJAPFUW3SLTI2DTPM7VVHV","target":"record","payload":{"canonical_record":{"source":{"id":"1602.04467","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2016-02-14T15:38:14Z","cross_cats_sorted":[],"title_canon_sha256":"c742e1c2e74793b72ef1f47ee398c4e63617a1c93b2ddc6405b2570d73109861","abstract_canon_sha256":"84410a1a7341fab5486560324ce69ee5b9bc38f420b7b85d1ed2efedda82fcf9"},"schema_version":"1.0"},"canonical_sha256":"6b2ed6240f2d2db92e68d0e6f67eb53d4b2990806a36436a2c00e43f050971a1","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:51:05.640640Z","signature_b64":"TkKTe0hNV9Q+GdjSt2gjBooHbuxFBsUzv8ABIhU58uFd/jqcbdz5iYlJ5HZZB+SUUwhsBpaiTRJl1o/92oPIBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6b2ed6240f2d2db92e68d0e6f67eb53d4b2990806a36436a2c00e43f050971a1","last_reissued_at":"2026-05-18T00:51:05.640028Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:51:05.640028Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1602.04467","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":"2026-05-18T00:51:05Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"cDyAVJX0/NVkDKqyYXBqMmp+DtMCyNp1RnDv1m1ff++OLqUDBJ7tz0IsSJ5kci5XNBnFH22dyg3IqH1n3gJ4AA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T02:59:56.130328Z"},"content_sha256":"f8f898b669ed52eca548b4998e86c348b9019e56e8adfc032657a176980c11d0","schema_version":"1.0","event_id":"sha256:f8f898b669ed52eca548b4998e86c348b9019e56e8adfc032657a176980c11d0"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:NMXNMJAPFUW3SLTI2DTPM7VVHV","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Quantitative homogenization of degenerate random environments","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Arianna Giunti, Jean-Christophe Mourrat","submitted_at":"2016-02-14T15:38:14Z","abstract_excerpt":"We study discrete linear divergence-form operators with random coefficients, also known as the random conductance model. We assume that the conductances are bounded, independent and stationary; the law of a conductance may depend on the orientation of the associated edge. We give a simple necessary and sufficient condition for the relaxation of the environment seen by the particle to be diffusive, in the sense of every polynomial moment. As a consequence, we derive polynomial moment estimates on the corrector."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1602.04467","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":"2026-05-18T00:51:05Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"9cSGBPpqlV3H4GkxOkDSzOx+ScCmXWgj2/xO6hYVjZHizx976X/r7nfJVjH4zGld8Qa6pq0aHHfYmcgiVpsMDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T02:59:56.130980Z"},"content_sha256":"5b7e029c9fa05e04688ab6d2c473983027e9b9aab993f7aa333311bd57d1121f","schema_version":"1.0","event_id":"sha256:5b7e029c9fa05e04688ab6d2c473983027e9b9aab993f7aa333311bd57d1121f"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/NMXNMJAPFUW3SLTI2DTPM7VVHV/bundle.json","state_url":"https://pith.science/pith/NMXNMJAPFUW3SLTI2DTPM7VVHV/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/NMXNMJAPFUW3SLTI2DTPM7VVHV/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":"2026-05-31T02:59:56Z","links":{"resolver":"https://pith.science/pith/NMXNMJAPFUW3SLTI2DTPM7VVHV","bundle":"https://pith.science/pith/NMXNMJAPFUW3SLTI2DTPM7VVHV/bundle.json","state":"https://pith.science/pith/NMXNMJAPFUW3SLTI2DTPM7VVHV/state.json","well_known_bundle":"https://pith.science/.well-known/pith/NMXNMJAPFUW3SLTI2DTPM7VVHV/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:NMXNMJAPFUW3SLTI2DTPM7VVHV","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":"84410a1a7341fab5486560324ce69ee5b9bc38f420b7b85d1ed2efedda82fcf9","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2016-02-14T15:38:14Z","title_canon_sha256":"c742e1c2e74793b72ef1f47ee398c4e63617a1c93b2ddc6405b2570d73109861"},"schema_version":"1.0","source":{"id":"1602.04467","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1602.04467","created_at":"2026-05-18T00:51:05Z"},{"alias_kind":"arxiv_version","alias_value":"1602.04467v3","created_at":"2026-05-18T00:51:05Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1602.04467","created_at":"2026-05-18T00:51:05Z"},{"alias_kind":"pith_short_12","alias_value":"NMXNMJAPFUW3","created_at":"2026-05-18T12:30:32Z"},{"alias_kind":"pith_short_16","alias_value":"NMXNMJAPFUW3SLTI","created_at":"2026-05-18T12:30:32Z"},{"alias_kind":"pith_short_8","alias_value":"NMXNMJAP","created_at":"2026-05-18T12:30:32Z"}],"graph_snapshots":[{"event_id":"sha256:5b7e029c9fa05e04688ab6d2c473983027e9b9aab993f7aa333311bd57d1121f","target":"graph","created_at":"2026-05-18T00:51:05Z","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":"We study discrete linear divergence-form operators with random coefficients, also known as the random conductance model. We assume that the conductances are bounded, independent and stationary; the law of a conductance may depend on the orientation of the associated edge. We give a simple necessary and sufficient condition for the relaxation of the environment seen by the particle to be diffusive, in the sense of every polynomial moment. As a consequence, we derive polynomial moment estimates on the corrector.","authors_text":"Arianna Giunti, Jean-Christophe Mourrat","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2016-02-14T15:38:14Z","title":"Quantitative homogenization of degenerate random environments"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1602.04467","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:f8f898b669ed52eca548b4998e86c348b9019e56e8adfc032657a176980c11d0","target":"record","created_at":"2026-05-18T00:51:05Z","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":"84410a1a7341fab5486560324ce69ee5b9bc38f420b7b85d1ed2efedda82fcf9","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2016-02-14T15:38:14Z","title_canon_sha256":"c742e1c2e74793b72ef1f47ee398c4e63617a1c93b2ddc6405b2570d73109861"},"schema_version":"1.0","source":{"id":"1602.04467","kind":"arxiv","version":3}},"canonical_sha256":"6b2ed6240f2d2db92e68d0e6f67eb53d4b2990806a36436a2c00e43f050971a1","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6b2ed6240f2d2db92e68d0e6f67eb53d4b2990806a36436a2c00e43f050971a1","first_computed_at":"2026-05-18T00:51:05.640028Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:51:05.640028Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"TkKTe0hNV9Q+GdjSt2gjBooHbuxFBsUzv8ABIhU58uFd/jqcbdz5iYlJ5HZZB+SUUwhsBpaiTRJl1o/92oPIBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:51:05.640640Z","signed_message":"canonical_sha256_bytes"},"source_id":"1602.04467","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f8f898b669ed52eca548b4998e86c348b9019e56e8adfc032657a176980c11d0","sha256:5b7e029c9fa05e04688ab6d2c473983027e9b9aab993f7aa333311bd57d1121f"],"state_sha256":"ac7dffa4feb5566129f9fe9ffc7cf1b2a2c45954e35e01b79ea3266e6054f4cb"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/SDZsCKgyITI8L4J3DtswQB+x/h5NSMFxGnZz1oLzXFvqwakK/3GoNbSYH+X4+Cz2MA4FtLn1rzHvR7L0uCzCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-31T02:59:56.134197Z","bundle_sha256":"ab53a43cb5701d2749f37435dd6ddcdcc45270178141fcafb567ebcb06b42ba4"}}