{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:KQP6VDPFRD7KUQQ4RTVR2SRKNY","short_pith_number":"pith:KQP6VDPF","canonical_record":{"source":{"id":"1412.6313","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2014-12-19T12:24:02Z","cross_cats_sorted":[],"title_canon_sha256":"1355932795a3bb94ad9e2d962f115ec5c047b4e7a086be2b1a1eb734a2fc285c","abstract_canon_sha256":"ddcc8f58e9482d019c05ea46c8785c1cdb2ee3e7c36e0b4afd8dd5584b0f7507"},"schema_version":"1.0"},"canonical_sha256":"541fea8de588feaa421c8ceb1d4a2a6e2efbe349b37ecaed55aba3c559deb732","source":{"kind":"arxiv","id":"1412.6313","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1412.6313","created_at":"2026-05-18T02:25:48Z"},{"alias_kind":"arxiv_version","alias_value":"1412.6313v2","created_at":"2026-05-18T02:25:48Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1412.6313","created_at":"2026-05-18T02:25:48Z"},{"alias_kind":"pith_short_12","alias_value":"KQP6VDPFRD7K","created_at":"2026-05-18T12:28:35Z"},{"alias_kind":"pith_short_16","alias_value":"KQP6VDPFRD7KUQQ4","created_at":"2026-05-18T12:28:35Z"},{"alias_kind":"pith_short_8","alias_value":"KQP6VDPF","created_at":"2026-05-18T12:28:35Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:KQP6VDPFRD7KUQQ4RTVR2SRKNY","target":"record","payload":{"canonical_record":{"source":{"id":"1412.6313","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2014-12-19T12:24:02Z","cross_cats_sorted":[],"title_canon_sha256":"1355932795a3bb94ad9e2d962f115ec5c047b4e7a086be2b1a1eb734a2fc285c","abstract_canon_sha256":"ddcc8f58e9482d019c05ea46c8785c1cdb2ee3e7c36e0b4afd8dd5584b0f7507"},"schema_version":"1.0"},"canonical_sha256":"541fea8de588feaa421c8ceb1d4a2a6e2efbe349b37ecaed55aba3c559deb732","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:25:48.763198Z","signature_b64":"X4KajD7dq7iJsMs63mNHG5RqQpsY5XLay84Aoue5P0/a4BLSHjiun/sg3ktj1muAhAxKQTl7LBSdxd+ODQsVAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"541fea8de588feaa421c8ceb1d4a2a6e2efbe349b37ecaed55aba3c559deb732","last_reissued_at":"2026-05-18T02:25:48.762737Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:25:48.762737Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1412.6313","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":"2026-05-18T02:25:48Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"D/cxGP81WRqNFEHCOPwtu4bDjcGSiP2Iom3pYblimNGO9aZUpN+mw0ttf9x8eccrspFiQZuN//RaA/2Ps2uBBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T15:36:33.446648Z"},"content_sha256":"6f2b151a3d635a47bbb7a8b192ef49ae2aa8eb1570e6b375e2be967f1d25a74b","schema_version":"1.0","event_id":"sha256:6f2b151a3d635a47bbb7a8b192ef49ae2aa8eb1570e6b375e2be967f1d25a74b"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:KQP6VDPFRD7KUQQ4RTVR2SRKNY","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Diffusive Decay of the Environment Viewed by the Particle","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Jean-Christophe Mourrat, Paul de Buyer","submitted_at":"2014-12-19T12:24:02Z","abstract_excerpt":"We prove an optimal diffusive decay of the environment viewed by the particle in random walk among random independent conductances, with, as a main assumption, finite second moment of the conductance. Our proof, using the analytic approach of Gloria, Neukamm and Otto, is very short and elementary."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1412.6313","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":""},"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":"2026-05-18T02:25:48Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"N88QHAIqT/OIm7fgsmnw4TGqzXlnIzmRhFIxtD6Fv/cCsupTj5FfNee5lX40s8fShWRCdxsGDsHY+gXspyBmBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T15:36:33.446995Z"},"content_sha256":"6f9f35e78e60022073b71cc52a6bed3449356bb3438ec40dab938e8da8c32ed3","schema_version":"1.0","event_id":"sha256:6f9f35e78e60022073b71cc52a6bed3449356bb3438ec40dab938e8da8c32ed3"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/KQP6VDPFRD7KUQQ4RTVR2SRKNY/bundle.json","state_url":"https://pith.science/pith/KQP6VDPFRD7KUQQ4RTVR2SRKNY/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/KQP6VDPFRD7KUQQ4RTVR2SRKNY/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":"2026-06-01T15:36:33Z","links":{"resolver":"https://pith.science/pith/KQP6VDPFRD7KUQQ4RTVR2SRKNY","bundle":"https://pith.science/pith/KQP6VDPFRD7KUQQ4RTVR2SRKNY/bundle.json","state":"https://pith.science/pith/KQP6VDPFRD7KUQQ4RTVR2SRKNY/state.json","well_known_bundle":"https://pith.science/.well-known/pith/KQP6VDPFRD7KUQQ4RTVR2SRKNY/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:KQP6VDPFRD7KUQQ4RTVR2SRKNY","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":"ddcc8f58e9482d019c05ea46c8785c1cdb2ee3e7c36e0b4afd8dd5584b0f7507","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2014-12-19T12:24:02Z","title_canon_sha256":"1355932795a3bb94ad9e2d962f115ec5c047b4e7a086be2b1a1eb734a2fc285c"},"schema_version":"1.0","source":{"id":"1412.6313","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1412.6313","created_at":"2026-05-18T02:25:48Z"},{"alias_kind":"arxiv_version","alias_value":"1412.6313v2","created_at":"2026-05-18T02:25:48Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1412.6313","created_at":"2026-05-18T02:25:48Z"},{"alias_kind":"pith_short_12","alias_value":"KQP6VDPFRD7K","created_at":"2026-05-18T12:28:35Z"},{"alias_kind":"pith_short_16","alias_value":"KQP6VDPFRD7KUQQ4","created_at":"2026-05-18T12:28:35Z"},{"alias_kind":"pith_short_8","alias_value":"KQP6VDPF","created_at":"2026-05-18T12:28:35Z"}],"graph_snapshots":[{"event_id":"sha256:6f9f35e78e60022073b71cc52a6bed3449356bb3438ec40dab938e8da8c32ed3","target":"graph","created_at":"2026-05-18T02:25:48Z","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 prove an optimal diffusive decay of the environment viewed by the particle in random walk among random independent conductances, with, as a main assumption, finite second moment of the conductance. Our proof, using the analytic approach of Gloria, Neukamm and Otto, is very short and elementary.","authors_text":"Jean-Christophe Mourrat, Paul de Buyer","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2014-12-19T12:24:02Z","title":"Diffusive Decay of the Environment Viewed by the Particle"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1412.6313","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":"sha256:6f2b151a3d635a47bbb7a8b192ef49ae2aa8eb1570e6b375e2be967f1d25a74b","target":"record","created_at":"2026-05-18T02:25:48Z","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":"ddcc8f58e9482d019c05ea46c8785c1cdb2ee3e7c36e0b4afd8dd5584b0f7507","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2014-12-19T12:24:02Z","title_canon_sha256":"1355932795a3bb94ad9e2d962f115ec5c047b4e7a086be2b1a1eb734a2fc285c"},"schema_version":"1.0","source":{"id":"1412.6313","kind":"arxiv","version":2}},"canonical_sha256":"541fea8de588feaa421c8ceb1d4a2a6e2efbe349b37ecaed55aba3c559deb732","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"541fea8de588feaa421c8ceb1d4a2a6e2efbe349b37ecaed55aba3c559deb732","first_computed_at":"2026-05-18T02:25:48.762737Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:25:48.762737Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"X4KajD7dq7iJsMs63mNHG5RqQpsY5XLay84Aoue5P0/a4BLSHjiun/sg3ktj1muAhAxKQTl7LBSdxd+ODQsVAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:25:48.763198Z","signed_message":"canonical_sha256_bytes"},"source_id":"1412.6313","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6f2b151a3d635a47bbb7a8b192ef49ae2aa8eb1570e6b375e2be967f1d25a74b","sha256:6f9f35e78e60022073b71cc52a6bed3449356bb3438ec40dab938e8da8c32ed3"],"state_sha256":"f3a4ba59f0632eeed9afa4269ebb221b9219a50bf8b3716171455ec2c042e685"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"dQBWTlmGuYAok6YRt3QIwIiUejysQQvny1faP/+PQC0q1jvRvLnzGG2SI2qhFbLDhTrpRTuo5HiLGdbYTcCKDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-01T15:36:33.448971Z","bundle_sha256":"779de079a25440525b2957ab932f19295dfb3178bb42f3dc4f24f26f56abd93d"}}