{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:RFFVDXQHQYUZ3PRDCQZGWYC5PA","short_pith_number":"pith:RFFVDXQH","canonical_record":{"source":{"id":"1401.2859","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2014-01-13T15:04:03Z","cross_cats_sorted":[],"title_canon_sha256":"7dbfb39acd675aecf4c7d4d71cb8abe61665dd907dce8688105948ac1e770353","abstract_canon_sha256":"b9a3bd83850a0a6e5e84d3d6d4a21e975474ab1af994c5b99d903eeb2552ce29"},"schema_version":"1.0"},"canonical_sha256":"894b51de0786299dbe2314326b605d781b450a562a64c6b9220a324c75aeacc6","source":{"kind":"arxiv","id":"1401.2859","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1401.2859","created_at":"2026-05-18T03:01:45Z"},{"alias_kind":"arxiv_version","alias_value":"1401.2859v2","created_at":"2026-05-18T03:01:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1401.2859","created_at":"2026-05-18T03:01:45Z"},{"alias_kind":"pith_short_12","alias_value":"RFFVDXQHQYUZ","created_at":"2026-05-18T12:28:46Z"},{"alias_kind":"pith_short_16","alias_value":"RFFVDXQHQYUZ3PRD","created_at":"2026-05-18T12:28:46Z"},{"alias_kind":"pith_short_8","alias_value":"RFFVDXQH","created_at":"2026-05-18T12:28:46Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:RFFVDXQHQYUZ3PRDCQZGWYC5PA","target":"record","payload":{"canonical_record":{"source":{"id":"1401.2859","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2014-01-13T15:04:03Z","cross_cats_sorted":[],"title_canon_sha256":"7dbfb39acd675aecf4c7d4d71cb8abe61665dd907dce8688105948ac1e770353","abstract_canon_sha256":"b9a3bd83850a0a6e5e84d3d6d4a21e975474ab1af994c5b99d903eeb2552ce29"},"schema_version":"1.0"},"canonical_sha256":"894b51de0786299dbe2314326b605d781b450a562a64c6b9220a324c75aeacc6","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:01:45.664646Z","signature_b64":"FpN2KdC8vKJoNDIkN1EabgTbeOX7dUnJ7hu7ZIzf4goZ2TyX08djAxbHoziOjAjCROdD2Hvsa9xc2CducYCQBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"894b51de0786299dbe2314326b605d781b450a562a64c6b9220a324c75aeacc6","last_reissued_at":"2026-05-18T03:01:45.664203Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:01:45.664203Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1401.2859","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":"2026-05-18T03:01:45Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"hcsoqMjSteCZTzqM4mKifuI7oc9KrNSeY7Z9CkuzyF2bJCJILXA6NtolNTq0BWqUmAQ7gHpsUdB4mUYe98HcCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-30T08:14:11.031864Z"},"content_sha256":"90291eabd6b009b9cfa655b557595fad3071273300b31e7d6c99953b0d638e84","schema_version":"1.0","event_id":"sha256:90291eabd6b009b9cfa655b557595fad3071273300b31e7d6c99953b0d638e84"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:RFFVDXQHQYUZ3PRDCQZGWYC5PA","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On annealed elliptic Green function estimates","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Daniel Marahrens, Felix Otto","submitted_at":"2014-01-13T15:04:03Z","abstract_excerpt":"We consider a random, uniformly elliptic coefficient field $a$ on the lattice $\\mathbb{Z}^d$. The distribution $\\langle \\cdot \\rangle$ of the coefficient field is assumed to be stationary. Delmotte and Deuschel showed that the gradient and second mixed derivative of the parabolic Green function $G(t,x,y)$ satisfy optimal annealed estimates which are $L^2$ resp. $L^1$ in probability, i.e. they obtained bounds on $\\langle |\\nabla_x G(t,x,y)|^2 \\rangle^{\\frac{1}{2}}$ and $\\langle |\\nabla_x \\nabla_y G(t,x,y)| \\rangle$, see T. Delmotte and J.-D. Deuschel: On estimating the derivatives of symmetric "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1401.2859","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":"2026-05-18T03:01:45Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"9bGijUgyzEakSac7F9UPIJUbH3C6EQ+sjDUd0niAK/wR9c/oO+Y7mHKlfmbV8zEpn7RLojqT9i/7sxhKgUqKCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-30T08:14:11.032210Z"},"content_sha256":"9e2941e63e6ec4fe6a05902c1dfff33b9e3b2df1dc9365ff5cc3829ebb4d18cc","schema_version":"1.0","event_id":"sha256:9e2941e63e6ec4fe6a05902c1dfff33b9e3b2df1dc9365ff5cc3829ebb4d18cc"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/RFFVDXQHQYUZ3PRDCQZGWYC5PA/bundle.json","state_url":"https://pith.science/pith/RFFVDXQHQYUZ3PRDCQZGWYC5PA/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/RFFVDXQHQYUZ3PRDCQZGWYC5PA/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":"2026-06-30T08:14:11Z","links":{"resolver":"https://pith.science/pith/RFFVDXQHQYUZ3PRDCQZGWYC5PA","bundle":"https://pith.science/pith/RFFVDXQHQYUZ3PRDCQZGWYC5PA/bundle.json","state":"https://pith.science/pith/RFFVDXQHQYUZ3PRDCQZGWYC5PA/state.json","well_known_bundle":"https://pith.science/.well-known/pith/RFFVDXQHQYUZ3PRDCQZGWYC5PA/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:RFFVDXQHQYUZ3PRDCQZGWYC5PA","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":"b9a3bd83850a0a6e5e84d3d6d4a21e975474ab1af994c5b99d903eeb2552ce29","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2014-01-13T15:04:03Z","title_canon_sha256":"7dbfb39acd675aecf4c7d4d71cb8abe61665dd907dce8688105948ac1e770353"},"schema_version":"1.0","source":{"id":"1401.2859","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1401.2859","created_at":"2026-05-18T03:01:45Z"},{"alias_kind":"arxiv_version","alias_value":"1401.2859v2","created_at":"2026-05-18T03:01:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1401.2859","created_at":"2026-05-18T03:01:45Z"},{"alias_kind":"pith_short_12","alias_value":"RFFVDXQHQYUZ","created_at":"2026-05-18T12:28:46Z"},{"alias_kind":"pith_short_16","alias_value":"RFFVDXQHQYUZ3PRD","created_at":"2026-05-18T12:28:46Z"},{"alias_kind":"pith_short_8","alias_value":"RFFVDXQH","created_at":"2026-05-18T12:28:46Z"}],"graph_snapshots":[{"event_id":"sha256:9e2941e63e6ec4fe6a05902c1dfff33b9e3b2df1dc9365ff5cc3829ebb4d18cc","target":"graph","created_at":"2026-05-18T03:01:45Z","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 consider a random, uniformly elliptic coefficient field $a$ on the lattice $\\mathbb{Z}^d$. The distribution $\\langle \\cdot \\rangle$ of the coefficient field is assumed to be stationary. Delmotte and Deuschel showed that the gradient and second mixed derivative of the parabolic Green function $G(t,x,y)$ satisfy optimal annealed estimates which are $L^2$ resp. $L^1$ in probability, i.e. they obtained bounds on $\\langle |\\nabla_x G(t,x,y)|^2 \\rangle^{\\frac{1}{2}}$ and $\\langle |\\nabla_x \\nabla_y G(t,x,y)| \\rangle$, see T. Delmotte and J.-D. Deuschel: On estimating the derivatives of symmetric ","authors_text":"Daniel Marahrens, Felix Otto","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2014-01-13T15:04:03Z","title":"On annealed elliptic Green function estimates"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1401.2859","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":"sha256:90291eabd6b009b9cfa655b557595fad3071273300b31e7d6c99953b0d638e84","target":"record","created_at":"2026-05-18T03:01:45Z","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":"b9a3bd83850a0a6e5e84d3d6d4a21e975474ab1af994c5b99d903eeb2552ce29","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2014-01-13T15:04:03Z","title_canon_sha256":"7dbfb39acd675aecf4c7d4d71cb8abe61665dd907dce8688105948ac1e770353"},"schema_version":"1.0","source":{"id":"1401.2859","kind":"arxiv","version":2}},"canonical_sha256":"894b51de0786299dbe2314326b605d781b450a562a64c6b9220a324c75aeacc6","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"894b51de0786299dbe2314326b605d781b450a562a64c6b9220a324c75aeacc6","first_computed_at":"2026-05-18T03:01:45.664203Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:01:45.664203Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"FpN2KdC8vKJoNDIkN1EabgTbeOX7dUnJ7hu7ZIzf4goZ2TyX08djAxbHoziOjAjCROdD2Hvsa9xc2CducYCQBw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:01:45.664646Z","signed_message":"canonical_sha256_bytes"},"source_id":"1401.2859","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:90291eabd6b009b9cfa655b557595fad3071273300b31e7d6c99953b0d638e84","sha256:9e2941e63e6ec4fe6a05902c1dfff33b9e3b2df1dc9365ff5cc3829ebb4d18cc"],"state_sha256":"ede756eb26fc552b252179147d850824db0b2b9d69d6d76975ba2d76d02da75e"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"NOFFZ8yZpYoWFRoHBtazDlDn/RO+c8jBE0+AGQHfLG07t2l0AmZfK7qF3GNNYUn3/YhYbFh7h2bTrf/QuNjxAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-30T08:14:11.034151Z","bundle_sha256":"d6cb039170c9e845d78b6067716a3d32b5d408ee49c273edd9f636af2d646da2"}}