{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2010:3BFOLZTQWU4CFNPXGGMYZYTWQQ","short_pith_number":"pith:3BFOLZTQ","canonical_record":{"source":{"id":"1009.1965","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2010-09-10T09:41:29Z","cross_cats_sorted":[],"title_canon_sha256":"dec620530e8329bb87f167cc6688cfa4aed300568fa587edaea2d6368e3e9f1b","abstract_canon_sha256":"34d86d37015526c7c18fd35b2ad092e056feb955be8f8321146f56f709bc14cb"},"schema_version":"1.0"},"canonical_sha256":"d84ae5e670b53822b5f731998ce276842a02cd411d186ac3ec1a1220c05b2870","source":{"kind":"arxiv","id":"1009.1965","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1009.1965","created_at":"2026-05-18T04:40:09Z"},{"alias_kind":"arxiv_version","alias_value":"1009.1965v2","created_at":"2026-05-18T04:40:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1009.1965","created_at":"2026-05-18T04:40:09Z"},{"alias_kind":"pith_short_12","alias_value":"3BFOLZTQWU4C","created_at":"2026-05-18T12:26:03Z"},{"alias_kind":"pith_short_16","alias_value":"3BFOLZTQWU4CFNPX","created_at":"2026-05-18T12:26:03Z"},{"alias_kind":"pith_short_8","alias_value":"3BFOLZTQ","created_at":"2026-05-18T12:26:03Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2010:3BFOLZTQWU4CFNPXGGMYZYTWQQ","target":"record","payload":{"canonical_record":{"source":{"id":"1009.1965","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2010-09-10T09:41:29Z","cross_cats_sorted":[],"title_canon_sha256":"dec620530e8329bb87f167cc6688cfa4aed300568fa587edaea2d6368e3e9f1b","abstract_canon_sha256":"34d86d37015526c7c18fd35b2ad092e056feb955be8f8321146f56f709bc14cb"},"schema_version":"1.0"},"canonical_sha256":"d84ae5e670b53822b5f731998ce276842a02cd411d186ac3ec1a1220c05b2870","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:40:09.206058Z","signature_b64":"JDLoBfY4TgJ2OiazkgGRIvJrs4DVmpUY246op+UplgBXhk8WwqtShyrwhF59p1GNDuOXtkeT0i+GYJNUNqEaCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d84ae5e670b53822b5f731998ce276842a02cd411d186ac3ec1a1220c05b2870","last_reissued_at":"2026-05-18T04:40:09.205586Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:40:09.205586Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1009.1965","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":"2026-05-18T04:40:09Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"3ZWrgG347BmlBAcpcQNVybrAxSh0xKZpSKjMb0b5HXMADN+Nxq/ihqwUV2QRvWRdfdf4iozXhdyeFvbH7hxLCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-23T13:13:45.850531Z"},"content_sha256":"f6b5304d6996a88a39d01f7feaf9c6709556aab8250628f49da68de59e4c6fa1","schema_version":"1.0","event_id":"sha256:f6b5304d6996a88a39d01f7feaf9c6709556aab8250628f49da68de59e4c6fa1"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2010:3BFOLZTQWU4CFNPXGGMYZYTWQQ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Gradient Estimate on the Neumann Semigroup and Applications","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Feng-Yu Wang, Lixin Yan","submitted_at":"2010-09-10T09:41:29Z","abstract_excerpt":"We prove the following sharp upper bound for the gradient of the Neumann semigroup $P_t$ on a $d$-dimensional compact domain $\\OO$ with boundary either $C^2$-smooth or convex:\n  $$\\|\\nn P_t\\|_{1\\to \\infty}\\le \\ff{c}{t^{(d+1)/2}},\\ \\ t>0,$$ where $c>0$ is a constant depending on the domain and $\\|\\cdot\\|_{1\\to\\infty}$ is the operator norm from $L^1(\\OO)$ to $L^\\infty(\\OO)$. This estimate implies a Gaussian type point-wise upper bound for the gradient of the Neumann heat kernel, which is applied to the study of the Hardy spaces, Riesz transforms, and regularity of solutions to the inhomogeneous "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1009.1965","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":"2026-05-18T04:40:09Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"NhnYrQuxVtYWTEOGel6g3ZuAJW+hyCjFtxlNwkBfIb6Pt9IdDrFcDDKtOMKAOvi5xm0FzPruObUARsXBqQSsCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-23T13:13:45.851251Z"},"content_sha256":"bf99e04cb4f326549b9dc4f18344fee9e4e020c114c80102e329fa144963f36a","schema_version":"1.0","event_id":"sha256:bf99e04cb4f326549b9dc4f18344fee9e4e020c114c80102e329fa144963f36a"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/3BFOLZTQWU4CFNPXGGMYZYTWQQ/bundle.json","state_url":"https://pith.science/pith/3BFOLZTQWU4CFNPXGGMYZYTWQQ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/3BFOLZTQWU4CFNPXGGMYZYTWQQ/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":"2026-05-23T13:13:45Z","links":{"resolver":"https://pith.science/pith/3BFOLZTQWU4CFNPXGGMYZYTWQQ","bundle":"https://pith.science/pith/3BFOLZTQWU4CFNPXGGMYZYTWQQ/bundle.json","state":"https://pith.science/pith/3BFOLZTQWU4CFNPXGGMYZYTWQQ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/3BFOLZTQWU4CFNPXGGMYZYTWQQ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:3BFOLZTQWU4CFNPXGGMYZYTWQQ","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":"34d86d37015526c7c18fd35b2ad092e056feb955be8f8321146f56f709bc14cb","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2010-09-10T09:41:29Z","title_canon_sha256":"dec620530e8329bb87f167cc6688cfa4aed300568fa587edaea2d6368e3e9f1b"},"schema_version":"1.0","source":{"id":"1009.1965","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1009.1965","created_at":"2026-05-18T04:40:09Z"},{"alias_kind":"arxiv_version","alias_value":"1009.1965v2","created_at":"2026-05-18T04:40:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1009.1965","created_at":"2026-05-18T04:40:09Z"},{"alias_kind":"pith_short_12","alias_value":"3BFOLZTQWU4C","created_at":"2026-05-18T12:26:03Z"},{"alias_kind":"pith_short_16","alias_value":"3BFOLZTQWU4CFNPX","created_at":"2026-05-18T12:26:03Z"},{"alias_kind":"pith_short_8","alias_value":"3BFOLZTQ","created_at":"2026-05-18T12:26:03Z"}],"graph_snapshots":[{"event_id":"sha256:bf99e04cb4f326549b9dc4f18344fee9e4e020c114c80102e329fa144963f36a","target":"graph","created_at":"2026-05-18T04:40:09Z","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 the following sharp upper bound for the gradient of the Neumann semigroup $P_t$ on a $d$-dimensional compact domain $\\OO$ with boundary either $C^2$-smooth or convex:\n  $$\\|\\nn P_t\\|_{1\\to \\infty}\\le \\ff{c}{t^{(d+1)/2}},\\ \\ t>0,$$ where $c>0$ is a constant depending on the domain and $\\|\\cdot\\|_{1\\to\\infty}$ is the operator norm from $L^1(\\OO)$ to $L^\\infty(\\OO)$. This estimate implies a Gaussian type point-wise upper bound for the gradient of the Neumann heat kernel, which is applied to the study of the Hardy spaces, Riesz transforms, and regularity of solutions to the inhomogeneous ","authors_text":"Feng-Yu Wang, Lixin Yan","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2010-09-10T09:41:29Z","title":"Gradient Estimate on the Neumann Semigroup and Applications"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1009.1965","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:f6b5304d6996a88a39d01f7feaf9c6709556aab8250628f49da68de59e4c6fa1","target":"record","created_at":"2026-05-18T04:40:09Z","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":"34d86d37015526c7c18fd35b2ad092e056feb955be8f8321146f56f709bc14cb","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2010-09-10T09:41:29Z","title_canon_sha256":"dec620530e8329bb87f167cc6688cfa4aed300568fa587edaea2d6368e3e9f1b"},"schema_version":"1.0","source":{"id":"1009.1965","kind":"arxiv","version":2}},"canonical_sha256":"d84ae5e670b53822b5f731998ce276842a02cd411d186ac3ec1a1220c05b2870","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d84ae5e670b53822b5f731998ce276842a02cd411d186ac3ec1a1220c05b2870","first_computed_at":"2026-05-18T04:40:09.205586Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:40:09.205586Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"JDLoBfY4TgJ2OiazkgGRIvJrs4DVmpUY246op+UplgBXhk8WwqtShyrwhF59p1GNDuOXtkeT0i+GYJNUNqEaCA==","signature_status":"signed_v1","signed_at":"2026-05-18T04:40:09.206058Z","signed_message":"canonical_sha256_bytes"},"source_id":"1009.1965","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f6b5304d6996a88a39d01f7feaf9c6709556aab8250628f49da68de59e4c6fa1","sha256:bf99e04cb4f326549b9dc4f18344fee9e4e020c114c80102e329fa144963f36a"],"state_sha256":"7348ab29f75358e8f925792556a468d315d94f96ecba1068790d0226fe990667"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"8h1t1VB83lJHu9/LBxwvLWIxE1aR3h2hiTHovRAowLPX7Tj5DORKWARqSv4AyEMpECnGcDBcebHzB8d9M/FEAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-23T13:13:45.855078Z","bundle_sha256":"4b5d005bc62e72a1b16a92ddfb685a8c709d3dd5e2bd1b728a02d27772fb4d10"}}