{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:HQXAT3XGNRL4TVUS6K44ZSCBYA","short_pith_number":"pith:HQXAT3XG","canonical_record":{"source":{"id":"1307.5447","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-07-20T18:16:42Z","cross_cats_sorted":[],"title_canon_sha256":"3076e93dea9fb85910375245c59997d03f3c1fad49fd732395ca62472e826252","abstract_canon_sha256":"99479aef01339ecc75a2db20f18a25eae17f88edebd7981fa251ab21803b6e9a"},"schema_version":"1.0"},"canonical_sha256":"3c2e09eee66c57c9d692f2b9ccc841c034eff0c301d6636b7143ed935879a7ad","source":{"kind":"arxiv","id":"1307.5447","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1307.5447","created_at":"2026-05-18T03:17:55Z"},{"alias_kind":"arxiv_version","alias_value":"1307.5447v1","created_at":"2026-05-18T03:17:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1307.5447","created_at":"2026-05-18T03:17:55Z"},{"alias_kind":"pith_short_12","alias_value":"HQXAT3XGNRL4","created_at":"2026-05-18T12:27:46Z"},{"alias_kind":"pith_short_16","alias_value":"HQXAT3XGNRL4TVUS","created_at":"2026-05-18T12:27:46Z"},{"alias_kind":"pith_short_8","alias_value":"HQXAT3XG","created_at":"2026-05-18T12:27:46Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:HQXAT3XGNRL4TVUS6K44ZSCBYA","target":"record","payload":{"canonical_record":{"source":{"id":"1307.5447","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-07-20T18:16:42Z","cross_cats_sorted":[],"title_canon_sha256":"3076e93dea9fb85910375245c59997d03f3c1fad49fd732395ca62472e826252","abstract_canon_sha256":"99479aef01339ecc75a2db20f18a25eae17f88edebd7981fa251ab21803b6e9a"},"schema_version":"1.0"},"canonical_sha256":"3c2e09eee66c57c9d692f2b9ccc841c034eff0c301d6636b7143ed935879a7ad","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:17:55.698747Z","signature_b64":"uZ3iBMap5jZ5botCgfa0UCW/ce7fqai8yc/F72RZHV/3AUfxld3pYkRMAzAkDjBrs/IkZCEZH6qoyYdg+R7KCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3c2e09eee66c57c9d692f2b9ccc841c034eff0c301d6636b7143ed935879a7ad","last_reissued_at":"2026-05-18T03:17:55.698009Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:17:55.698009Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1307.5447","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:17:55Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"2kKIWvap4bFzo5R22VH+LEK8YSvfc+mlRhwAis4Ajc57l957NgCmdMggn8SMoBQQKI2vHIumx3V44t1shiHBDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-25T22:45:49.727786Z"},"content_sha256":"b16321934c65cd25ffabb47a35a4212eefbbe492cfc02dee36e131b022abc7b3","schema_version":"1.0","event_id":"sha256:b16321934c65cd25ffabb47a35a4212eefbbe492cfc02dee36e131b022abc7b3"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:HQXAT3XGNRL4TVUS6K44ZSCBYA","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On the Dirichlet and Neumann evolution operators in R^d_+","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Luca Lorenzi, Luciana Angiuli","submitted_at":"2013-07-20T18:16:42Z","abstract_excerpt":"We prove some uniform and pointwise gradient estimates for the Dirichlet and the Neumann evolution operators $G_{\\mathcal{D}}(t,s)$ and $G_{\\mathcal{N}}(t,s)$ associated with a class of nonautonomous elliptic operators $\\A(t)$ with unbounded coefficients defined in $I\\times \\Rd_+$ (where $I$ is a right-halfline or $I=\\R$). We also prove the existence and the uniqueness of a tight evolution system of measures $\\{\\mu_t^{\\mathcal{N}}\\}_{t \\in I}$ associated with $G_{\\mathcal{N}}(t,s)$, which turns out to be sub-invariant for $G_{\\mathcal{D}}(t,s)$, and we study the asymptotic behaviour of the evo"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1307.5447","kind":"arxiv","version":1},"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":"2026-05-18T03:17:55Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"g1dDgw6qMxYYT46G8l8WTQjNh6SDnn2SCBvnZMU14mzgTpmwrOFB/pVkJs3DKteUCTcGl3X0HAsdNqnlPQ+yAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-25T22:45:49.728119Z"},"content_sha256":"15012c171cd029b0b3d3142754f427e84077e53cb3bc40d2e18998d0e6eebf2c","schema_version":"1.0","event_id":"sha256:15012c171cd029b0b3d3142754f427e84077e53cb3bc40d2e18998d0e6eebf2c"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/HQXAT3XGNRL4TVUS6K44ZSCBYA/bundle.json","state_url":"https://pith.science/pith/HQXAT3XGNRL4TVUS6K44ZSCBYA/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/HQXAT3XGNRL4TVUS6K44ZSCBYA/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":"2026-06-25T22:45:49Z","links":{"resolver":"https://pith.science/pith/HQXAT3XGNRL4TVUS6K44ZSCBYA","bundle":"https://pith.science/pith/HQXAT3XGNRL4TVUS6K44ZSCBYA/bundle.json","state":"https://pith.science/pith/HQXAT3XGNRL4TVUS6K44ZSCBYA/state.json","well_known_bundle":"https://pith.science/.well-known/pith/HQXAT3XGNRL4TVUS6K44ZSCBYA/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:HQXAT3XGNRL4TVUS6K44ZSCBYA","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":"99479aef01339ecc75a2db20f18a25eae17f88edebd7981fa251ab21803b6e9a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-07-20T18:16:42Z","title_canon_sha256":"3076e93dea9fb85910375245c59997d03f3c1fad49fd732395ca62472e826252"},"schema_version":"1.0","source":{"id":"1307.5447","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1307.5447","created_at":"2026-05-18T03:17:55Z"},{"alias_kind":"arxiv_version","alias_value":"1307.5447v1","created_at":"2026-05-18T03:17:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1307.5447","created_at":"2026-05-18T03:17:55Z"},{"alias_kind":"pith_short_12","alias_value":"HQXAT3XGNRL4","created_at":"2026-05-18T12:27:46Z"},{"alias_kind":"pith_short_16","alias_value":"HQXAT3XGNRL4TVUS","created_at":"2026-05-18T12:27:46Z"},{"alias_kind":"pith_short_8","alias_value":"HQXAT3XG","created_at":"2026-05-18T12:27:46Z"}],"graph_snapshots":[{"event_id":"sha256:15012c171cd029b0b3d3142754f427e84077e53cb3bc40d2e18998d0e6eebf2c","target":"graph","created_at":"2026-05-18T03:17:55Z","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 some uniform and pointwise gradient estimates for the Dirichlet and the Neumann evolution operators $G_{\\mathcal{D}}(t,s)$ and $G_{\\mathcal{N}}(t,s)$ associated with a class of nonautonomous elliptic operators $\\A(t)$ with unbounded coefficients defined in $I\\times \\Rd_+$ (where $I$ is a right-halfline or $I=\\R$). We also prove the existence and the uniqueness of a tight evolution system of measures $\\{\\mu_t^{\\mathcal{N}}\\}_{t \\in I}$ associated with $G_{\\mathcal{N}}(t,s)$, which turns out to be sub-invariant for $G_{\\mathcal{D}}(t,s)$, and we study the asymptotic behaviour of the evo","authors_text":"Luca Lorenzi, Luciana Angiuli","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-07-20T18:16:42Z","title":"On the Dirichlet and Neumann evolution operators in R^d_+"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1307.5447","kind":"arxiv","version":1},"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:b16321934c65cd25ffabb47a35a4212eefbbe492cfc02dee36e131b022abc7b3","target":"record","created_at":"2026-05-18T03:17:55Z","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":"99479aef01339ecc75a2db20f18a25eae17f88edebd7981fa251ab21803b6e9a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-07-20T18:16:42Z","title_canon_sha256":"3076e93dea9fb85910375245c59997d03f3c1fad49fd732395ca62472e826252"},"schema_version":"1.0","source":{"id":"1307.5447","kind":"arxiv","version":1}},"canonical_sha256":"3c2e09eee66c57c9d692f2b9ccc841c034eff0c301d6636b7143ed935879a7ad","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3c2e09eee66c57c9d692f2b9ccc841c034eff0c301d6636b7143ed935879a7ad","first_computed_at":"2026-05-18T03:17:55.698009Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:17:55.698009Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"uZ3iBMap5jZ5botCgfa0UCW/ce7fqai8yc/F72RZHV/3AUfxld3pYkRMAzAkDjBrs/IkZCEZH6qoyYdg+R7KCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:17:55.698747Z","signed_message":"canonical_sha256_bytes"},"source_id":"1307.5447","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b16321934c65cd25ffabb47a35a4212eefbbe492cfc02dee36e131b022abc7b3","sha256:15012c171cd029b0b3d3142754f427e84077e53cb3bc40d2e18998d0e6eebf2c"],"state_sha256":"0fd601ab21d8e27cb986537cdc0bdedd5c7efb12306a9f604255d3874af6a3f8"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"pCLIO79OjO32ODL6KswcGnmtoE9ZRpP4IeAIKtJcTszicoo5wsoXErCMTp0Oq3nXAIujt9p1s4pdKu0HXUYdDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-25T22:45:49.730022Z","bundle_sha256":"24f36e726033c7546d8f02b8f9fdbc40fd2e2b8eb6465a37cd4cf8044cd7c7c8"}}