{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:C5DB3LR3AOQ7RPXL2POAQRTQUU","short_pith_number":"pith:C5DB3LR3","canonical_record":{"source":{"id":"1104.0785","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2011-04-05T09:34:30Z","cross_cats_sorted":["math-ph","math.MP","math.SP"],"title_canon_sha256":"2f0ec9462d8c94f8e0da5bacc7ab5c85985fb27b59f6279b9e38ec415585cb97","abstract_canon_sha256":"b1b8d61320714ca91d88390108cfc6eda85d8094507c38a51641d4f97200ccd2"},"schema_version":"1.0"},"canonical_sha256":"17461dae3b03a1f8beebd3dc084670a517b9d102cf6a09ded7708c5ec4c030a5","source":{"kind":"arxiv","id":"1104.0785","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1104.0785","created_at":"2026-05-18T04:18:04Z"},{"alias_kind":"arxiv_version","alias_value":"1104.0785v3","created_at":"2026-05-18T04:18:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1104.0785","created_at":"2026-05-18T04:18:04Z"},{"alias_kind":"pith_short_12","alias_value":"C5DB3LR3AOQ7","created_at":"2026-05-18T12:26:24Z"},{"alias_kind":"pith_short_16","alias_value":"C5DB3LR3AOQ7RPXL","created_at":"2026-05-18T12:26:24Z"},{"alias_kind":"pith_short_8","alias_value":"C5DB3LR3","created_at":"2026-05-18T12:26:24Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:C5DB3LR3AOQ7RPXL2POAQRTQUU","target":"record","payload":{"canonical_record":{"source":{"id":"1104.0785","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2011-04-05T09:34:30Z","cross_cats_sorted":["math-ph","math.MP","math.SP"],"title_canon_sha256":"2f0ec9462d8c94f8e0da5bacc7ab5c85985fb27b59f6279b9e38ec415585cb97","abstract_canon_sha256":"b1b8d61320714ca91d88390108cfc6eda85d8094507c38a51641d4f97200ccd2"},"schema_version":"1.0"},"canonical_sha256":"17461dae3b03a1f8beebd3dc084670a517b9d102cf6a09ded7708c5ec4c030a5","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:18:04.040900Z","signature_b64":"LkwizqXXljbgKkIQc42gweHjixzGDBl6XE/HM53/K6SZOhdZ5t419ZaVUu01dkcnCgXmPRbpnxAPWrvzffOsBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"17461dae3b03a1f8beebd3dc084670a517b9d102cf6a09ded7708c5ec4c030a5","last_reissued_at":"2026-05-18T04:18:04.039995Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:18:04.039995Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1104.0785","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":"2026-05-18T04:18:04Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"VOtkksaPOJx61HB1/46gbfkqIoI71DIRtj8JUL+PqadHV/CzSN5x+iiKx+gkFd3cD7/H2mtjjw72AxHRTjL4Ag==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-03T15:51:14.642151Z"},"content_sha256":"a149ccfc73ca9e7a5c0121eebfc4ec956bccfe0482c63da0cafa90b17f49eb2d","schema_version":"1.0","event_id":"sha256:a149ccfc73ca9e7a5c0121eebfc4ec956bccfe0482c63da0cafa90b17f49eb2d"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:C5DB3LR3AOQ7RPXL2POAQRTQUU","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The mixed boundary value problem, Krein resolvent formulas and spectral asymptotic estimates","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP","math.SP"],"primary_cat":"math.AP","authors_text":"Gerd Grubb","submitted_at":"2011-04-05T09:34:30Z","abstract_excerpt":"For a second-order symmetric strongly elliptic operator A on a smooth bounded open set \\Omega in R^n with boundary \\Sigma, the mixed problem is defined by a Neumann-type condition on a part Sigma_+ of the boundary and a Dirichlet condition on the other part Sigma_-. We show a Krein resolvent formula, where the difference between its resolvent and the Dirichlet resolvent is expressed in terms of operators acting on Sobolev spaces over Sigma_+. This is used to obtain a new Weyl-type spectral asymptotics formula for the resolvent difference (where upper estimates were known before), namely s_j j^"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1104.0785","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":"2026-05-18T04:18:04Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"8XpyGXZOgzS24h1Y3s7gfk1qAwLxf/llYje4sa+3vhf8NKpEvcnEzAQu1j0ANxRWF2VYM4vLkR8dziy4CiezDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-03T15:51:14.642597Z"},"content_sha256":"846815e2722d1c4df951c06dec4494972cd27cc8065e1a12a110c2c5288ec418","schema_version":"1.0","event_id":"sha256:846815e2722d1c4df951c06dec4494972cd27cc8065e1a12a110c2c5288ec418"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/C5DB3LR3AOQ7RPXL2POAQRTQUU/bundle.json","state_url":"https://pith.science/pith/C5DB3LR3AOQ7RPXL2POAQRTQUU/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/C5DB3LR3AOQ7RPXL2POAQRTQUU/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":"2026-08-03T15:51:14Z","links":{"resolver":"https://pith.science/pith/C5DB3LR3AOQ7RPXL2POAQRTQUU","bundle":"https://pith.science/pith/C5DB3LR3AOQ7RPXL2POAQRTQUU/bundle.json","state":"https://pith.science/pith/C5DB3LR3AOQ7RPXL2POAQRTQUU/state.json","well_known_bundle":"https://pith.science/.well-known/pith/C5DB3LR3AOQ7RPXL2POAQRTQUU/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:C5DB3LR3AOQ7RPXL2POAQRTQUU","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":"b1b8d61320714ca91d88390108cfc6eda85d8094507c38a51641d4f97200ccd2","cross_cats_sorted":["math-ph","math.MP","math.SP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2011-04-05T09:34:30Z","title_canon_sha256":"2f0ec9462d8c94f8e0da5bacc7ab5c85985fb27b59f6279b9e38ec415585cb97"},"schema_version":"1.0","source":{"id":"1104.0785","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1104.0785","created_at":"2026-05-18T04:18:04Z"},{"alias_kind":"arxiv_version","alias_value":"1104.0785v3","created_at":"2026-05-18T04:18:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1104.0785","created_at":"2026-05-18T04:18:04Z"},{"alias_kind":"pith_short_12","alias_value":"C5DB3LR3AOQ7","created_at":"2026-05-18T12:26:24Z"},{"alias_kind":"pith_short_16","alias_value":"C5DB3LR3AOQ7RPXL","created_at":"2026-05-18T12:26:24Z"},{"alias_kind":"pith_short_8","alias_value":"C5DB3LR3","created_at":"2026-05-18T12:26:24Z"}],"graph_snapshots":[{"event_id":"sha256:846815e2722d1c4df951c06dec4494972cd27cc8065e1a12a110c2c5288ec418","target":"graph","created_at":"2026-05-18T04:18:04Z","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":"For a second-order symmetric strongly elliptic operator A on a smooth bounded open set \\Omega in R^n with boundary \\Sigma, the mixed problem is defined by a Neumann-type condition on a part Sigma_+ of the boundary and a Dirichlet condition on the other part Sigma_-. We show a Krein resolvent formula, where the difference between its resolvent and the Dirichlet resolvent is expressed in terms of operators acting on Sobolev spaces over Sigma_+. This is used to obtain a new Weyl-type spectral asymptotics formula for the resolvent difference (where upper estimates were known before), namely s_j j^","authors_text":"Gerd Grubb","cross_cats":["math-ph","math.MP","math.SP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2011-04-05T09:34:30Z","title":"The mixed boundary value problem, Krein resolvent formulas and spectral asymptotic estimates"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1104.0785","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:a149ccfc73ca9e7a5c0121eebfc4ec956bccfe0482c63da0cafa90b17f49eb2d","target":"record","created_at":"2026-05-18T04:18:04Z","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":"b1b8d61320714ca91d88390108cfc6eda85d8094507c38a51641d4f97200ccd2","cross_cats_sorted":["math-ph","math.MP","math.SP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2011-04-05T09:34:30Z","title_canon_sha256":"2f0ec9462d8c94f8e0da5bacc7ab5c85985fb27b59f6279b9e38ec415585cb97"},"schema_version":"1.0","source":{"id":"1104.0785","kind":"arxiv","version":3}},"canonical_sha256":"17461dae3b03a1f8beebd3dc084670a517b9d102cf6a09ded7708c5ec4c030a5","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"17461dae3b03a1f8beebd3dc084670a517b9d102cf6a09ded7708c5ec4c030a5","first_computed_at":"2026-05-18T04:18:04.039995Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:18:04.039995Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"LkwizqXXljbgKkIQc42gweHjixzGDBl6XE/HM53/K6SZOhdZ5t419ZaVUu01dkcnCgXmPRbpnxAPWrvzffOsBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T04:18:04.040900Z","signed_message":"canonical_sha256_bytes"},"source_id":"1104.0785","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a149ccfc73ca9e7a5c0121eebfc4ec956bccfe0482c63da0cafa90b17f49eb2d","sha256:846815e2722d1c4df951c06dec4494972cd27cc8065e1a12a110c2c5288ec418"],"state_sha256":"8bdb3f936d0211b1dd10ab9e4817d4baec28f6db53056efd800397d8a3b06e4a"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"BX7sP2QssH8r4mqh+lQSgL5qlQ1U3okZIo40+TX9MMQFqRt4y9tJ9Tn06zbDb320vMZWB/1HhFtCPgatadGtDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-03T15:51:14.645637Z","bundle_sha256":"622002c9940b24293d4c3389164b21787c5c87f468bfd11e503adde0c12e1f57"}}