{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:4PYOFCBPQ4WVODATC76APE3JQ3","short_pith_number":"pith:4PYOFCBP","canonical_record":{"source":{"id":"1612.01628","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-12-06T01:58:05Z","cross_cats_sorted":[],"title_canon_sha256":"6bd6425b04f900beae3c7ecf0f197c2eabab52956c59d92192330b0d8ec7c71a","abstract_canon_sha256":"5bd51f72f4fd41495b076cab9b2b7d862d68d7ad7b695b51798fe304908abe41"},"schema_version":"1.0"},"canonical_sha256":"e3f0e2882f872d570c1317fc07936986de05af4ef82fc74e4ddf6c4172a7ef86","source":{"kind":"arxiv","id":"1612.01628","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1612.01628","created_at":"2026-05-18T00:05:14Z"},{"alias_kind":"arxiv_version","alias_value":"1612.01628v2","created_at":"2026-05-18T00:05:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1612.01628","created_at":"2026-05-18T00:05:14Z"},{"alias_kind":"pith_short_12","alias_value":"4PYOFCBPQ4WV","created_at":"2026-05-18T12:29:58Z"},{"alias_kind":"pith_short_16","alias_value":"4PYOFCBPQ4WVODAT","created_at":"2026-05-18T12:29:58Z"},{"alias_kind":"pith_short_8","alias_value":"4PYOFCBP","created_at":"2026-05-18T12:29:58Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:4PYOFCBPQ4WVODATC76APE3JQ3","target":"record","payload":{"canonical_record":{"source":{"id":"1612.01628","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-12-06T01:58:05Z","cross_cats_sorted":[],"title_canon_sha256":"6bd6425b04f900beae3c7ecf0f197c2eabab52956c59d92192330b0d8ec7c71a","abstract_canon_sha256":"5bd51f72f4fd41495b076cab9b2b7d862d68d7ad7b695b51798fe304908abe41"},"schema_version":"1.0"},"canonical_sha256":"e3f0e2882f872d570c1317fc07936986de05af4ef82fc74e4ddf6c4172a7ef86","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:05:14.737993Z","signature_b64":"iqQV6JgZbqsHnSwowusjr6Hirq1ZL+A5dRqaZKMq2bwoz9rBAwz8KolpFiWAC45I5+NSNi4gbCI8i5rzNe45CA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e3f0e2882f872d570c1317fc07936986de05af4ef82fc74e4ddf6c4172a7ef86","last_reissued_at":"2026-05-18T00:05:14.737523Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:05:14.737523Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1612.01628","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":"2026-05-18T00:05:14Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"c6zGiSACmqSG+bqECAc8O3Ipv/5TI738FaNmU8FvZtZODX7rk8TQj+z9lwvbpuka9JnAWLLvF1EIU0n66M3DAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T06:12:13.449569Z"},"content_sha256":"975ba65aac4c41507ad622cc6edf5aec2e79ac3eae3ed68c5e8419442ce3aa81","schema_version":"1.0","event_id":"sha256:975ba65aac4c41507ad622cc6edf5aec2e79ac3eae3ed68c5e8419442ce3aa81"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:4PYOFCBPQ4WVODATC76APE3JQ3","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Function spaces and extension results for nonlocal Dirichlet problems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Bartlomiej Dyda, Moritz Kassmann","submitted_at":"2016-12-06T01:58:05Z","abstract_excerpt":"We study function spaces and extension results in relation with Dirichlet problems involving integrodifferential operators. For such problems, data are prescribed on the complement of a given domain in the Euclidean space. We introduce a function space that serves as a trace space for nonlocal Dirichlet problems and study related extension results."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1612.01628","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":"2026-05-18T00:05:14Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"XarY1YqeNExYL9b2dAz90RZsSC0VSzLO/d6M0um56zWRXfXIW8axZw9ZU+cRCXsrMIoMZcNvOKmf9yPkvM55Bg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T06:12:13.450257Z"},"content_sha256":"9e4b1d52fe3bc629d13c7357ac5c71ab0c6b8dcb36237c7464bf4eb37298b5b9","schema_version":"1.0","event_id":"sha256:9e4b1d52fe3bc629d13c7357ac5c71ab0c6b8dcb36237c7464bf4eb37298b5b9"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/4PYOFCBPQ4WVODATC76APE3JQ3/bundle.json","state_url":"https://pith.science/pith/4PYOFCBPQ4WVODATC76APE3JQ3/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/4PYOFCBPQ4WVODATC76APE3JQ3/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":"2026-05-31T06:12:13Z","links":{"resolver":"https://pith.science/pith/4PYOFCBPQ4WVODATC76APE3JQ3","bundle":"https://pith.science/pith/4PYOFCBPQ4WVODATC76APE3JQ3/bundle.json","state":"https://pith.science/pith/4PYOFCBPQ4WVODATC76APE3JQ3/state.json","well_known_bundle":"https://pith.science/.well-known/pith/4PYOFCBPQ4WVODATC76APE3JQ3/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:4PYOFCBPQ4WVODATC76APE3JQ3","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":"5bd51f72f4fd41495b076cab9b2b7d862d68d7ad7b695b51798fe304908abe41","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-12-06T01:58:05Z","title_canon_sha256":"6bd6425b04f900beae3c7ecf0f197c2eabab52956c59d92192330b0d8ec7c71a"},"schema_version":"1.0","source":{"id":"1612.01628","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1612.01628","created_at":"2026-05-18T00:05:14Z"},{"alias_kind":"arxiv_version","alias_value":"1612.01628v2","created_at":"2026-05-18T00:05:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1612.01628","created_at":"2026-05-18T00:05:14Z"},{"alias_kind":"pith_short_12","alias_value":"4PYOFCBPQ4WV","created_at":"2026-05-18T12:29:58Z"},{"alias_kind":"pith_short_16","alias_value":"4PYOFCBPQ4WVODAT","created_at":"2026-05-18T12:29:58Z"},{"alias_kind":"pith_short_8","alias_value":"4PYOFCBP","created_at":"2026-05-18T12:29:58Z"}],"graph_snapshots":[{"event_id":"sha256:9e4b1d52fe3bc629d13c7357ac5c71ab0c6b8dcb36237c7464bf4eb37298b5b9","target":"graph","created_at":"2026-05-18T00:05:14Z","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 study function spaces and extension results in relation with Dirichlet problems involving integrodifferential operators. For such problems, data are prescribed on the complement of a given domain in the Euclidean space. We introduce a function space that serves as a trace space for nonlocal Dirichlet problems and study related extension results.","authors_text":"Bartlomiej Dyda, Moritz Kassmann","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-12-06T01:58:05Z","title":"Function spaces and extension results for nonlocal Dirichlet problems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1612.01628","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":"sha256:975ba65aac4c41507ad622cc6edf5aec2e79ac3eae3ed68c5e8419442ce3aa81","target":"record","created_at":"2026-05-18T00:05:14Z","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":"5bd51f72f4fd41495b076cab9b2b7d862d68d7ad7b695b51798fe304908abe41","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-12-06T01:58:05Z","title_canon_sha256":"6bd6425b04f900beae3c7ecf0f197c2eabab52956c59d92192330b0d8ec7c71a"},"schema_version":"1.0","source":{"id":"1612.01628","kind":"arxiv","version":2}},"canonical_sha256":"e3f0e2882f872d570c1317fc07936986de05af4ef82fc74e4ddf6c4172a7ef86","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e3f0e2882f872d570c1317fc07936986de05af4ef82fc74e4ddf6c4172a7ef86","first_computed_at":"2026-05-18T00:05:14.737523Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:05:14.737523Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"iqQV6JgZbqsHnSwowusjr6Hirq1ZL+A5dRqaZKMq2bwoz9rBAwz8KolpFiWAC45I5+NSNi4gbCI8i5rzNe45CA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:05:14.737993Z","signed_message":"canonical_sha256_bytes"},"source_id":"1612.01628","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:975ba65aac4c41507ad622cc6edf5aec2e79ac3eae3ed68c5e8419442ce3aa81","sha256:9e4b1d52fe3bc629d13c7357ac5c71ab0c6b8dcb36237c7464bf4eb37298b5b9"],"state_sha256":"5da9ff725cb4cd68f5a5c9eea20f5c6a6679269bf2520c06567e3cac1250fb46"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"fWiQuHZ8bteCAaH00UvLKF/nvfcEvcbzoXR9B1fLGg3h3+2tdJuTxwPafwddlM+a0nHi49XXwb6ds00uP1s/AQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-31T06:12:13.454081Z","bundle_sha256":"2c2ed29338a92012165d9bad3365e2ca11aa5007d1ab1f2f80c598f667b7874c"}}