{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:55MSMWVJNLVTQOTNQJJXMUPL7Z","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":"9502bc14e66841fda3512f01c1c3382fbe6d8028bf1847f22946148e24b22ac9","cross_cats_sorted":["math.CA","math.CV"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2014-03-31T07:19:22Z","title_canon_sha256":"8aedd3f74f45dbdb25fb34b5c35df8475b52b227c9db8dd1b8f657d8c59ed368"},"schema_version":"1.0","source":{"id":"1403.7891","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1403.7891","created_at":"2026-05-18T01:03:24Z"},{"alias_kind":"arxiv_version","alias_value":"1403.7891v1","created_at":"2026-05-18T01:03:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1403.7891","created_at":"2026-05-18T01:03:24Z"},{"alias_kind":"pith_short_12","alias_value":"55MSMWVJNLVT","created_at":"2026-05-18T12:28:14Z"},{"alias_kind":"pith_short_16","alias_value":"55MSMWVJNLVTQOTN","created_at":"2026-05-18T12:28:14Z"},{"alias_kind":"pith_short_8","alias_value":"55MSMWVJ","created_at":"2026-05-18T12:28:14Z"}],"graph_snapshots":[{"event_id":"sha256:c0431abf8972a9aba8f7e2db8ae36778a86cce37632ff31a56ddd45eafd2a96d","target":"graph","created_at":"2026-05-18T01:03:24Z","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":"In the framework of Clifford analysis, a chain of harmonic and monogenic potentials in the upper half of (m+1)-dimensional Euclidean space was recently constructed, including a higher dimensional analogue of the logarithmic function in the complex plane, and their distributional boundary values were computed. In this paper we determine these potentials in lower half-space, and investigate whether they can be extended through the boundary R^m. This is a stepping stone to the representation of a doubly infinite sequence of distributions in R^m, consisting of positive and negative integer powers ","authors_text":"Fred Brackx, Hendrik De Bie, Hennie De Schepper","cross_cats":["math.CA","math.CV"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2014-03-31T07:19:22Z","title":"Representation of Distributions by Harmonic and Monogenic Potentials in Euclidean Space"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1403.7891","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:c3a9d5b1ad1ab797b308541ae6790badcc66120ea166f184bf0a966143040a65","target":"record","created_at":"2026-05-18T01:03:24Z","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":"9502bc14e66841fda3512f01c1c3382fbe6d8028bf1847f22946148e24b22ac9","cross_cats_sorted":["math.CA","math.CV"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2014-03-31T07:19:22Z","title_canon_sha256":"8aedd3f74f45dbdb25fb34b5c35df8475b52b227c9db8dd1b8f657d8c59ed368"},"schema_version":"1.0","source":{"id":"1403.7891","kind":"arxiv","version":1}},"canonical_sha256":"ef59265aa96aeb383a6d82537651ebfe78c506c4184eecba633f3b5ddc4cce25","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ef59265aa96aeb383a6d82537651ebfe78c506c4184eecba633f3b5ddc4cce25","first_computed_at":"2026-05-18T01:03:24.226215Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:03:24.226215Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"x/+ecAcPwmBPep+UqGOtGQb77Avra+lCYhRLxLYIrzC1RX504iDbMU6/coYuB4bmDRPfBQscA7gaLW6E/0gHDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:03:24.226780Z","signed_message":"canonical_sha256_bytes"},"source_id":"1403.7891","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c3a9d5b1ad1ab797b308541ae6790badcc66120ea166f184bf0a966143040a65","sha256:c0431abf8972a9aba8f7e2db8ae36778a86cce37632ff31a56ddd45eafd2a96d"],"state_sha256":"ec649cebf6fa6b492e4c8339f6cc69e9f74ebdeffd8df83ced5d14566d08cfe9"}