{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:CEBQ75JB43CZYQQH62AE3UT7CG","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":"c580d85ca125b6149acc4ed5adfa4f5a2877486ee6aff8980ddd1d00044fb4aa","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2024-01-10T02:55:24Z","title_canon_sha256":"caeebd0ad11afe2e0412f050ea61f137674a00cd318556112760de4018b51732"},"schema_version":"1.0","source":{"id":"2401.04895","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2401.04895","created_at":"2026-07-05T10:01:11Z"},{"alias_kind":"arxiv_version","alias_value":"2401.04895v2","created_at":"2026-07-05T10:01:11Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2401.04895","created_at":"2026-07-05T10:01:11Z"},{"alias_kind":"pith_short_12","alias_value":"CEBQ75JB43CZ","created_at":"2026-07-05T10:01:11Z"},{"alias_kind":"pith_short_16","alias_value":"CEBQ75JB43CZYQQH","created_at":"2026-07-05T10:01:11Z"},{"alias_kind":"pith_short_8","alias_value":"CEBQ75JB","created_at":"2026-07-05T10:01:11Z"}],"graph_snapshots":[{"event_id":"sha256:c860b7473f89b6b47cc075bdb45707891399b2a88214ef900b8ef565dc777783","target":"graph","created_at":"2026-07-05T10:01:11Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2401.04895/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"The primary objective of this paper is to establish an algebraic framework for the space of weakly slice regular functions over several quaternionic variables. We recently introduced a $*$-product that maintains the path-slice property within the class of path-slice functions. It is noteworthy that this $*$-product is directly applicable to weakly slice regular functions, as every slice regular function defined on a slice-open set inherently possesses path-slice properties. Building on this foundation, we propose a precise definition of an open neighborhood for a path $\\gamma$ in the path spac","authors_text":"Guangbin Ren, Ming Jin, Ting Yang, Xinyuan Dou","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2024-01-10T02:55:24Z","title":"Algebra of slice regular functions on non-symmetric domains in several quaternionic variables"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2401.04895","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":"sha256:6d7d3bfc587544b3361952af1d12b7f210d405b017aac0ce8c1bb4e896aab0d0","target":"record","created_at":"2026-07-05T10:01:11Z","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":"c580d85ca125b6149acc4ed5adfa4f5a2877486ee6aff8980ddd1d00044fb4aa","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2024-01-10T02:55:24Z","title_canon_sha256":"caeebd0ad11afe2e0412f050ea61f137674a00cd318556112760de4018b51732"},"schema_version":"1.0","source":{"id":"2401.04895","kind":"arxiv","version":2}},"canonical_sha256":"11030ff521e6c59c4207f6804dd27f11ac1327672ec4d23a5dba6496c7600b78","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"11030ff521e6c59c4207f6804dd27f11ac1327672ec4d23a5dba6496c7600b78","first_computed_at":"2026-07-05T10:01:11.388183Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T10:01:11.388183Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Iyrk0ThXoUt+p4+dxhomiRyIOc1cxtcsj6V/1+cRWw1qLXmGDAzE/nXMjiJidBgUpM3vOLwIdRJ+K3lyi/TfBg==","signature_status":"signed_v1","signed_at":"2026-07-05T10:01:11.388629Z","signed_message":"canonical_sha256_bytes"},"source_id":"2401.04895","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6d7d3bfc587544b3361952af1d12b7f210d405b017aac0ce8c1bb4e896aab0d0","sha256:c860b7473f89b6b47cc075bdb45707891399b2a88214ef900b8ef565dc777783"],"state_sha256":"a58c5b79bd4e493840e520eedb39c33c82bbf572aa7802aec1f7493085886a60"}