{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:5BNVDIXVUKXRXIAFXHQWJFPOMD","short_pith_number":"pith:5BNVDIXV","canonical_record":{"source":{"id":"1205.6290","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2012-05-29T08:07:17Z","cross_cats_sorted":["math.RA"],"title_canon_sha256":"01d2674ac85cc37b01a3605ad0fc73b304ec0cb1fbbefe811723b6ebe75e9ab8","abstract_canon_sha256":"6690fe3087037dddb06cd5df0f8ae91b181b9f8b91d357b48849bd6ffcf41580"},"schema_version":"1.0"},"canonical_sha256":"e85b51a2f5a2af1ba005b9e16495ee60e3f462e7f6c1b1d5c0121e40b9257565","source":{"kind":"arxiv","id":"1205.6290","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1205.6290","created_at":"2026-05-18T00:12:06Z"},{"alias_kind":"arxiv_version","alias_value":"1205.6290v1","created_at":"2026-05-18T00:12:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1205.6290","created_at":"2026-05-18T00:12:06Z"},{"alias_kind":"pith_short_12","alias_value":"5BNVDIXVUKXR","created_at":"2026-05-18T12:26:53Z"},{"alias_kind":"pith_short_16","alias_value":"5BNVDIXVUKXRXIAF","created_at":"2026-05-18T12:26:53Z"},{"alias_kind":"pith_short_8","alias_value":"5BNVDIXV","created_at":"2026-05-18T12:26:53Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:5BNVDIXVUKXRXIAFXHQWJFPOMD","target":"record","payload":{"canonical_record":{"source":{"id":"1205.6290","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2012-05-29T08:07:17Z","cross_cats_sorted":["math.RA"],"title_canon_sha256":"01d2674ac85cc37b01a3605ad0fc73b304ec0cb1fbbefe811723b6ebe75e9ab8","abstract_canon_sha256":"6690fe3087037dddb06cd5df0f8ae91b181b9f8b91d357b48849bd6ffcf41580"},"schema_version":"1.0"},"canonical_sha256":"e85b51a2f5a2af1ba005b9e16495ee60e3f462e7f6c1b1d5c0121e40b9257565","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:12:06.708038Z","signature_b64":"6HQ5jU+xNp0sDjjNKW0cho4Zp1MFYXoLhfrIvl0UskdldTv/Ew18upmb79AgoLXmQVYbSQOrTelINaLEsQ0BDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e85b51a2f5a2af1ba005b9e16495ee60e3f462e7f6c1b1d5c0121e40b9257565","last_reissued_at":"2026-05-18T00:12:06.707506Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:12:06.707506Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1205.6290","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":"2026-05-18T00:12:06Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"AqP8zvrFUjYQEJBWqVs3uzgPLacgXbwTZeItNrKLC28akPhBU2zC+O0GD6j0uwnAIVlxqJ6E6kFqRwoyrbiHCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-29T16:52:48.392417Z"},"content_sha256":"fbd19464039ab0ee032f5953c25e4fa4d969df1727fab0f066603df5d80cfe84","schema_version":"1.0","event_id":"sha256:fbd19464039ab0ee032f5953c25e4fa4d969df1727fab0f066603df5d80cfe84"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:5BNVDIXVUKXRXIAFXHQWJFPOMD","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Volume Cauchy formulas for slice functions on real associative *-algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RA"],"primary_cat":"math.CV","authors_text":"Alessandro Perotti, Riccardo Ghiloni","submitted_at":"2012-05-29T08:07:17Z","abstract_excerpt":"We introduce a family of Cauchy integral formulas for slice and slice regular functions on a real associative *-algebra. For each suitable choice of a real vector subspace of the algebra, a different formula is given, in which the domains of integration are subsets of the subspace. In particular, in the quaternionic case, we get a volume Cauchy formula. In the Clifford algebra case, the choice of the paravector subspace R^(n+1) gives a volume Cauchy formula for slice monogenic functions."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1205.6290","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":"2026-05-18T00:12:06Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"KHc7NCUYe5InZHuoBhWgDDhOYCP5kMe9S7ZCZeaGiQpda+t2hyNo3bILkbY8OIFwDHntR8F+XGcuzQ+ebXgzBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-29T16:52:48.392775Z"},"content_sha256":"9b539e7476bf40ee0db1be7709b0cef91c228cdb0e78b1728fe9e58c2fa1d108","schema_version":"1.0","event_id":"sha256:9b539e7476bf40ee0db1be7709b0cef91c228cdb0e78b1728fe9e58c2fa1d108"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/5BNVDIXVUKXRXIAFXHQWJFPOMD/bundle.json","state_url":"https://pith.science/pith/5BNVDIXVUKXRXIAFXHQWJFPOMD/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/5BNVDIXVUKXRXIAFXHQWJFPOMD/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":"2026-05-29T16:52:48Z","links":{"resolver":"https://pith.science/pith/5BNVDIXVUKXRXIAFXHQWJFPOMD","bundle":"https://pith.science/pith/5BNVDIXVUKXRXIAFXHQWJFPOMD/bundle.json","state":"https://pith.science/pith/5BNVDIXVUKXRXIAFXHQWJFPOMD/state.json","well_known_bundle":"https://pith.science/.well-known/pith/5BNVDIXVUKXRXIAFXHQWJFPOMD/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:5BNVDIXVUKXRXIAFXHQWJFPOMD","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":"6690fe3087037dddb06cd5df0f8ae91b181b9f8b91d357b48849bd6ffcf41580","cross_cats_sorted":["math.RA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2012-05-29T08:07:17Z","title_canon_sha256":"01d2674ac85cc37b01a3605ad0fc73b304ec0cb1fbbefe811723b6ebe75e9ab8"},"schema_version":"1.0","source":{"id":"1205.6290","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1205.6290","created_at":"2026-05-18T00:12:06Z"},{"alias_kind":"arxiv_version","alias_value":"1205.6290v1","created_at":"2026-05-18T00:12:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1205.6290","created_at":"2026-05-18T00:12:06Z"},{"alias_kind":"pith_short_12","alias_value":"5BNVDIXVUKXR","created_at":"2026-05-18T12:26:53Z"},{"alias_kind":"pith_short_16","alias_value":"5BNVDIXVUKXRXIAF","created_at":"2026-05-18T12:26:53Z"},{"alias_kind":"pith_short_8","alias_value":"5BNVDIXV","created_at":"2026-05-18T12:26:53Z"}],"graph_snapshots":[{"event_id":"sha256:9b539e7476bf40ee0db1be7709b0cef91c228cdb0e78b1728fe9e58c2fa1d108","target":"graph","created_at":"2026-05-18T00:12:06Z","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 introduce a family of Cauchy integral formulas for slice and slice regular functions on a real associative *-algebra. For each suitable choice of a real vector subspace of the algebra, a different formula is given, in which the domains of integration are subsets of the subspace. In particular, in the quaternionic case, we get a volume Cauchy formula. In the Clifford algebra case, the choice of the paravector subspace R^(n+1) gives a volume Cauchy formula for slice monogenic functions.","authors_text":"Alessandro Perotti, Riccardo Ghiloni","cross_cats":["math.RA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2012-05-29T08:07:17Z","title":"Volume Cauchy formulas for slice functions on real associative *-algebras"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1205.6290","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:fbd19464039ab0ee032f5953c25e4fa4d969df1727fab0f066603df5d80cfe84","target":"record","created_at":"2026-05-18T00:12:06Z","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":"6690fe3087037dddb06cd5df0f8ae91b181b9f8b91d357b48849bd6ffcf41580","cross_cats_sorted":["math.RA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2012-05-29T08:07:17Z","title_canon_sha256":"01d2674ac85cc37b01a3605ad0fc73b304ec0cb1fbbefe811723b6ebe75e9ab8"},"schema_version":"1.0","source":{"id":"1205.6290","kind":"arxiv","version":1}},"canonical_sha256":"e85b51a2f5a2af1ba005b9e16495ee60e3f462e7f6c1b1d5c0121e40b9257565","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e85b51a2f5a2af1ba005b9e16495ee60e3f462e7f6c1b1d5c0121e40b9257565","first_computed_at":"2026-05-18T00:12:06.707506Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:12:06.707506Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"6HQ5jU+xNp0sDjjNKW0cho4Zp1MFYXoLhfrIvl0UskdldTv/Ew18upmb79AgoLXmQVYbSQOrTelINaLEsQ0BDw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:12:06.708038Z","signed_message":"canonical_sha256_bytes"},"source_id":"1205.6290","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:fbd19464039ab0ee032f5953c25e4fa4d969df1727fab0f066603df5d80cfe84","sha256:9b539e7476bf40ee0db1be7709b0cef91c228cdb0e78b1728fe9e58c2fa1d108"],"state_sha256":"f926d157e7013f81e425b1eff731f498db79893174db6d0cf261e6857b216696"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"VTJn8ENO+XVxg30+4bDJP9C5fCIGUJxgx5VS+CY8dC3Gs0g76c2tYwAQP/r8lUAL+mtIvATeWNW/1gGJhALwCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-29T16:52:48.394879Z","bundle_sha256":"c2f3bac506cb8932f84e9e60810af420e82cea931556eb606e0be615945c5bca"}}