{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:N2HNHVHX2Y4ECQU2K3OAYZUYES","short_pith_number":"pith:N2HNHVHX","canonical_record":{"source":{"id":"1701.07741","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2017-01-26T15:35:16Z","cross_cats_sorted":[],"title_canon_sha256":"25eca6329f88b32d551d9df103dd45d40747c5f5596f97050b82ba249077fb66","abstract_canon_sha256":"ea9bd2af90ce0277d0d7eb5ce65a69e5a5d9044df022c2e76cb8c82ba8f0974c"},"schema_version":"1.0"},"canonical_sha256":"6e8ed3d4f7d63841429a56dc0c669824b26bb5d40c98c5e19e1d4b0a9d35a779","source":{"kind":"arxiv","id":"1701.07741","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1701.07741","created_at":"2026-05-18T00:52:02Z"},{"alias_kind":"arxiv_version","alias_value":"1701.07741v1","created_at":"2026-05-18T00:52:02Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1701.07741","created_at":"2026-05-18T00:52:02Z"},{"alias_kind":"pith_short_12","alias_value":"N2HNHVHX2Y4E","created_at":"2026-05-18T12:31:31Z"},{"alias_kind":"pith_short_16","alias_value":"N2HNHVHX2Y4ECQU2","created_at":"2026-05-18T12:31:31Z"},{"alias_kind":"pith_short_8","alias_value":"N2HNHVHX","created_at":"2026-05-18T12:31:31Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:N2HNHVHX2Y4ECQU2K3OAYZUYES","target":"record","payload":{"canonical_record":{"source":{"id":"1701.07741","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2017-01-26T15:35:16Z","cross_cats_sorted":[],"title_canon_sha256":"25eca6329f88b32d551d9df103dd45d40747c5f5596f97050b82ba249077fb66","abstract_canon_sha256":"ea9bd2af90ce0277d0d7eb5ce65a69e5a5d9044df022c2e76cb8c82ba8f0974c"},"schema_version":"1.0"},"canonical_sha256":"6e8ed3d4f7d63841429a56dc0c669824b26bb5d40c98c5e19e1d4b0a9d35a779","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:52:02.707638Z","signature_b64":"6k7GLbN85anK5wXSylDHURLzxr1fDUGLbtJSVekEMU37jnrB4xQeoumeyaqvxddLA7eMpAgGK9VI+YKBT3nxBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6e8ed3d4f7d63841429a56dc0c669824b26bb5d40c98c5e19e1d4b0a9d35a779","last_reissued_at":"2026-05-18T00:52:02.707156Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:52:02.707156Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1701.07741","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":"2026-05-18T00:52:02Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Iz48/QFuHUnlnFped9Fwcf4bTQIwDcS8JSUUId/+n8PSspjGpsNeyb5mg1jnSADZKy5DBjMcgKnfESKJPFtECg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T16:54:04.783545Z"},"content_sha256":"71388ecfbea63557aec6d8f53df84c22676af97de707becae437726e93ce8f0e","schema_version":"1.0","event_id":"sha256:71388ecfbea63557aec6d8f53df84c22676af97de707becae437726e93ce8f0e"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:N2HNHVHX2Y4ECQU2K3OAYZUYES","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Spinorspaces in discrete Clifford analysis","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Hilde De Ridder, Tim Raeymaekers","submitted_at":"2017-01-26T15:35:16Z","abstract_excerpt":"In this paper we work in the `split' discrete Clifford analysis setting, i.e. the m-dimensional function theory concerning null-functions, defined on the grid Z^m, of the discrete Dirac operator D, involving both forward and backward differences, which factorizes the (discrete) Star-Laplacian (Delta = D^2). We show how the space M_k of discrete homogeneous spherical monogenics of degree k, is decomposable into 2^{2m-n} isomorphic irreducible representations with highest weight (k + 1/2, 1/2,...,1/2) in the odd-dimensional case and two times 2^{2m-n} isomorphic irreducible representations with "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1701.07741","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":"2026-05-18T00:52:02Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"nHbx0USPJwkgMNku5XeYhDnFaMvG9HP66hjBRFWnqSyLtI6f47MDaq25ZzlAmLRkOIJpfj7BM0EBBwNK8pXxDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T16:54:04.784260Z"},"content_sha256":"81bed8faf8d6aa34f2e3ff878bbcbe1c5c45e5a514a1c51bc22a6a0001ed4abc","schema_version":"1.0","event_id":"sha256:81bed8faf8d6aa34f2e3ff878bbcbe1c5c45e5a514a1c51bc22a6a0001ed4abc"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/N2HNHVHX2Y4ECQU2K3OAYZUYES/bundle.json","state_url":"https://pith.science/pith/N2HNHVHX2Y4ECQU2K3OAYZUYES/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/N2HNHVHX2Y4ECQU2K3OAYZUYES/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":"2026-06-11T16:54:04Z","links":{"resolver":"https://pith.science/pith/N2HNHVHX2Y4ECQU2K3OAYZUYES","bundle":"https://pith.science/pith/N2HNHVHX2Y4ECQU2K3OAYZUYES/bundle.json","state":"https://pith.science/pith/N2HNHVHX2Y4ECQU2K3OAYZUYES/state.json","well_known_bundle":"https://pith.science/.well-known/pith/N2HNHVHX2Y4ECQU2K3OAYZUYES/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:N2HNHVHX2Y4ECQU2K3OAYZUYES","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":"ea9bd2af90ce0277d0d7eb5ce65a69e5a5d9044df022c2e76cb8c82ba8f0974c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2017-01-26T15:35:16Z","title_canon_sha256":"25eca6329f88b32d551d9df103dd45d40747c5f5596f97050b82ba249077fb66"},"schema_version":"1.0","source":{"id":"1701.07741","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1701.07741","created_at":"2026-05-18T00:52:02Z"},{"alias_kind":"arxiv_version","alias_value":"1701.07741v1","created_at":"2026-05-18T00:52:02Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1701.07741","created_at":"2026-05-18T00:52:02Z"},{"alias_kind":"pith_short_12","alias_value":"N2HNHVHX2Y4E","created_at":"2026-05-18T12:31:31Z"},{"alias_kind":"pith_short_16","alias_value":"N2HNHVHX2Y4ECQU2","created_at":"2026-05-18T12:31:31Z"},{"alias_kind":"pith_short_8","alias_value":"N2HNHVHX","created_at":"2026-05-18T12:31:31Z"}],"graph_snapshots":[{"event_id":"sha256:81bed8faf8d6aa34f2e3ff878bbcbe1c5c45e5a514a1c51bc22a6a0001ed4abc","target":"graph","created_at":"2026-05-18T00:52:02Z","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 this paper we work in the `split' discrete Clifford analysis setting, i.e. the m-dimensional function theory concerning null-functions, defined on the grid Z^m, of the discrete Dirac operator D, involving both forward and backward differences, which factorizes the (discrete) Star-Laplacian (Delta = D^2). We show how the space M_k of discrete homogeneous spherical monogenics of degree k, is decomposable into 2^{2m-n} isomorphic irreducible representations with highest weight (k + 1/2, 1/2,...,1/2) in the odd-dimensional case and two times 2^{2m-n} isomorphic irreducible representations with ","authors_text":"Hilde De Ridder, Tim Raeymaekers","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2017-01-26T15:35:16Z","title":"Spinorspaces in discrete Clifford analysis"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1701.07741","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":"sha256:71388ecfbea63557aec6d8f53df84c22676af97de707becae437726e93ce8f0e","target":"record","created_at":"2026-05-18T00:52:02Z","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":"ea9bd2af90ce0277d0d7eb5ce65a69e5a5d9044df022c2e76cb8c82ba8f0974c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2017-01-26T15:35:16Z","title_canon_sha256":"25eca6329f88b32d551d9df103dd45d40747c5f5596f97050b82ba249077fb66"},"schema_version":"1.0","source":{"id":"1701.07741","kind":"arxiv","version":1}},"canonical_sha256":"6e8ed3d4f7d63841429a56dc0c669824b26bb5d40c98c5e19e1d4b0a9d35a779","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6e8ed3d4f7d63841429a56dc0c669824b26bb5d40c98c5e19e1d4b0a9d35a779","first_computed_at":"2026-05-18T00:52:02.707156Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:52:02.707156Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"6k7GLbN85anK5wXSylDHURLzxr1fDUGLbtJSVekEMU37jnrB4xQeoumeyaqvxddLA7eMpAgGK9VI+YKBT3nxBg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:52:02.707638Z","signed_message":"canonical_sha256_bytes"},"source_id":"1701.07741","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:71388ecfbea63557aec6d8f53df84c22676af97de707becae437726e93ce8f0e","sha256:81bed8faf8d6aa34f2e3ff878bbcbe1c5c45e5a514a1c51bc22a6a0001ed4abc"],"state_sha256":"d7ba4aefb332a9fdbf929652f23ce4afaa5b53db2bd6e16a8750377973fc2ff3"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"mSOKKrg3NkpeinZnTeaB3wgxvWm6wTta1Vp46G2+UdSZFs+V5+Ppl95iivrcf5nPgdmRBdb1sgVF/7uYetqIBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-11T16:54:04.788195Z","bundle_sha256":"31678a1fbad17c6680e200b5f472f3554ff016f67a0fdf52466434c7bcb5f0ae"}}