{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:CFPTITNE3ENHSU6Y3QPQ26QOCQ","short_pith_number":"pith:CFPTITNE","canonical_record":{"source":{"id":"1607.08746","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-07-29T09:43:47Z","cross_cats_sorted":["math.CA"],"title_canon_sha256":"1b1b4db307005afa90b244ddd1ab6b80ad5abc1bde00b7e05e05090cab4a9af4","abstract_canon_sha256":"c6375779380bbfbf97479d1007d61385c7b14e40cbb32af163b1618f0c9845dd"},"schema_version":"1.0"},"canonical_sha256":"115f344da4d91a7953d8dc1f0d7a0e1405494cab00d57cb7bdcfd9a2deea5b61","source":{"kind":"arxiv","id":"1607.08746","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1607.08746","created_at":"2026-05-18T01:09:54Z"},{"alias_kind":"arxiv_version","alias_value":"1607.08746v1","created_at":"2026-05-18T01:09:54Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1607.08746","created_at":"2026-05-18T01:09:54Z"},{"alias_kind":"pith_short_12","alias_value":"CFPTITNE3ENH","created_at":"2026-05-18T12:30:09Z"},{"alias_kind":"pith_short_16","alias_value":"CFPTITNE3ENHSU6Y","created_at":"2026-05-18T12:30:09Z"},{"alias_kind":"pith_short_8","alias_value":"CFPTITNE","created_at":"2026-05-18T12:30:09Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:CFPTITNE3ENHSU6Y3QPQ26QOCQ","target":"record","payload":{"canonical_record":{"source":{"id":"1607.08746","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-07-29T09:43:47Z","cross_cats_sorted":["math.CA"],"title_canon_sha256":"1b1b4db307005afa90b244ddd1ab6b80ad5abc1bde00b7e05e05090cab4a9af4","abstract_canon_sha256":"c6375779380bbfbf97479d1007d61385c7b14e40cbb32af163b1618f0c9845dd"},"schema_version":"1.0"},"canonical_sha256":"115f344da4d91a7953d8dc1f0d7a0e1405494cab00d57cb7bdcfd9a2deea5b61","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:09:54.388111Z","signature_b64":"WLjz1txL4u/gix9GXNZsHOEYq7qXGq6NsdnoeTe8kh7I77jaBPHR6H47VKwok26rjpl3TwKzoAL8paXTcC8dBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"115f344da4d91a7953d8dc1f0d7a0e1405494cab00d57cb7bdcfd9a2deea5b61","last_reissued_at":"2026-05-18T01:09:54.387401Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:09:54.387401Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1607.08746","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":"2026-05-18T01:09:54Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"gXfZhQvMwZEKnb7CAJC1Z2ybWtBrONHWrtGm/BcQCEB6JjCoqDYoXpnG+GJ6C6IPCjSY5PKF//SpAnXwmkF2AQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T01:18:19.979330Z"},"content_sha256":"599f61da14403609e5b4c49113602cd2bea07f7548e8183857fe653bed417e12","schema_version":"1.0","event_id":"sha256:599f61da14403609e5b4c49113602cd2bea07f7548e8183857fe653bed417e12"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:CFPTITNE3ENHSU6Y3QPQ26QOCQ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On the Green function and Poisson integrals of the Dunkl Laplacian","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CA"],"primary_cat":"math.AP","authors_text":"Margit R\\\"osler, Piotr Graczyk, Tomasz Luks","submitted_at":"2016-07-29T09:43:47Z","abstract_excerpt":"We prove the existence and study properties of the Green function of the unit ball for the Dunkl Laplacian $\\Delta_k$ in $\\mathbb{R}^d$. As applications we derive the Poisson-Jensen formula for $\\Delta_k$-subharmonic functions and Hardy-Stein identities for the Poisson integrals of $\\Delta_k$. We also obtain sharp estimates of the Newton potential kernel, Green function and Poisson kernel in the rank one case in $\\mathbb{R}^d$. These estimates contrast sharply with the well-known results in the potential theory of the classical Laplacian."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1607.08746","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":"2026-05-18T01:09:54Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"rBaayCAoNWoWnf91ZB2VqOTzhzkNaxVcequZBfjGlPOF79OqR7mgYFfI+Q85KRwnXFTmy2m+jvJxiZPKg8mZCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T01:18:19.979709Z"},"content_sha256":"4062e03cf51ef897d8efb7fa89057aa847c9bceec9809291e89a0f09fd8f12fa","schema_version":"1.0","event_id":"sha256:4062e03cf51ef897d8efb7fa89057aa847c9bceec9809291e89a0f09fd8f12fa"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/CFPTITNE3ENHSU6Y3QPQ26QOCQ/bundle.json","state_url":"https://pith.science/pith/CFPTITNE3ENHSU6Y3QPQ26QOCQ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/CFPTITNE3ENHSU6Y3QPQ26QOCQ/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":"2026-06-05T01:18:19Z","links":{"resolver":"https://pith.science/pith/CFPTITNE3ENHSU6Y3QPQ26QOCQ","bundle":"https://pith.science/pith/CFPTITNE3ENHSU6Y3QPQ26QOCQ/bundle.json","state":"https://pith.science/pith/CFPTITNE3ENHSU6Y3QPQ26QOCQ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/CFPTITNE3ENHSU6Y3QPQ26QOCQ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:CFPTITNE3ENHSU6Y3QPQ26QOCQ","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":"c6375779380bbfbf97479d1007d61385c7b14e40cbb32af163b1618f0c9845dd","cross_cats_sorted":["math.CA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-07-29T09:43:47Z","title_canon_sha256":"1b1b4db307005afa90b244ddd1ab6b80ad5abc1bde00b7e05e05090cab4a9af4"},"schema_version":"1.0","source":{"id":"1607.08746","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1607.08746","created_at":"2026-05-18T01:09:54Z"},{"alias_kind":"arxiv_version","alias_value":"1607.08746v1","created_at":"2026-05-18T01:09:54Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1607.08746","created_at":"2026-05-18T01:09:54Z"},{"alias_kind":"pith_short_12","alias_value":"CFPTITNE3ENH","created_at":"2026-05-18T12:30:09Z"},{"alias_kind":"pith_short_16","alias_value":"CFPTITNE3ENHSU6Y","created_at":"2026-05-18T12:30:09Z"},{"alias_kind":"pith_short_8","alias_value":"CFPTITNE","created_at":"2026-05-18T12:30:09Z"}],"graph_snapshots":[{"event_id":"sha256:4062e03cf51ef897d8efb7fa89057aa847c9bceec9809291e89a0f09fd8f12fa","target":"graph","created_at":"2026-05-18T01:09:54Z","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 prove the existence and study properties of the Green function of the unit ball for the Dunkl Laplacian $\\Delta_k$ in $\\mathbb{R}^d$. As applications we derive the Poisson-Jensen formula for $\\Delta_k$-subharmonic functions and Hardy-Stein identities for the Poisson integrals of $\\Delta_k$. We also obtain sharp estimates of the Newton potential kernel, Green function and Poisson kernel in the rank one case in $\\mathbb{R}^d$. These estimates contrast sharply with the well-known results in the potential theory of the classical Laplacian.","authors_text":"Margit R\\\"osler, Piotr Graczyk, Tomasz Luks","cross_cats":["math.CA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-07-29T09:43:47Z","title":"On the Green function and Poisson integrals of the Dunkl Laplacian"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1607.08746","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":"sha256:599f61da14403609e5b4c49113602cd2bea07f7548e8183857fe653bed417e12","target":"record","created_at":"2026-05-18T01:09:54Z","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":"c6375779380bbfbf97479d1007d61385c7b14e40cbb32af163b1618f0c9845dd","cross_cats_sorted":["math.CA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-07-29T09:43:47Z","title_canon_sha256":"1b1b4db307005afa90b244ddd1ab6b80ad5abc1bde00b7e05e05090cab4a9af4"},"schema_version":"1.0","source":{"id":"1607.08746","kind":"arxiv","version":1}},"canonical_sha256":"115f344da4d91a7953d8dc1f0d7a0e1405494cab00d57cb7bdcfd9a2deea5b61","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"115f344da4d91a7953d8dc1f0d7a0e1405494cab00d57cb7bdcfd9a2deea5b61","first_computed_at":"2026-05-18T01:09:54.387401Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:09:54.387401Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"WLjz1txL4u/gix9GXNZsHOEYq7qXGq6NsdnoeTe8kh7I77jaBPHR6H47VKwok26rjpl3TwKzoAL8paXTcC8dBA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:09:54.388111Z","signed_message":"canonical_sha256_bytes"},"source_id":"1607.08746","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:599f61da14403609e5b4c49113602cd2bea07f7548e8183857fe653bed417e12","sha256:4062e03cf51ef897d8efb7fa89057aa847c9bceec9809291e89a0f09fd8f12fa"],"state_sha256":"5d1829477e5f61596c0e7644ec7fb2fa8b37377f1787328b795dc956241bc328"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"WY7b3mmYPqzRO0fHuVTCk7kCeNB+VAZNSflKKv3/mWA7de21kUJitAteI0ckCpkoGhEgNuWm+a7J2o4AYdNQBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-05T01:18:19.983144Z","bundle_sha256":"fa5356e221d546bf549191193ea246b8f7370cf95e14824533394d35210167bb"}}