{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:6PENOU7573NMGXKXBNCNNPIQOO","short_pith_number":"pith:6PENOU75","canonical_record":{"source":{"id":"1810.02394","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2018-10-04T19:13:51Z","cross_cats_sorted":[],"title_canon_sha256":"25cb3f80cded78eb23b3e5098fdf203b505c8bd917020487746b03003029b09c","abstract_canon_sha256":"233c8b9826f17d668f20ff5886dce1b496410f80bdccaa5e14ddcf53888f6b79"},"schema_version":"1.0"},"canonical_sha256":"f3c8d753fdfedac35d570b44d6bd1073962f5f8e0c65d56a64ae031c196a7415","source":{"kind":"arxiv","id":"1810.02394","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1810.02394","created_at":"2026-05-18T00:04:02Z"},{"alias_kind":"arxiv_version","alias_value":"1810.02394v1","created_at":"2026-05-18T00:04:02Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1810.02394","created_at":"2026-05-18T00:04:02Z"},{"alias_kind":"pith_short_12","alias_value":"6PENOU7573NM","created_at":"2026-05-18T12:32:11Z"},{"alias_kind":"pith_short_16","alias_value":"6PENOU7573NMGXKX","created_at":"2026-05-18T12:32:11Z"},{"alias_kind":"pith_short_8","alias_value":"6PENOU75","created_at":"2026-05-18T12:32:11Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:6PENOU7573NMGXKXBNCNNPIQOO","target":"record","payload":{"canonical_record":{"source":{"id":"1810.02394","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2018-10-04T19:13:51Z","cross_cats_sorted":[],"title_canon_sha256":"25cb3f80cded78eb23b3e5098fdf203b505c8bd917020487746b03003029b09c","abstract_canon_sha256":"233c8b9826f17d668f20ff5886dce1b496410f80bdccaa5e14ddcf53888f6b79"},"schema_version":"1.0"},"canonical_sha256":"f3c8d753fdfedac35d570b44d6bd1073962f5f8e0c65d56a64ae031c196a7415","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:04:02.011536Z","signature_b64":"Ue4tXMie/FH4bfQvawpbYwb7+sbCWCmO4H2Aaoy4Jcaz4O+oQM7ui7ehJAy72BKU4j1PTludwm+AybFLXa8FAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f3c8d753fdfedac35d570b44d6bd1073962f5f8e0c65d56a64ae031c196a7415","last_reissued_at":"2026-05-18T00:04:02.010906Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:04:02.010906Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1810.02394","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":"2026-05-18T00:04:02Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"RZQ5NmcVDGlRm0rJUJToYolxbxo87naFNnrhSTXQQ3uZ0l0WPx52tPwOF+CmQN+eyQRexURiw7WjzAGTFAsfCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-26T09:33:00.718560Z"},"content_sha256":"492c7bfbd025a0513f7c3fe82364561c2a6d2ccdea9723aabcd9296c771dc11e","schema_version":"1.0","event_id":"sha256:492c7bfbd025a0513f7c3fe82364561c2a6d2ccdea9723aabcd9296c771dc11e"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:6PENOU7573NMGXKXBNCNNPIQOO","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On the estimates of the Dunkl Kernel","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Abdessalem Gasmi, B\\'echir Amri","submitted_at":"2018-10-04T19:13:51Z","abstract_excerpt":"In this paper, we are interested in the estimates of the Dunkl Kernel on some special sets, following the work of M.F.E. de Jeu and M. R\\\"{o}sler in \\cite{R3}."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1810.02394","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":"2026-05-18T00:04:02Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"2W0QUpfQDEaqRKtk/7rP9YyF2yPbdDMnWKJYrUhMijPtM6f3DUcgRQBTZybmEr6X4dGY+hdwhg6BZ/HAmu50Bw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-26T09:33:00.718902Z"},"content_sha256":"6bac91d496adac4e3216f6c8097ab4029a2fa22bab64c32606ad0f313ee38c3a","schema_version":"1.0","event_id":"sha256:6bac91d496adac4e3216f6c8097ab4029a2fa22bab64c32606ad0f313ee38c3a"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/6PENOU7573NMGXKXBNCNNPIQOO/bundle.json","state_url":"https://pith.science/pith/6PENOU7573NMGXKXBNCNNPIQOO/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/6PENOU7573NMGXKXBNCNNPIQOO/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":"2026-06-26T09:33:00Z","links":{"resolver":"https://pith.science/pith/6PENOU7573NMGXKXBNCNNPIQOO","bundle":"https://pith.science/pith/6PENOU7573NMGXKXBNCNNPIQOO/bundle.json","state":"https://pith.science/pith/6PENOU7573NMGXKXBNCNNPIQOO/state.json","well_known_bundle":"https://pith.science/.well-known/pith/6PENOU7573NMGXKXBNCNNPIQOO/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:6PENOU7573NMGXKXBNCNNPIQOO","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":"233c8b9826f17d668f20ff5886dce1b496410f80bdccaa5e14ddcf53888f6b79","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2018-10-04T19:13:51Z","title_canon_sha256":"25cb3f80cded78eb23b3e5098fdf203b505c8bd917020487746b03003029b09c"},"schema_version":"1.0","source":{"id":"1810.02394","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1810.02394","created_at":"2026-05-18T00:04:02Z"},{"alias_kind":"arxiv_version","alias_value":"1810.02394v1","created_at":"2026-05-18T00:04:02Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1810.02394","created_at":"2026-05-18T00:04:02Z"},{"alias_kind":"pith_short_12","alias_value":"6PENOU7573NM","created_at":"2026-05-18T12:32:11Z"},{"alias_kind":"pith_short_16","alias_value":"6PENOU7573NMGXKX","created_at":"2026-05-18T12:32:11Z"},{"alias_kind":"pith_short_8","alias_value":"6PENOU75","created_at":"2026-05-18T12:32:11Z"}],"graph_snapshots":[{"event_id":"sha256:6bac91d496adac4e3216f6c8097ab4029a2fa22bab64c32606ad0f313ee38c3a","target":"graph","created_at":"2026-05-18T00:04:02Z","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 are interested in the estimates of the Dunkl Kernel on some special sets, following the work of M.F.E. de Jeu and M. R\\\"{o}sler in \\cite{R3}.","authors_text":"Abdessalem Gasmi, B\\'echir Amri","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2018-10-04T19:13:51Z","title":"On the estimates of the Dunkl Kernel"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1810.02394","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":"sha256:492c7bfbd025a0513f7c3fe82364561c2a6d2ccdea9723aabcd9296c771dc11e","target":"record","created_at":"2026-05-18T00:04:02Z","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":"233c8b9826f17d668f20ff5886dce1b496410f80bdccaa5e14ddcf53888f6b79","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2018-10-04T19:13:51Z","title_canon_sha256":"25cb3f80cded78eb23b3e5098fdf203b505c8bd917020487746b03003029b09c"},"schema_version":"1.0","source":{"id":"1810.02394","kind":"arxiv","version":1}},"canonical_sha256":"f3c8d753fdfedac35d570b44d6bd1073962f5f8e0c65d56a64ae031c196a7415","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f3c8d753fdfedac35d570b44d6bd1073962f5f8e0c65d56a64ae031c196a7415","first_computed_at":"2026-05-18T00:04:02.010906Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:04:02.010906Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Ue4tXMie/FH4bfQvawpbYwb7+sbCWCmO4H2Aaoy4Jcaz4O+oQM7ui7ehJAy72BKU4j1PTludwm+AybFLXa8FAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:04:02.011536Z","signed_message":"canonical_sha256_bytes"},"source_id":"1810.02394","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:492c7bfbd025a0513f7c3fe82364561c2a6d2ccdea9723aabcd9296c771dc11e","sha256:6bac91d496adac4e3216f6c8097ab4029a2fa22bab64c32606ad0f313ee38c3a"],"state_sha256":"798a8d59aa0063f43db2f6fdc6912731101a2462605fa2a78978db90b443d355"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+hZMcNITOXRpXgOOFaES3N3m32+E07m5euH+kz+PcQ576OxwIBKmMxATDc65+3LBjjzqLMYh0T9i9lEF6ZYcDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-26T09:33:00.721034Z","bundle_sha256":"fc2bc07a3e71822921479ecd6567b80071651551bed77953509f28d6c59b9fdc"}}