{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:ICC7HNP4O4HP5MN43KOS353WAD","short_pith_number":"pith:ICC7HNP4","canonical_record":{"source":{"id":"1111.2699","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2011-11-11T10:15:02Z","cross_cats_sorted":["math.AP","math.CV"],"title_canon_sha256":"8f1328ca9b3dca4c20e8158fce9a0546af6d344db13474bc69075c74df9ca29b","abstract_canon_sha256":"11f844b3c87104f98ada8c39c38858b326ea7b9570888519b856393d14c0c3f1"},"schema_version":"1.0"},"canonical_sha256":"4085f3b5fc770efeb1bcda9d2df77600fc246c0a7576c1f8cd929266bdb99b4c","source":{"kind":"arxiv","id":"1111.2699","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1111.2699","created_at":"2026-05-18T04:08:32Z"},{"alias_kind":"arxiv_version","alias_value":"1111.2699v1","created_at":"2026-05-18T04:08:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1111.2699","created_at":"2026-05-18T04:08:32Z"},{"alias_kind":"pith_short_12","alias_value":"ICC7HNP4O4HP","created_at":"2026-05-18T12:26:30Z"},{"alias_kind":"pith_short_16","alias_value":"ICC7HNP4O4HP5MN4","created_at":"2026-05-18T12:26:30Z"},{"alias_kind":"pith_short_8","alias_value":"ICC7HNP4","created_at":"2026-05-18T12:26:30Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:ICC7HNP4O4HP5MN43KOS353WAD","target":"record","payload":{"canonical_record":{"source":{"id":"1111.2699","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2011-11-11T10:15:02Z","cross_cats_sorted":["math.AP","math.CV"],"title_canon_sha256":"8f1328ca9b3dca4c20e8158fce9a0546af6d344db13474bc69075c74df9ca29b","abstract_canon_sha256":"11f844b3c87104f98ada8c39c38858b326ea7b9570888519b856393d14c0c3f1"},"schema_version":"1.0"},"canonical_sha256":"4085f3b5fc770efeb1bcda9d2df77600fc246c0a7576c1f8cd929266bdb99b4c","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:08:32.956777Z","signature_b64":"KHUpunlD30d8g8lhuaaEFklsR+vygS2T8Tg1xAOpgeHkV5Nu1sUi7b42W8W1iQT6e15jxUq8q6mkRJb8Arr0DA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4085f3b5fc770efeb1bcda9d2df77600fc246c0a7576c1f8cd929266bdb99b4c","last_reissued_at":"2026-05-18T04:08:32.956247Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:08:32.956247Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1111.2699","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":"2026-05-18T04:08:32Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"B5FONNikOe4meUJkRZFBCLQLDqTVVvVIApwNGbZypsHtf8c3WsOF5UrUo/rDjT5DnaFdHMaLGsUH2i/dcAtoBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T09:42:43.184225Z"},"content_sha256":"6f961ebca32f681bb48db9ee5cf5850934789949e6e3d4f96eaed29ff0ee098c","schema_version":"1.0","event_id":"sha256:6f961ebca32f681bb48db9ee5cf5850934789949e6e3d4f96eaed29ff0ee098c"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:ICC7HNP4O4HP5MN43KOS353WAD","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Holomorphic Continuation via Laplace-Fourier series","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP","math.CV"],"primary_cat":"math.FA","authors_text":"H. Render, O. Kounchev","submitted_at":"2011-11-11T10:15:02Z","abstract_excerpt":"Let $B_{R}$ be the ball in the euclidean space $\\mathbb{R}^{n}$ with center 0 and radius $R$ and let $f$ be a complex-valued, infinitely differentiable function on $B_{R}.$ We show that the Laplace-Fourier series of $f$ has a holomorphic extension which converges compactly in the Lie ball $\\hat {B_{R}}$ in the complex space $\\mathbb{C}^{n}$ when one assumes a natural estimate for the Laplace-Fourier coefficients."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1111.2699","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":"2026-05-18T04:08:32Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"qwmknbzjkhnUUYMy6nVXk68FrzB9THHWnOB7/MxoYuXQELQU8+0tr7k7JdtJ6D8a4cJIzarI6TZuVMaxsbm3Dg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T09:42:43.184588Z"},"content_sha256":"1b836f13ee36ff178e7eae855c7d7c57ec11479ca15abc55c7bd32e2e77ad0c9","schema_version":"1.0","event_id":"sha256:1b836f13ee36ff178e7eae855c7d7c57ec11479ca15abc55c7bd32e2e77ad0c9"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/ICC7HNP4O4HP5MN43KOS353WAD/bundle.json","state_url":"https://pith.science/pith/ICC7HNP4O4HP5MN43KOS353WAD/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/ICC7HNP4O4HP5MN43KOS353WAD/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":"2026-06-03T09:42:43Z","links":{"resolver":"https://pith.science/pith/ICC7HNP4O4HP5MN43KOS353WAD","bundle":"https://pith.science/pith/ICC7HNP4O4HP5MN43KOS353WAD/bundle.json","state":"https://pith.science/pith/ICC7HNP4O4HP5MN43KOS353WAD/state.json","well_known_bundle":"https://pith.science/.well-known/pith/ICC7HNP4O4HP5MN43KOS353WAD/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:ICC7HNP4O4HP5MN43KOS353WAD","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":"11f844b3c87104f98ada8c39c38858b326ea7b9570888519b856393d14c0c3f1","cross_cats_sorted":["math.AP","math.CV"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2011-11-11T10:15:02Z","title_canon_sha256":"8f1328ca9b3dca4c20e8158fce9a0546af6d344db13474bc69075c74df9ca29b"},"schema_version":"1.0","source":{"id":"1111.2699","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1111.2699","created_at":"2026-05-18T04:08:32Z"},{"alias_kind":"arxiv_version","alias_value":"1111.2699v1","created_at":"2026-05-18T04:08:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1111.2699","created_at":"2026-05-18T04:08:32Z"},{"alias_kind":"pith_short_12","alias_value":"ICC7HNP4O4HP","created_at":"2026-05-18T12:26:30Z"},{"alias_kind":"pith_short_16","alias_value":"ICC7HNP4O4HP5MN4","created_at":"2026-05-18T12:26:30Z"},{"alias_kind":"pith_short_8","alias_value":"ICC7HNP4","created_at":"2026-05-18T12:26:30Z"}],"graph_snapshots":[{"event_id":"sha256:1b836f13ee36ff178e7eae855c7d7c57ec11479ca15abc55c7bd32e2e77ad0c9","target":"graph","created_at":"2026-05-18T04:08:32Z","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":"Let $B_{R}$ be the ball in the euclidean space $\\mathbb{R}^{n}$ with center 0 and radius $R$ and let $f$ be a complex-valued, infinitely differentiable function on $B_{R}.$ We show that the Laplace-Fourier series of $f$ has a holomorphic extension which converges compactly in the Lie ball $\\hat {B_{R}}$ in the complex space $\\mathbb{C}^{n}$ when one assumes a natural estimate for the Laplace-Fourier coefficients.","authors_text":"H. Render, O. Kounchev","cross_cats":["math.AP","math.CV"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2011-11-11T10:15:02Z","title":"Holomorphic Continuation via Laplace-Fourier series"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1111.2699","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":"sha256:6f961ebca32f681bb48db9ee5cf5850934789949e6e3d4f96eaed29ff0ee098c","target":"record","created_at":"2026-05-18T04:08:32Z","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":"11f844b3c87104f98ada8c39c38858b326ea7b9570888519b856393d14c0c3f1","cross_cats_sorted":["math.AP","math.CV"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2011-11-11T10:15:02Z","title_canon_sha256":"8f1328ca9b3dca4c20e8158fce9a0546af6d344db13474bc69075c74df9ca29b"},"schema_version":"1.0","source":{"id":"1111.2699","kind":"arxiv","version":1}},"canonical_sha256":"4085f3b5fc770efeb1bcda9d2df77600fc246c0a7576c1f8cd929266bdb99b4c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4085f3b5fc770efeb1bcda9d2df77600fc246c0a7576c1f8cd929266bdb99b4c","first_computed_at":"2026-05-18T04:08:32.956247Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:08:32.956247Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"KHUpunlD30d8g8lhuaaEFklsR+vygS2T8Tg1xAOpgeHkV5Nu1sUi7b42W8W1iQT6e15jxUq8q6mkRJb8Arr0DA==","signature_status":"signed_v1","signed_at":"2026-05-18T04:08:32.956777Z","signed_message":"canonical_sha256_bytes"},"source_id":"1111.2699","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6f961ebca32f681bb48db9ee5cf5850934789949e6e3d4f96eaed29ff0ee098c","sha256:1b836f13ee36ff178e7eae855c7d7c57ec11479ca15abc55c7bd32e2e77ad0c9"],"state_sha256":"0c36cf25c61d2aaacea6c7f3a79be79b3754714c9d01c793d591dc466ec317ca"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"aNE85gdY4HxyErrEGaRe2AAPzZaD4KdKnk/YiOap6BLj8uFLYnlY3XLfAltLpwn36DVhpC5g9yHjaF+zaxZEAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-03T09:42:43.186666Z","bundle_sha256":"532590acf81f130abf1a6275b8b5d1f16afe2f10a25ca0b352bfb4130c40fd3f"}}