{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:FKGMVJNP7BTTCAVCCESEHFN67A","short_pith_number":"pith:FKGMVJNP","canonical_record":{"source":{"id":"1409.0197","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2014-08-31T09:10:50Z","cross_cats_sorted":["math.CV"],"title_canon_sha256":"516a2b501ab565480fa5e214b4a357d57cec7a242241e0d18fbf5b848b16b5f1","abstract_canon_sha256":"0e71eb8e3012adec1c6d6c47de3e4adec312c0cad5bad1164217e4ffe715da96"},"schema_version":"1.0"},"canonical_sha256":"2a8ccaa5aff8673102a211244395bef805107b68b9e9d3981c9a660d5e0d49ad","source":{"kind":"arxiv","id":"1409.0197","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1409.0197","created_at":"2026-05-18T01:36:20Z"},{"alias_kind":"arxiv_version","alias_value":"1409.0197v2","created_at":"2026-05-18T01:36:20Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1409.0197","created_at":"2026-05-18T01:36:20Z"},{"alias_kind":"pith_short_12","alias_value":"FKGMVJNP7BTT","created_at":"2026-05-18T12:28:28Z"},{"alias_kind":"pith_short_16","alias_value":"FKGMVJNP7BTTCAVC","created_at":"2026-05-18T12:28:28Z"},{"alias_kind":"pith_short_8","alias_value":"FKGMVJNP","created_at":"2026-05-18T12:28:28Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:FKGMVJNP7BTTCAVCCESEHFN67A","target":"record","payload":{"canonical_record":{"source":{"id":"1409.0197","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2014-08-31T09:10:50Z","cross_cats_sorted":["math.CV"],"title_canon_sha256":"516a2b501ab565480fa5e214b4a357d57cec7a242241e0d18fbf5b848b16b5f1","abstract_canon_sha256":"0e71eb8e3012adec1c6d6c47de3e4adec312c0cad5bad1164217e4ffe715da96"},"schema_version":"1.0"},"canonical_sha256":"2a8ccaa5aff8673102a211244395bef805107b68b9e9d3981c9a660d5e0d49ad","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:36:20.526545Z","signature_b64":"W5ujOztM1chuDUfDBzukiZ9SW0MorY5+xVwMSGe9BncFuKUzESItfptcGQ5+iudD1ZWWOl7Re7SotRmE+jffDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2a8ccaa5aff8673102a211244395bef805107b68b9e9d3981c9a660d5e0d49ad","last_reissued_at":"2026-05-18T01:36:20.526068Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:36:20.526068Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1409.0197","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:36:20Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"LSol9ok/52Vf4GHXtQhZ9tHI/lq3P/smJgtau7Leyu1LV0/HSD9TtJ7zaB92x+7graHRqc52XLmbs5MhlkgPAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T11:17:52.088386Z"},"content_sha256":"a5913e46855000c8f2a0aed81e8c613d71dea4b7c0a9a6bfed33707a5de4beec","schema_version":"1.0","event_id":"sha256:a5913e46855000c8f2a0aed81e8c613d71dea4b7c0a9a6bfed33707a5de4beec"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:FKGMVJNP7BTTCAVCCESEHFN67A","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Boundary values of holomorphic functions and heat kernel method in translation-invariant distribution spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CV"],"primary_cat":"math.FA","authors_text":"Jasson Vindas, Pavel Dimovski, Stevan Pilipovic","submitted_at":"2014-08-31T09:10:50Z","abstract_excerpt":"We study boundary values of holomorphic functions in translation-invariant distribution spaces of type $\\mathcal{D}'_{E'_{\\ast}}$. New edge of the wedge theorems are obtained. The results are then applied to represent $\\mathcal{D}'_{E'_{\\ast}}$ as a quotient space of holomorphic functions. We also give representations of elements of $\\mathcal{D}'_{E'_{\\ast}}$ via the heat kernel method. Our results cover as particular instances the cases of boundary values, analytic representations, and heat kernel representations in the context of the Schwartz spaces $\\mathcal{D}'_{L^{p}}$, $\\mathcal{B}'$, an"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1409.0197","kind":"arxiv","version":2},"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":"2026-05-18T01:36:20Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"5OVwfkxVKByorsUBH7KQEEKUSbXdUFtEcSyc53BAVVSHHaEkN5mGAAGbuI7df2/Ce1hkqKMr//elPgW0eU1DAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T11:17:52.088881Z"},"content_sha256":"b44f26dbb9b8cbb14dfeb1a0d5379557096cdf95db4ff7e608d472a538b028cd","schema_version":"1.0","event_id":"sha256:b44f26dbb9b8cbb14dfeb1a0d5379557096cdf95db4ff7e608d472a538b028cd"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/FKGMVJNP7BTTCAVCCESEHFN67A/bundle.json","state_url":"https://pith.science/pith/FKGMVJNP7BTTCAVCCESEHFN67A/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/FKGMVJNP7BTTCAVCCESEHFN67A/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":"2026-05-27T11:17:52Z","links":{"resolver":"https://pith.science/pith/FKGMVJNP7BTTCAVCCESEHFN67A","bundle":"https://pith.science/pith/FKGMVJNP7BTTCAVCCESEHFN67A/bundle.json","state":"https://pith.science/pith/FKGMVJNP7BTTCAVCCESEHFN67A/state.json","well_known_bundle":"https://pith.science/.well-known/pith/FKGMVJNP7BTTCAVCCESEHFN67A/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:FKGMVJNP7BTTCAVCCESEHFN67A","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":"0e71eb8e3012adec1c6d6c47de3e4adec312c0cad5bad1164217e4ffe715da96","cross_cats_sorted":["math.CV"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2014-08-31T09:10:50Z","title_canon_sha256":"516a2b501ab565480fa5e214b4a357d57cec7a242241e0d18fbf5b848b16b5f1"},"schema_version":"1.0","source":{"id":"1409.0197","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1409.0197","created_at":"2026-05-18T01:36:20Z"},{"alias_kind":"arxiv_version","alias_value":"1409.0197v2","created_at":"2026-05-18T01:36:20Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1409.0197","created_at":"2026-05-18T01:36:20Z"},{"alias_kind":"pith_short_12","alias_value":"FKGMVJNP7BTT","created_at":"2026-05-18T12:28:28Z"},{"alias_kind":"pith_short_16","alias_value":"FKGMVJNP7BTTCAVC","created_at":"2026-05-18T12:28:28Z"},{"alias_kind":"pith_short_8","alias_value":"FKGMVJNP","created_at":"2026-05-18T12:28:28Z"}],"graph_snapshots":[{"event_id":"sha256:b44f26dbb9b8cbb14dfeb1a0d5379557096cdf95db4ff7e608d472a538b028cd","target":"graph","created_at":"2026-05-18T01:36:20Z","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 study boundary values of holomorphic functions in translation-invariant distribution spaces of type $\\mathcal{D}'_{E'_{\\ast}}$. New edge of the wedge theorems are obtained. The results are then applied to represent $\\mathcal{D}'_{E'_{\\ast}}$ as a quotient space of holomorphic functions. We also give representations of elements of $\\mathcal{D}'_{E'_{\\ast}}$ via the heat kernel method. Our results cover as particular instances the cases of boundary values, analytic representations, and heat kernel representations in the context of the Schwartz spaces $\\mathcal{D}'_{L^{p}}$, $\\mathcal{B}'$, an","authors_text":"Jasson Vindas, Pavel Dimovski, Stevan Pilipovic","cross_cats":["math.CV"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2014-08-31T09:10:50Z","title":"Boundary values of holomorphic functions and heat kernel method in translation-invariant distribution spaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1409.0197","kind":"arxiv","version":2},"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:a5913e46855000c8f2a0aed81e8c613d71dea4b7c0a9a6bfed33707a5de4beec","target":"record","created_at":"2026-05-18T01:36:20Z","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":"0e71eb8e3012adec1c6d6c47de3e4adec312c0cad5bad1164217e4ffe715da96","cross_cats_sorted":["math.CV"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2014-08-31T09:10:50Z","title_canon_sha256":"516a2b501ab565480fa5e214b4a357d57cec7a242241e0d18fbf5b848b16b5f1"},"schema_version":"1.0","source":{"id":"1409.0197","kind":"arxiv","version":2}},"canonical_sha256":"2a8ccaa5aff8673102a211244395bef805107b68b9e9d3981c9a660d5e0d49ad","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2a8ccaa5aff8673102a211244395bef805107b68b9e9d3981c9a660d5e0d49ad","first_computed_at":"2026-05-18T01:36:20.526068Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:36:20.526068Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"W5ujOztM1chuDUfDBzukiZ9SW0MorY5+xVwMSGe9BncFuKUzESItfptcGQ5+iudD1ZWWOl7Re7SotRmE+jffDw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:36:20.526545Z","signed_message":"canonical_sha256_bytes"},"source_id":"1409.0197","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a5913e46855000c8f2a0aed81e8c613d71dea4b7c0a9a6bfed33707a5de4beec","sha256:b44f26dbb9b8cbb14dfeb1a0d5379557096cdf95db4ff7e608d472a538b028cd"],"state_sha256":"fd532b03b39a89a9780c21e59ba65981343f798325d010534c81de7b761df502"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"m69yA7JBQ7B8xcoCfOcb1vQ7+gZOzuPxujmobZKsqjP2f9/OfZ4JchTTw3Eu/Ku/WZxdpDjKaFhNmtPWp6i3Dg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-27T11:17:52.091593Z","bundle_sha256":"6dcd59f82feaa16af454cf7c29ddcddc5207c3904de6a49119b574f09d69e0a0"}}