{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2019:TM4UHKAJ6WQ47PNAX3JOWPRDXD","short_pith_number":"pith:TM4UHKAJ","canonical_record":{"source":{"id":"1904.12836","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2019-04-29T17:38:05Z","cross_cats_sorted":[],"title_canon_sha256":"e9e430446a70c7ada0b9e91ea6fcbd9d5663229dc672c0065e228d9c2e27a0be","abstract_canon_sha256":"999c0000c016c0ba87e06a502a31d1555d1c34128f812da5f499ca8d6b8f53c9"},"schema_version":"1.0"},"canonical_sha256":"9b3943a809f5a1cfbda0bed2eb3e23b8d44bdac255c4e3c7282affdb584f654b","source":{"kind":"arxiv","id":"1904.12836","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1904.12836","created_at":"2026-05-17T23:47:32Z"},{"alias_kind":"arxiv_version","alias_value":"1904.12836v1","created_at":"2026-05-17T23:47:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1904.12836","created_at":"2026-05-17T23:47:32Z"},{"alias_kind":"pith_short_12","alias_value":"TM4UHKAJ6WQ4","created_at":"2026-05-18T12:33:30Z"},{"alias_kind":"pith_short_16","alias_value":"TM4UHKAJ6WQ47PNA","created_at":"2026-05-18T12:33:30Z"},{"alias_kind":"pith_short_8","alias_value":"TM4UHKAJ","created_at":"2026-05-18T12:33:30Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2019:TM4UHKAJ6WQ47PNAX3JOWPRDXD","target":"record","payload":{"canonical_record":{"source":{"id":"1904.12836","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2019-04-29T17:38:05Z","cross_cats_sorted":[],"title_canon_sha256":"e9e430446a70c7ada0b9e91ea6fcbd9d5663229dc672c0065e228d9c2e27a0be","abstract_canon_sha256":"999c0000c016c0ba87e06a502a31d1555d1c34128f812da5f499ca8d6b8f53c9"},"schema_version":"1.0"},"canonical_sha256":"9b3943a809f5a1cfbda0bed2eb3e23b8d44bdac255c4e3c7282affdb584f654b","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:47:32.124456Z","signature_b64":"zU+JBDSqR5Zy4b/rF8r9O0dc+H4B4qXvUAf20SdqkvBC94xfwOkQcp1+MAH/FxJntrJ80RCl0ZBqi9mNbMuuBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9b3943a809f5a1cfbda0bed2eb3e23b8d44bdac255c4e3c7282affdb584f654b","last_reissued_at":"2026-05-17T23:47:32.123826Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:47:32.123826Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1904.12836","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":"2026-05-17T23:47:32Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"1c3+RB/8esziqUxWn1+CQvd7OGeEVWFsxx9kTuN+WT04vo/AsyxO2oFBcVr095logJ5LWNVbMNBx1B1BzNapAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T19:13:39.237079Z"},"content_sha256":"8a8bbed2d7ce07bcc5ef224cb4c17359b1003233e3c37cae34b7df2c74a33bed","schema_version":"1.0","event_id":"sha256:8a8bbed2d7ce07bcc5ef224cb4c17359b1003233e3c37cae34b7df2c74a33bed"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2019:TM4UHKAJ6WQ47PNAX3JOWPRDXD","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A linear topological invariant for spaces of quasianalytic functions of Roumieu type","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Andreas Debrouwere","submitted_at":"2019-04-29T17:38:05Z","abstract_excerpt":"We show that the spaces $\\mathcal{E}_{\\{\\omega\\}}(\\Omega)$ of ultradifferentiable functions of Roumieu type satisfy the dual interpolation estimate for small theta, where $\\omega$ is a quasianalytic weight function and $\\Omega$ is an arbitrary open subset of $\\mathbb{R}^d$. This result was previously shown by Bonet and Doma\\'nski [2] under the additional assumptions that $\\Omega$ is convex and $\\omega$ satisfies the condition $(\\alpha_1)$. In particular, our work solves Problem 9.7 in [1]."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1904.12836","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":"2026-05-17T23:47:32Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Jb0n5lgnt/Wf0NfLbggnDZQK90SKhEh3DLO+7+wewKlZNsbo03eAxPyrGq6UYrmOT1AfH8VkOIxEakOasEacBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T19:13:39.237445Z"},"content_sha256":"da4ea94bbd412baf08eae9fe9cd1247bd5d67a1052a728308c4a2d7cd4ea71ee","schema_version":"1.0","event_id":"sha256:da4ea94bbd412baf08eae9fe9cd1247bd5d67a1052a728308c4a2d7cd4ea71ee"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/TM4UHKAJ6WQ47PNAX3JOWPRDXD/bundle.json","state_url":"https://pith.science/pith/TM4UHKAJ6WQ47PNAX3JOWPRDXD/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/TM4UHKAJ6WQ47PNAX3JOWPRDXD/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":"2026-05-27T19:13:39Z","links":{"resolver":"https://pith.science/pith/TM4UHKAJ6WQ47PNAX3JOWPRDXD","bundle":"https://pith.science/pith/TM4UHKAJ6WQ47PNAX3JOWPRDXD/bundle.json","state":"https://pith.science/pith/TM4UHKAJ6WQ47PNAX3JOWPRDXD/state.json","well_known_bundle":"https://pith.science/.well-known/pith/TM4UHKAJ6WQ47PNAX3JOWPRDXD/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:TM4UHKAJ6WQ47PNAX3JOWPRDXD","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":"999c0000c016c0ba87e06a502a31d1555d1c34128f812da5f499ca8d6b8f53c9","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2019-04-29T17:38:05Z","title_canon_sha256":"e9e430446a70c7ada0b9e91ea6fcbd9d5663229dc672c0065e228d9c2e27a0be"},"schema_version":"1.0","source":{"id":"1904.12836","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1904.12836","created_at":"2026-05-17T23:47:32Z"},{"alias_kind":"arxiv_version","alias_value":"1904.12836v1","created_at":"2026-05-17T23:47:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1904.12836","created_at":"2026-05-17T23:47:32Z"},{"alias_kind":"pith_short_12","alias_value":"TM4UHKAJ6WQ4","created_at":"2026-05-18T12:33:30Z"},{"alias_kind":"pith_short_16","alias_value":"TM4UHKAJ6WQ47PNA","created_at":"2026-05-18T12:33:30Z"},{"alias_kind":"pith_short_8","alias_value":"TM4UHKAJ","created_at":"2026-05-18T12:33:30Z"}],"graph_snapshots":[{"event_id":"sha256:da4ea94bbd412baf08eae9fe9cd1247bd5d67a1052a728308c4a2d7cd4ea71ee","target":"graph","created_at":"2026-05-17T23:47:32Z","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":"We show that the spaces $\\mathcal{E}_{\\{\\omega\\}}(\\Omega)$ of ultradifferentiable functions of Roumieu type satisfy the dual interpolation estimate for small theta, where $\\omega$ is a quasianalytic weight function and $\\Omega$ is an arbitrary open subset of $\\mathbb{R}^d$. This result was previously shown by Bonet and Doma\\'nski [2] under the additional assumptions that $\\Omega$ is convex and $\\omega$ satisfies the condition $(\\alpha_1)$. In particular, our work solves Problem 9.7 in [1].","authors_text":"Andreas Debrouwere","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2019-04-29T17:38:05Z","title":"A linear topological invariant for spaces of quasianalytic functions of Roumieu type"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1904.12836","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":"sha256:8a8bbed2d7ce07bcc5ef224cb4c17359b1003233e3c37cae34b7df2c74a33bed","target":"record","created_at":"2026-05-17T23:47:32Z","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":"999c0000c016c0ba87e06a502a31d1555d1c34128f812da5f499ca8d6b8f53c9","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2019-04-29T17:38:05Z","title_canon_sha256":"e9e430446a70c7ada0b9e91ea6fcbd9d5663229dc672c0065e228d9c2e27a0be"},"schema_version":"1.0","source":{"id":"1904.12836","kind":"arxiv","version":1}},"canonical_sha256":"9b3943a809f5a1cfbda0bed2eb3e23b8d44bdac255c4e3c7282affdb584f654b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9b3943a809f5a1cfbda0bed2eb3e23b8d44bdac255c4e3c7282affdb584f654b","first_computed_at":"2026-05-17T23:47:32.123826Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:47:32.123826Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"zU+JBDSqR5Zy4b/rF8r9O0dc+H4B4qXvUAf20SdqkvBC94xfwOkQcp1+MAH/FxJntrJ80RCl0ZBqi9mNbMuuBA==","signature_status":"signed_v1","signed_at":"2026-05-17T23:47:32.124456Z","signed_message":"canonical_sha256_bytes"},"source_id":"1904.12836","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8a8bbed2d7ce07bcc5ef224cb4c17359b1003233e3c37cae34b7df2c74a33bed","sha256:da4ea94bbd412baf08eae9fe9cd1247bd5d67a1052a728308c4a2d7cd4ea71ee"],"state_sha256":"46f31a980994e3e9a72563ae61227711220771ba52ca84294e82bfdca211b1d5"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"oMDXuNy1uvLQGnT3Q+XOd56wXNzh1G/Zka14AsMN9100PnzJk0MBimLcXXcjuJKDgAQ6AxhI99MOdyaabt8TAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-27T19:13:39.240157Z","bundle_sha256":"23c368796a6050d48f85e82319dbb48bb54881b2606eeef03d8cd1a469c832bd"}}