{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:BE2X6A6AF7TP5UORRSDVBWK65V","short_pith_number":"pith:BE2X6A6A","canonical_record":{"source":{"id":"1203.3418","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2012-03-15T16:56:37Z","cross_cats_sorted":[],"title_canon_sha256":"25a03059b4a31ab9409ee5b443b2e4de2d9ade0203e97730781276ddb75dc480","abstract_canon_sha256":"40287c6e76cfb004cd112e98c8af86465076d3a3c0a77e3dc90bb9ab1a445c06"},"schema_version":"1.0"},"canonical_sha256":"09357f03c02fe6fed1d18c8750d95eed435fe8ed483188c6039fce4dbf188346","source":{"kind":"arxiv","id":"1203.3418","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1203.3418","created_at":"2026-05-18T02:29:25Z"},{"alias_kind":"arxiv_version","alias_value":"1203.3418v3","created_at":"2026-05-18T02:29:25Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1203.3418","created_at":"2026-05-18T02:29:25Z"},{"alias_kind":"pith_short_12","alias_value":"BE2X6A6AF7TP","created_at":"2026-05-18T12:26:58Z"},{"alias_kind":"pith_short_16","alias_value":"BE2X6A6AF7TP5UOR","created_at":"2026-05-18T12:26:58Z"},{"alias_kind":"pith_short_8","alias_value":"BE2X6A6A","created_at":"2026-05-18T12:26:58Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:BE2X6A6AF7TP5UORRSDVBWK65V","target":"record","payload":{"canonical_record":{"source":{"id":"1203.3418","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2012-03-15T16:56:37Z","cross_cats_sorted":[],"title_canon_sha256":"25a03059b4a31ab9409ee5b443b2e4de2d9ade0203e97730781276ddb75dc480","abstract_canon_sha256":"40287c6e76cfb004cd112e98c8af86465076d3a3c0a77e3dc90bb9ab1a445c06"},"schema_version":"1.0"},"canonical_sha256":"09357f03c02fe6fed1d18c8750d95eed435fe8ed483188c6039fce4dbf188346","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:29:25.450464Z","signature_b64":"BW7TimvgQiwMrjftr3+YiRJWySXM16Cy4eBXnpx2Du1mgB8XfT/jlbAAMW7WHWI3xzlUR6I/PZ66AGVDTH+nAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"09357f03c02fe6fed1d18c8750d95eed435fe8ed483188c6039fce4dbf188346","last_reissued_at":"2026-05-18T02:29:25.450064Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:29:25.450064Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1203.3418","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:29:25Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"LygPQ5bT7DRVnkNPSZh9RcLGvkllZIDkLtNPRTQi59wWvcISJWBT+8al+X4J4CjUN8G/maf1xJ9D3CiREd2IDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T18:41:36.825428Z"},"content_sha256":"a03477beb2eaf29627f0ef405f4ee05f53fd4aff10b831f73d9ed66ebe4f7544","schema_version":"1.0","event_id":"sha256:a03477beb2eaf29627f0ef405f4ee05f53fd4aff10b831f73d9ed66ebe4f7544"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:BE2X6A6AF7TP5UORRSDVBWK65V","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Continuity of LF-algebra representations associated to representations of Lie groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Helge Glockner","submitted_at":"2012-03-15T16:56:37Z","abstract_excerpt":"Let G be a Lie group and E be a locally convex topological G-module.\n  If E is sequentially complete, then E and its space of smooth vectors are modules for the algebra D(G) of compactly supported smooth functions on G. However, the module multiplication need not be continuous. The pathology can be ruled out if E is (or embeds into) a projective limit of Banach G-modules.\n  Moreover, in this case the space of analytic vectors is a module for the algebra A(G) of superdecaying analytic functions introduced by Gimperlein, Kroetz and Schlichtkrull. We prove that the space of analytic vectors is a "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1203.3418","kind":"arxiv","version":3},"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":"2026-05-18T02:29:25Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"vOnqlDWo41ma6qM2c18BVQepD1oiS+KDX+wQd01Py3vQIVdQ+3TYMY9svaHMbdWXuSlMjjUE2ynwJ35Ffi0/BQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T18:41:36.825782Z"},"content_sha256":"714e3f0b8a0ec52fda03caa7897e0e763b92868a257a7562d9b5b417e3fc15f2","schema_version":"1.0","event_id":"sha256:714e3f0b8a0ec52fda03caa7897e0e763b92868a257a7562d9b5b417e3fc15f2"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/BE2X6A6AF7TP5UORRSDVBWK65V/bundle.json","state_url":"https://pith.science/pith/BE2X6A6AF7TP5UORRSDVBWK65V/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/BE2X6A6AF7TP5UORRSDVBWK65V/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":"2026-06-01T18:41:36Z","links":{"resolver":"https://pith.science/pith/BE2X6A6AF7TP5UORRSDVBWK65V","bundle":"https://pith.science/pith/BE2X6A6AF7TP5UORRSDVBWK65V/bundle.json","state":"https://pith.science/pith/BE2X6A6AF7TP5UORRSDVBWK65V/state.json","well_known_bundle":"https://pith.science/.well-known/pith/BE2X6A6AF7TP5UORRSDVBWK65V/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:BE2X6A6AF7TP5UORRSDVBWK65V","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":"40287c6e76cfb004cd112e98c8af86465076d3a3c0a77e3dc90bb9ab1a445c06","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2012-03-15T16:56:37Z","title_canon_sha256":"25a03059b4a31ab9409ee5b443b2e4de2d9ade0203e97730781276ddb75dc480"},"schema_version":"1.0","source":{"id":"1203.3418","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1203.3418","created_at":"2026-05-18T02:29:25Z"},{"alias_kind":"arxiv_version","alias_value":"1203.3418v3","created_at":"2026-05-18T02:29:25Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1203.3418","created_at":"2026-05-18T02:29:25Z"},{"alias_kind":"pith_short_12","alias_value":"BE2X6A6AF7TP","created_at":"2026-05-18T12:26:58Z"},{"alias_kind":"pith_short_16","alias_value":"BE2X6A6AF7TP5UOR","created_at":"2026-05-18T12:26:58Z"},{"alias_kind":"pith_short_8","alias_value":"BE2X6A6A","created_at":"2026-05-18T12:26:58Z"}],"graph_snapshots":[{"event_id":"sha256:714e3f0b8a0ec52fda03caa7897e0e763b92868a257a7562d9b5b417e3fc15f2","target":"graph","created_at":"2026-05-18T02:29:25Z","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 G be a Lie group and E be a locally convex topological G-module.\n  If E is sequentially complete, then E and its space of smooth vectors are modules for the algebra D(G) of compactly supported smooth functions on G. However, the module multiplication need not be continuous. The pathology can be ruled out if E is (or embeds into) a projective limit of Banach G-modules.\n  Moreover, in this case the space of analytic vectors is a module for the algebra A(G) of superdecaying analytic functions introduced by Gimperlein, Kroetz and Schlichtkrull. We prove that the space of analytic vectors is a ","authors_text":"Helge Glockner","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2012-03-15T16:56:37Z","title":"Continuity of LF-algebra representations associated to representations of Lie groups"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1203.3418","kind":"arxiv","version":3},"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:a03477beb2eaf29627f0ef405f4ee05f53fd4aff10b831f73d9ed66ebe4f7544","target":"record","created_at":"2026-05-18T02:29:25Z","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":"40287c6e76cfb004cd112e98c8af86465076d3a3c0a77e3dc90bb9ab1a445c06","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2012-03-15T16:56:37Z","title_canon_sha256":"25a03059b4a31ab9409ee5b443b2e4de2d9ade0203e97730781276ddb75dc480"},"schema_version":"1.0","source":{"id":"1203.3418","kind":"arxiv","version":3}},"canonical_sha256":"09357f03c02fe6fed1d18c8750d95eed435fe8ed483188c6039fce4dbf188346","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"09357f03c02fe6fed1d18c8750d95eed435fe8ed483188c6039fce4dbf188346","first_computed_at":"2026-05-18T02:29:25.450064Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:29:25.450064Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"BW7TimvgQiwMrjftr3+YiRJWySXM16Cy4eBXnpx2Du1mgB8XfT/jlbAAMW7WHWI3xzlUR6I/PZ66AGVDTH+nAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:29:25.450464Z","signed_message":"canonical_sha256_bytes"},"source_id":"1203.3418","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a03477beb2eaf29627f0ef405f4ee05f53fd4aff10b831f73d9ed66ebe4f7544","sha256:714e3f0b8a0ec52fda03caa7897e0e763b92868a257a7562d9b5b417e3fc15f2"],"state_sha256":"809e6c10009ebd8399634893cc789475faa718646c49128a7476a1426a6bb5e2"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"V3Eywz49Gg+xvgkR2vW4oV1Q/M+VoFIzE8xjdetwIwgyTAjwyZM+v/iJ8nh5C+/Ne8BViJNj5cC6xCV5WaDKDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-01T18:41:36.827597Z","bundle_sha256":"ef2542846d54e4d1716876ca8d589fc4265dab18749f9cb11a7880b03d05be6e"}}