{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:5QZ4DQLAAFLPKRVKRAWBULG6NK","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":"3be58e9d9d6b454d1d149ef938be8e1b2243cd0e89bb5e6c770c68d02cb6d865","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2014-07-10T16:05:41Z","title_canon_sha256":"0a0567269cc5bff8eff7bfcd3edf9826e4ecef26080210cfa198f312e4561902"},"schema_version":"1.0","source":{"id":"1407.2842","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1407.2842","created_at":"2026-05-18T00:49:08Z"},{"alias_kind":"arxiv_version","alias_value":"1407.2842v1","created_at":"2026-05-18T00:49:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1407.2842","created_at":"2026-05-18T00:49:08Z"},{"alias_kind":"pith_short_12","alias_value":"5QZ4DQLAAFLP","created_at":"2026-05-18T12:28:14Z"},{"alias_kind":"pith_short_16","alias_value":"5QZ4DQLAAFLPKRVK","created_at":"2026-05-18T12:28:14Z"},{"alias_kind":"pith_short_8","alias_value":"5QZ4DQLA","created_at":"2026-05-18T12:28:14Z"}],"graph_snapshots":[{"event_id":"sha256:d2527409b9f0d75b268651167319553c3e58b758604fb8b296dfe9dbea18adcf","target":"graph","created_at":"2026-05-18T00:49:08Z","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":"It is well known, as follows from the Banach-Steinhaus theorem, that if a sequence $\\left\\{y_{n}\\right\\}_{n=1}^{\\infty}$ of linear continuous functionals in a Fr\\'echet space converges pointwise to a linear functional $Y,$ $Y\\left( x\\right) =\\lim_{n\\rightarrow\\infty}\\left\\langle y_{n},x\\right\\rangle $ for all $x,$ then $Y$ is actually continuous. In this article we prove that in a Fr\\'echet space the continuity of $Y$ still holds if $Y$ is the \\emph{finite part} of the limit of $\\left\\langle y_{n},x\\right\\rangle $ as $n\\rightarrow\\infty.$ We also show that the continuity of finite part limits ","authors_text":"Jasson Vindas, Ricardo Estrada","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2014-07-10T16:05:41Z","title":"A generalization of the Banach-Steinhaus theorem for finite part limits"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1407.2842","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":"sha256:8a6af732314cb20e1476231d39a06cc61d24cf6bc6844ebe88a631e2e5b9f5d9","target":"record","created_at":"2026-05-18T00:49:08Z","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":"3be58e9d9d6b454d1d149ef938be8e1b2243cd0e89bb5e6c770c68d02cb6d865","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2014-07-10T16:05:41Z","title_canon_sha256":"0a0567269cc5bff8eff7bfcd3edf9826e4ecef26080210cfa198f312e4561902"},"schema_version":"1.0","source":{"id":"1407.2842","kind":"arxiv","version":1}},"canonical_sha256":"ec33c1c1600156f546aa882c1a2cde6a952f1a7e3bd72edc39ebb38b8ac1e22b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ec33c1c1600156f546aa882c1a2cde6a952f1a7e3bd72edc39ebb38b8ac1e22b","first_computed_at":"2026-05-18T00:49:08.788673Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:49:08.788673Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"IshMssdciYoEJZFnxJWBUbmzMkMju6QwYdcDwhUlgSmYtyn/9CfB1fLfa0zliF/TGD3Fyz8E9D0qnQgCK7z2Bg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:49:08.789099Z","signed_message":"canonical_sha256_bytes"},"source_id":"1407.2842","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8a6af732314cb20e1476231d39a06cc61d24cf6bc6844ebe88a631e2e5b9f5d9","sha256:d2527409b9f0d75b268651167319553c3e58b758604fb8b296dfe9dbea18adcf"],"state_sha256":"bbe78c387781a2ddf91116d0ed10fc330854bade79e72db1196534e5943ada46"}