{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:2JVKHVZVGYGC62DBV6TLHJGC2P","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":"168ce07eb181adf6ac9714be148f079064eab0a243454dc4dd8de0d46afc1299","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2010-09-15T15:28:07Z","title_canon_sha256":"d797c3960488e0ed8a956b974f7a03cbf28b0c5d2bce2ad91f46ceb9170f6e50"},"schema_version":"1.0","source":{"id":"1009.2954","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1009.2954","created_at":"2026-05-18T04:39:58Z"},{"alias_kind":"arxiv_version","alias_value":"1009.2954v2","created_at":"2026-05-18T04:39:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1009.2954","created_at":"2026-05-18T04:39:58Z"},{"alias_kind":"pith_short_12","alias_value":"2JVKHVZVGYGC","created_at":"2026-05-18T12:26:03Z"},{"alias_kind":"pith_short_16","alias_value":"2JVKHVZVGYGC62DB","created_at":"2026-05-18T12:26:03Z"},{"alias_kind":"pith_short_8","alias_value":"2JVKHVZV","created_at":"2026-05-18T12:26:03Z"}],"graph_snapshots":[{"event_id":"sha256:8e1e03c477e0c113fb26f77465e3dc3c4b23ced909c567c187c7bd90e45f3bde","target":"graph","created_at":"2026-05-18T04:39:58Z","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":"Given a sequence of real numbers, we consider its subsequences converging to possibly different limits and associate to each of them an index of convergence which depends on the density of the associated subsequences. This index turns out to be useful for a complete description of some phenomena in interpolation theory at points of discontinuity of the first kind. In particular we give some applications to Lagrange and Shepard operators.","authors_text":"Cristian Tacelli, Giusy Mazzone, Michele Campiti","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2010-09-15T15:28:07Z","title":"On the interpolation of discontinuous functions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1009.2954","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":"sha256:720b131adb3787e97fd4a13118ee0566fafabf001ff8ea31af7698643b6726fb","target":"record","created_at":"2026-05-18T04:39:58Z","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":"168ce07eb181adf6ac9714be148f079064eab0a243454dc4dd8de0d46afc1299","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2010-09-15T15:28:07Z","title_canon_sha256":"d797c3960488e0ed8a956b974f7a03cbf28b0c5d2bce2ad91f46ceb9170f6e50"},"schema_version":"1.0","source":{"id":"1009.2954","kind":"arxiv","version":2}},"canonical_sha256":"d26aa3d735360c2f6861afa6b3a4c2d3e4e6487fda1feb75fa5e328b32070550","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d26aa3d735360c2f6861afa6b3a4c2d3e4e6487fda1feb75fa5e328b32070550","first_computed_at":"2026-05-18T04:39:58.934311Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:39:58.934311Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"PX/7A4SJ4/mSLbg0t2LAoFEr+KzTry/SStSAD7mN1PuCMVlcclVLZUN/kFG91DizLnjOOH1Nhlyj5U+94ys9Cg==","signature_status":"signed_v1","signed_at":"2026-05-18T04:39:58.934864Z","signed_message":"canonical_sha256_bytes"},"source_id":"1009.2954","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:720b131adb3787e97fd4a13118ee0566fafabf001ff8ea31af7698643b6726fb","sha256:8e1e03c477e0c113fb26f77465e3dc3c4b23ced909c567c187c7bd90e45f3bde"],"state_sha256":"6d7bd9b605d8a6a4af4c37386853cf2e5b9493ae69bf902f9ff4f771018c0e4d"}