{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2019:JQ6MC7AP54BTZUQRPM6FC2Y6ZO","short_pith_number":"pith:JQ6MC7AP","canonical_record":{"source":{"id":"1905.00514","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2019-05-01T21:55:59Z","cross_cats_sorted":["math.GN"],"title_canon_sha256":"c5b2ea44eae8cac8f90217e1daa95947b8ea4c346722453c2230fc9a99941085","abstract_canon_sha256":"60e42db4b9f58ce106d826fb74f05ebaec45a5efbf5386b0365265c22c201992"},"schema_version":"1.0"},"canonical_sha256":"4c3cc17c0fef033cd2117b3c516b1ecb98e86e3a692a0428e19479a39869cc9d","source":{"kind":"arxiv","id":"1905.00514","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1905.00514","created_at":"2026-05-17T23:47:11Z"},{"alias_kind":"arxiv_version","alias_value":"1905.00514v1","created_at":"2026-05-17T23:47:11Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1905.00514","created_at":"2026-05-17T23:47:11Z"},{"alias_kind":"pith_short_12","alias_value":"JQ6MC7AP54BT","created_at":"2026-05-18T12:33:21Z"},{"alias_kind":"pith_short_16","alias_value":"JQ6MC7AP54BTZUQR","created_at":"2026-05-18T12:33:21Z"},{"alias_kind":"pith_short_8","alias_value":"JQ6MC7AP","created_at":"2026-05-18T12:33:21Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2019:JQ6MC7AP54BTZUQRPM6FC2Y6ZO","target":"record","payload":{"canonical_record":{"source":{"id":"1905.00514","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2019-05-01T21:55:59Z","cross_cats_sorted":["math.GN"],"title_canon_sha256":"c5b2ea44eae8cac8f90217e1daa95947b8ea4c346722453c2230fc9a99941085","abstract_canon_sha256":"60e42db4b9f58ce106d826fb74f05ebaec45a5efbf5386b0365265c22c201992"},"schema_version":"1.0"},"canonical_sha256":"4c3cc17c0fef033cd2117b3c516b1ecb98e86e3a692a0428e19479a39869cc9d","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:47:11.666124Z","signature_b64":"B5dU8pW45JOGmDWdMBFG54Lx9TuSfuwxDjJp9a5MG8kpLFZm5pWZTtWFvilP3vQejH3HIrFIGBOCIp85xbaXDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4c3cc17c0fef033cd2117b3c516b1ecb98e86e3a692a0428e19479a39869cc9d","last_reissued_at":"2026-05-17T23:47:11.665711Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:47:11.665711Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1905.00514","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":"2026-05-17T23:47:11Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"c98sNv35r3PijO1a3IXw1/b0Knvp67Zubx89rSVDF+zTobkw3EOBkHvlUg6O2KRMthYUEDqOZ/0chQUScIFsBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-03T14:17:06.222427Z"},"content_sha256":"866d787ac4b532a42f126a1fca64d26092259a8678f404d4b5b33b890779abce","schema_version":"1.0","event_id":"sha256:866d787ac4b532a42f126a1fca64d26092259a8678f404d4b5b33b890779abce"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2019:JQ6MC7AP54BTZUQRPM6FC2Y6ZO","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Characterizations of the Ideal Core","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GN"],"primary_cat":"math.FA","authors_text":"Paolo Leonetti","submitted_at":"2019-05-01T21:55:59Z","abstract_excerpt":"Given an ideal $\\mathcal{I}$ on $\\omega$ and a sequence $x$ in a topological vector space, we let the $\\mathcal{I}$-core of $x$ be the least closed convex set containing $\\{x_n: n \\notin I\\}$ for all $I \\in \\mathcal{I}$. We show two characterizations of the $\\mathcal{I}$-core. This implies that the $\\mathcal{I}$-core of a bounded sequence in $\\mathbf{R}^k$ is simply the convex hull of its $\\mathcal{I}$-cluster points. As applications, we simplify and extend several results in the context of Pringsheim-convergence and $e$-convergence of double sequences."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1905.00514","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":"2026-05-17T23:47:11Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"sXMa6LNaqymYKy2fzsiRPpywC+fCjHWL5FgqxNjg3vBlKBUVSfqIED7BOGlENpqVg+5x65EpUE8maqMV+gqWAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-03T14:17:06.222765Z"},"content_sha256":"1faee829b8c28ed0b3a17c0cf2d559832559bd7aa55fb45cc16558869223fa40","schema_version":"1.0","event_id":"sha256:1faee829b8c28ed0b3a17c0cf2d559832559bd7aa55fb45cc16558869223fa40"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/JQ6MC7AP54BTZUQRPM6FC2Y6ZO/bundle.json","state_url":"https://pith.science/pith/JQ6MC7AP54BTZUQRPM6FC2Y6ZO/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/JQ6MC7AP54BTZUQRPM6FC2Y6ZO/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":"2026-07-03T14:17:06Z","links":{"resolver":"https://pith.science/pith/JQ6MC7AP54BTZUQRPM6FC2Y6ZO","bundle":"https://pith.science/pith/JQ6MC7AP54BTZUQRPM6FC2Y6ZO/bundle.json","state":"https://pith.science/pith/JQ6MC7AP54BTZUQRPM6FC2Y6ZO/state.json","well_known_bundle":"https://pith.science/.well-known/pith/JQ6MC7AP54BTZUQRPM6FC2Y6ZO/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:JQ6MC7AP54BTZUQRPM6FC2Y6ZO","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":"60e42db4b9f58ce106d826fb74f05ebaec45a5efbf5386b0365265c22c201992","cross_cats_sorted":["math.GN"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2019-05-01T21:55:59Z","title_canon_sha256":"c5b2ea44eae8cac8f90217e1daa95947b8ea4c346722453c2230fc9a99941085"},"schema_version":"1.0","source":{"id":"1905.00514","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1905.00514","created_at":"2026-05-17T23:47:11Z"},{"alias_kind":"arxiv_version","alias_value":"1905.00514v1","created_at":"2026-05-17T23:47:11Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1905.00514","created_at":"2026-05-17T23:47:11Z"},{"alias_kind":"pith_short_12","alias_value":"JQ6MC7AP54BT","created_at":"2026-05-18T12:33:21Z"},{"alias_kind":"pith_short_16","alias_value":"JQ6MC7AP54BTZUQR","created_at":"2026-05-18T12:33:21Z"},{"alias_kind":"pith_short_8","alias_value":"JQ6MC7AP","created_at":"2026-05-18T12:33:21Z"}],"graph_snapshots":[{"event_id":"sha256:1faee829b8c28ed0b3a17c0cf2d559832559bd7aa55fb45cc16558869223fa40","target":"graph","created_at":"2026-05-17T23:47:11Z","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 an ideal $\\mathcal{I}$ on $\\omega$ and a sequence $x$ in a topological vector space, we let the $\\mathcal{I}$-core of $x$ be the least closed convex set containing $\\{x_n: n \\notin I\\}$ for all $I \\in \\mathcal{I}$. We show two characterizations of the $\\mathcal{I}$-core. This implies that the $\\mathcal{I}$-core of a bounded sequence in $\\mathbf{R}^k$ is simply the convex hull of its $\\mathcal{I}$-cluster points. As applications, we simplify and extend several results in the context of Pringsheim-convergence and $e$-convergence of double sequences.","authors_text":"Paolo Leonetti","cross_cats":["math.GN"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2019-05-01T21:55:59Z","title":"Characterizations of the Ideal Core"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1905.00514","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":"sha256:866d787ac4b532a42f126a1fca64d26092259a8678f404d4b5b33b890779abce","target":"record","created_at":"2026-05-17T23:47:11Z","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":"60e42db4b9f58ce106d826fb74f05ebaec45a5efbf5386b0365265c22c201992","cross_cats_sorted":["math.GN"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2019-05-01T21:55:59Z","title_canon_sha256":"c5b2ea44eae8cac8f90217e1daa95947b8ea4c346722453c2230fc9a99941085"},"schema_version":"1.0","source":{"id":"1905.00514","kind":"arxiv","version":1}},"canonical_sha256":"4c3cc17c0fef033cd2117b3c516b1ecb98e86e3a692a0428e19479a39869cc9d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4c3cc17c0fef033cd2117b3c516b1ecb98e86e3a692a0428e19479a39869cc9d","first_computed_at":"2026-05-17T23:47:11.665711Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:47:11.665711Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"B5dU8pW45JOGmDWdMBFG54Lx9TuSfuwxDjJp9a5MG8kpLFZm5pWZTtWFvilP3vQejH3HIrFIGBOCIp85xbaXDA==","signature_status":"signed_v1","signed_at":"2026-05-17T23:47:11.666124Z","signed_message":"canonical_sha256_bytes"},"source_id":"1905.00514","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:866d787ac4b532a42f126a1fca64d26092259a8678f404d4b5b33b890779abce","sha256:1faee829b8c28ed0b3a17c0cf2d559832559bd7aa55fb45cc16558869223fa40"],"state_sha256":"d911f178d4b4fa3f562dccb9db938de8e29826cb1c44e272789e93bdef1571a9"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"688+FPRebj+Vp8+0gbC3SjvLKliGFtCyFQajiCnof4PDIhfHW8utIeqa20VwMNbZrHAoL1CT1cdbUXLrtjMsBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-03T14:17:06.224616Z","bundle_sha256":"af3fca92c2cea151ac20a324535fe5711d8e7521ee6d6d9ae7e6db4832c02dfb"}}