{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2019:NM42OGHZLONSUTX73WP6FXBJAQ","short_pith_number":"pith:NM42OGHZ","canonical_record":{"source":{"id":"1907.10645","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2019-07-24T18:15:41Z","cross_cats_sorted":[],"title_canon_sha256":"824d4ad69d26a1f44f37f4553d6554823b9c3c630547202d745cd43f9ced54fa","abstract_canon_sha256":"9495ab2b5199f86fe3bc382749397e164f17310deb752e23ada9c95271ffdeec"},"schema_version":"1.0"},"canonical_sha256":"6b39a718f95b9b2a4effdd9fe2dc29043832d234f9e4134bd044c632f3ac8096","source":{"kind":"arxiv","id":"1907.10645","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1907.10645","created_at":"2026-07-05T00:54:29Z"},{"alias_kind":"arxiv_version","alias_value":"1907.10645v2","created_at":"2026-07-05T00:54:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1907.10645","created_at":"2026-07-05T00:54:29Z"},{"alias_kind":"pith_short_12","alias_value":"NM42OGHZLONS","created_at":"2026-07-05T00:54:29Z"},{"alias_kind":"pith_short_16","alias_value":"NM42OGHZLONSUTX7","created_at":"2026-07-05T00:54:29Z"},{"alias_kind":"pith_short_8","alias_value":"NM42OGHZ","created_at":"2026-07-05T00:54:29Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2019:NM42OGHZLONSUTX73WP6FXBJAQ","target":"record","payload":{"canonical_record":{"source":{"id":"1907.10645","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2019-07-24T18:15:41Z","cross_cats_sorted":[],"title_canon_sha256":"824d4ad69d26a1f44f37f4553d6554823b9c3c630547202d745cd43f9ced54fa","abstract_canon_sha256":"9495ab2b5199f86fe3bc382749397e164f17310deb752e23ada9c95271ffdeec"},"schema_version":"1.0"},"canonical_sha256":"6b39a718f95b9b2a4effdd9fe2dc29043832d234f9e4134bd044c632f3ac8096","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T00:54:29.848652Z","signature_b64":"xq1cNwv3ybTYcTWUYVcVprPxHhAltYqJXtEUmBDzWVEA7OI3zbgVOqOcxlnPXncZSh37oQnYL3PJ1qWM9JjEAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6b39a718f95b9b2a4effdd9fe2dc29043832d234f9e4134bd044c632f3ac8096","last_reissued_at":"2026-07-05T00:54:29.848282Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T00:54:29.848282Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1907.10645","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T00:54:29Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"QdJplEMXrPzOWAjBgWekSxLIAwNW5JLExuL2UvIgVqhmHHKkkesXPBkWGbF23MO61IlBOR9qSu8DUsWbZgJqBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-05T06:05:04.022649Z"},"content_sha256":"0b6e2007e3a8e6a287acc9080db89a8cc037425d211e3ffcf27b5b966c769883","schema_version":"1.0","event_id":"sha256:0b6e2007e3a8e6a287acc9080db89a8cc037425d211e3ffcf27b5b966c769883"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2019:NM42OGHZLONSUTX73WP6FXBJAQ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Closed ideals of operators on the Tsirelson and Schreier spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Kevin Beanland, Niels Jakob Laustsen, Tomasz Kania","submitted_at":"2019-07-24T18:15:41Z","abstract_excerpt":"Let $\\mathscr{B}(X)$ denote the Banach algebra of bounded operators on $X$, where~$X$ is either Tsirelson's Banach space or the Schreier space of order $n$ for some $n\\in\\mathbb N$. We show that the lattice of closed ideals of~$\\mathscr{B}(X)$ has a very rich structure; in particular $\\mathscr{B}(X)$ contains at least continuum many maximal ideals.\n  Our approach is to study the closed ideals generated by the basis projections. Indeed, the unit vector basis is an unconditional basis for each of the above spaces, so there is a basis projection $P_N\\in\\mathscr{B}(X)$ corresponding to each non-em"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1907.10645","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/1907.10645/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-05T00:54:29Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"7uWGKmZyemSsx90F2MycbNwQ7ftZHGS/qSoH7WjymSPp8a0dRwJP9nfaxw1Km7T17LDWV4Hc9JDizoRQtvsyBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-05T06:05:04.023022Z"},"content_sha256":"8b0109bd987e384a8230961e302962b2f91c52980bc57eed16e487698976b4aa","schema_version":"1.0","event_id":"sha256:8b0109bd987e384a8230961e302962b2f91c52980bc57eed16e487698976b4aa"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/NM42OGHZLONSUTX73WP6FXBJAQ/bundle.json","state_url":"https://pith.science/pith/NM42OGHZLONSUTX73WP6FXBJAQ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/NM42OGHZLONSUTX73WP6FXBJAQ/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":"2026-08-05T06:05:04Z","links":{"resolver":"https://pith.science/pith/NM42OGHZLONSUTX73WP6FXBJAQ","bundle":"https://pith.science/pith/NM42OGHZLONSUTX73WP6FXBJAQ/bundle.json","state":"https://pith.science/pith/NM42OGHZLONSUTX73WP6FXBJAQ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/NM42OGHZLONSUTX73WP6FXBJAQ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:NM42OGHZLONSUTX73WP6FXBJAQ","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":"9495ab2b5199f86fe3bc382749397e164f17310deb752e23ada9c95271ffdeec","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2019-07-24T18:15:41Z","title_canon_sha256":"824d4ad69d26a1f44f37f4553d6554823b9c3c630547202d745cd43f9ced54fa"},"schema_version":"1.0","source":{"id":"1907.10645","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1907.10645","created_at":"2026-07-05T00:54:29Z"},{"alias_kind":"arxiv_version","alias_value":"1907.10645v2","created_at":"2026-07-05T00:54:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1907.10645","created_at":"2026-07-05T00:54:29Z"},{"alias_kind":"pith_short_12","alias_value":"NM42OGHZLONS","created_at":"2026-07-05T00:54:29Z"},{"alias_kind":"pith_short_16","alias_value":"NM42OGHZLONSUTX7","created_at":"2026-07-05T00:54:29Z"},{"alias_kind":"pith_short_8","alias_value":"NM42OGHZ","created_at":"2026-07-05T00:54:29Z"}],"graph_snapshots":[{"event_id":"sha256:8b0109bd987e384a8230961e302962b2f91c52980bc57eed16e487698976b4aa","target":"graph","created_at":"2026-07-05T00:54:29Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/1907.10645/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Let $\\mathscr{B}(X)$ denote the Banach algebra of bounded operators on $X$, where~$X$ is either Tsirelson's Banach space or the Schreier space of order $n$ for some $n\\in\\mathbb N$. We show that the lattice of closed ideals of~$\\mathscr{B}(X)$ has a very rich structure; in particular $\\mathscr{B}(X)$ contains at least continuum many maximal ideals.\n  Our approach is to study the closed ideals generated by the basis projections. Indeed, the unit vector basis is an unconditional basis for each of the above spaces, so there is a basis projection $P_N\\in\\mathscr{B}(X)$ corresponding to each non-em","authors_text":"Kevin Beanland, Niels Jakob Laustsen, Tomasz Kania","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2019-07-24T18:15:41Z","title":"Closed ideals of operators on the Tsirelson and Schreier spaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1907.10645","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":"sha256:0b6e2007e3a8e6a287acc9080db89a8cc037425d211e3ffcf27b5b966c769883","target":"record","created_at":"2026-07-05T00:54:29Z","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":"9495ab2b5199f86fe3bc382749397e164f17310deb752e23ada9c95271ffdeec","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2019-07-24T18:15:41Z","title_canon_sha256":"824d4ad69d26a1f44f37f4553d6554823b9c3c630547202d745cd43f9ced54fa"},"schema_version":"1.0","source":{"id":"1907.10645","kind":"arxiv","version":2}},"canonical_sha256":"6b39a718f95b9b2a4effdd9fe2dc29043832d234f9e4134bd044c632f3ac8096","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6b39a718f95b9b2a4effdd9fe2dc29043832d234f9e4134bd044c632f3ac8096","first_computed_at":"2026-07-05T00:54:29.848282Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T00:54:29.848282Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"xq1cNwv3ybTYcTWUYVcVprPxHhAltYqJXtEUmBDzWVEA7OI3zbgVOqOcxlnPXncZSh37oQnYL3PJ1qWM9JjEAg==","signature_status":"signed_v1","signed_at":"2026-07-05T00:54:29.848652Z","signed_message":"canonical_sha256_bytes"},"source_id":"1907.10645","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0b6e2007e3a8e6a287acc9080db89a8cc037425d211e3ffcf27b5b966c769883","sha256:8b0109bd987e384a8230961e302962b2f91c52980bc57eed16e487698976b4aa"],"state_sha256":"5c416be9aa92137005df9a621b9059337d93bdae543cb7a8cc251fb6704ca36d"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"IP9sH8l4kgD2ZMS0nU39y96+eQdwjaXpQZjlTGsIzghp1QPhpw/ZrfRcDWoLF7ObKXTwJBmBO5xGh0zu7XGcAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-05T06:05:04.026299Z","bundle_sha256":"958b1665be8755abed09a712cc17f537220e8b46b148880584610c7dac4840d8"}}