{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2026:2V5GWG75GS7EWFKO25NMPHTMWH","short_pith_number":"pith:2V5GWG75","schema_version":"1.0","canonical_sha256":"d57a6b1bfd34be4b154ed75ac79e6cb1f311ebb87ac16bf00737bdf574875c82","source":{"kind":"arxiv","id":"2608.11009","version":1},"attestation_state":"computed","paper":{"title":"Square root crystals and the square root of $B(\\infty)$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.RT","authors_text":"Eric Marberg, Travis Scrimshaw","submitted_at":"2026-08-11T14:56:31Z","abstract_excerpt":"We introduce a general monoidal category of $\\mathbf{N}$-root crystals and then study the special case of square root $\\mathfrak{gl}_n$-crystals. The latter objects include Yu's crystals on semistandard set-valued tableaux. Prior work of the first author, Tong, and Yu showed that regular square root $\\mathfrak{gl}_n$-crystals can be a useful tool for proving Grothendieck positivity results. The objects studied here go beyond the regular case and allow us to construct a square root analog of the direct limit crystal $B(\\infty)$. We give several descriptions of our square root of $B(\\infty)$, us"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"2608.11009","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2026-08-11T14:56:31Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"38d357464d265906abdf57b1aa2c5aceaa30a19a07b38f9b1d402eaf10f056d6","abstract_canon_sha256":"a6449f866c212a53e293a99e64c1ad86a0a991d5c31b2e3df7730be3200336cf"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-08-12T01:24:00.462498Z","signature_b64":"TSX9erJxo1jQasybIA50NVPw9SpbTz/MARLkKqxO2QWrlX1XyAyxYl8/0/PN6xz4fMMCHivqMg5Sb4xHdKXbCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d57a6b1bfd34be4b154ed75ac79e6cb1f311ebb87ac16bf00737bdf574875c82","last_reissued_at":"2026-08-12T01:24:00.460353Z","signature_status":"signed_v1","first_computed_at":"2026-08-12T01:24:00.460353Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Square root crystals and the square root of $B(\\infty)$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.RT","authors_text":"Eric Marberg, Travis Scrimshaw","submitted_at":"2026-08-11T14:56:31Z","abstract_excerpt":"We introduce a general monoidal category of $\\mathbf{N}$-root crystals and then study the special case of square root $\\mathfrak{gl}_n$-crystals. The latter objects include Yu's crystals on semistandard set-valued tableaux. Prior work of the first author, Tong, and Yu showed that regular square root $\\mathfrak{gl}_n$-crystals can be a useful tool for proving Grothendieck positivity results. The objects studied here go beyond the regular case and allow us to construct a square root analog of the direct limit crystal $B(\\infty)$. We give several descriptions of our square root of $B(\\infty)$, us"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2608.11009","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2608.11009/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"},"aliases":[{"alias_kind":"arxiv","alias_value":"2608.11009","created_at":"2026-08-12T01:24:00.464411+00:00"},{"alias_kind":"arxiv_version","alias_value":"2608.11009v1","created_at":"2026-08-12T01:24:00.464411+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2608.11009","created_at":"2026-08-12T01:24:00.464411+00:00"},{"alias_kind":"pith_short_12","alias_value":"2V5GWG75GS7E","created_at":"2026-08-12T01:24:00.464411+00:00"},{"alias_kind":"pith_short_16","alias_value":"2V5GWG75GS7EWFKO","created_at":"2026-08-12T01:24:00.464411+00:00"},{"alias_kind":"pith_short_8","alias_value":"2V5GWG75","created_at":"2026-08-12T01:24:00.464411+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/2V5GWG75GS7EWFKO25NMPHTMWH","json":"https://pith.science/pith/2V5GWG75GS7EWFKO25NMPHTMWH.json","graph_json":"https://pith.science/api/pith-number/2V5GWG75GS7EWFKO25NMPHTMWH/graph.json","events_json":"https://pith.science/api/pith-number/2V5GWG75GS7EWFKO25NMPHTMWH/events.json","paper":"https://pith.science/paper/2V5GWG75"},"agent_actions":{"view_html":"https://pith.science/pith/2V5GWG75GS7EWFKO25NMPHTMWH","download_json":"https://pith.science/pith/2V5GWG75GS7EWFKO25NMPHTMWH.json","view_paper":"https://pith.science/paper/2V5GWG75","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2608.11009&json=true","fetch_graph":"https://pith.science/api/pith-number/2V5GWG75GS7EWFKO25NMPHTMWH/graph.json","fetch_events":"https://pith.science/api/pith-number/2V5GWG75GS7EWFKO25NMPHTMWH/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/2V5GWG75GS7EWFKO25NMPHTMWH/action/timestamp_anchor","attest_storage":"https://pith.science/pith/2V5GWG75GS7EWFKO25NMPHTMWH/action/storage_attestation","attest_author":"https://pith.science/pith/2V5GWG75GS7EWFKO25NMPHTMWH/action/author_attestation","sign_citation":"https://pith.science/pith/2V5GWG75GS7EWFKO25NMPHTMWH/action/citation_signature","submit_replication":"https://pith.science/pith/2V5GWG75GS7EWFKO25NMPHTMWH/action/replication_record"}},"created_at":"2026-08-12T01:24:00.464411+00:00","updated_at":"2026-08-12T01:24:00.464411+00:00"}