{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:KE44QZJULM6YECB6A3VHZYO4XE","short_pith_number":"pith:KE44QZJU","schema_version":"1.0","canonical_sha256":"5139c865345b3d82083e06ea7ce1dcb91f8f0c80a142684e27164df782e5433b","source":{"kind":"arxiv","id":"1510.06840","version":1},"attestation_state":"computed","paper":{"title":"Light ladders and clasp conjectures","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Ben Elias","submitted_at":"2015-10-23T06:18:29Z","abstract_excerpt":"Morphisms between tensor products of fundamental representations of the quantum group of sl(n) are described by the sl(n)-webs of Cautis-Kamnitzer-Morrison. Using these webs, we provide an explicit, root-theoretic formula for the local intersection forms attached to each summand of the tensor product of an irreducible representation with a fundamental representation. We prove this formula for n at most 4, and conjecture that it holds for all n.\n  Given two sequences of fundamental weights which sum to the same dominant weight, the clasp is the morphism between the corresponding tensor products"},"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":"1510.06840","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2015-10-23T06:18:29Z","cross_cats_sorted":[],"title_canon_sha256":"5e03f079c9d5546b00ed0d4c41b63271a620cef28353fc071aebee715267de2c","abstract_canon_sha256":"fd45b3289cd13b3af7f5ebeb0a7c7d5440e0b8269995d3cfdc3ae142dc3e3a14"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:29:22.961348Z","signature_b64":"+bpkBuFsnQw5yaS7LzW/l4ge8AjjPKabS8PPKR47288y2l6LQIlgPhtCAxzSCd+5bWVJK57IwSxFV3PfxDDtCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5139c865345b3d82083e06ea7ce1dcb91f8f0c80a142684e27164df782e5433b","last_reissued_at":"2026-05-18T01:29:22.960579Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:29:22.960579Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Light ladders and clasp conjectures","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Ben Elias","submitted_at":"2015-10-23T06:18:29Z","abstract_excerpt":"Morphisms between tensor products of fundamental representations of the quantum group of sl(n) are described by the sl(n)-webs of Cautis-Kamnitzer-Morrison. Using these webs, we provide an explicit, root-theoretic formula for the local intersection forms attached to each summand of the tensor product of an irreducible representation with a fundamental representation. We prove this formula for n at most 4, and conjecture that it holds for all n.\n  Given two sequences of fundamental weights which sum to the same dominant weight, the clasp is the morphism between the corresponding tensor products"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1510.06840","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1510.06840","created_at":"2026-05-18T01:29:22.960678+00:00"},{"alias_kind":"arxiv_version","alias_value":"1510.06840v1","created_at":"2026-05-18T01:29:22.960678+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1510.06840","created_at":"2026-05-18T01:29:22.960678+00:00"},{"alias_kind":"pith_short_12","alias_value":"KE44QZJULM6Y","created_at":"2026-05-18T12:29:27.538025+00:00"},{"alias_kind":"pith_short_16","alias_value":"KE44QZJULM6YECB6","created_at":"2026-05-18T12:29:27.538025+00:00"},{"alias_kind":"pith_short_8","alias_value":"KE44QZJU","created_at":"2026-05-18T12:29:27.538025+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":4,"internal_anchor_count":4,"sample":[{"citing_arxiv_id":"2303.04264","citing_title":"On a symplectic quantum Howe duality","ref_index":22,"is_internal_anchor":true},{"citing_arxiv_id":"2306.12501","citing_title":"Rotation-invariant web bases from hourglass plabic graphs","ref_index":3,"is_internal_anchor":true},{"citing_arxiv_id":"2401.00704","citing_title":"Orthogonal webs and semisimplification","ref_index":17,"is_internal_anchor":true},{"citing_arxiv_id":"2409.01005","citing_title":"On Hecke and asymptotic categories for a family of complex reflection groups","ref_index":22,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/KE44QZJULM6YECB6A3VHZYO4XE","json":"https://pith.science/pith/KE44QZJULM6YECB6A3VHZYO4XE.json","graph_json":"https://pith.science/api/pith-number/KE44QZJULM6YECB6A3VHZYO4XE/graph.json","events_json":"https://pith.science/api/pith-number/KE44QZJULM6YECB6A3VHZYO4XE/events.json","paper":"https://pith.science/paper/KE44QZJU"},"agent_actions":{"view_html":"https://pith.science/pith/KE44QZJULM6YECB6A3VHZYO4XE","download_json":"https://pith.science/pith/KE44QZJULM6YECB6A3VHZYO4XE.json","view_paper":"https://pith.science/paper/KE44QZJU","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1510.06840&json=true","fetch_graph":"https://pith.science/api/pith-number/KE44QZJULM6YECB6A3VHZYO4XE/graph.json","fetch_events":"https://pith.science/api/pith-number/KE44QZJULM6YECB6A3VHZYO4XE/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/KE44QZJULM6YECB6A3VHZYO4XE/action/timestamp_anchor","attest_storage":"https://pith.science/pith/KE44QZJULM6YECB6A3VHZYO4XE/action/storage_attestation","attest_author":"https://pith.science/pith/KE44QZJULM6YECB6A3VHZYO4XE/action/author_attestation","sign_citation":"https://pith.science/pith/KE44QZJULM6YECB6A3VHZYO4XE/action/citation_signature","submit_replication":"https://pith.science/pith/KE44QZJULM6YECB6A3VHZYO4XE/action/replication_record"}},"created_at":"2026-05-18T01:29:22.960678+00:00","updated_at":"2026-05-18T01:29:22.960678+00:00"}