{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2025:YAPIWPWU2KRKRXNUY6CQ7H4QCA","short_pith_number":"pith:YAPIWPWU","schema_version":"1.0","canonical_sha256":"c01e8b3ed4d2a2a8ddb4c7850f9f90102bf7697e2c62d72a74a4b67841addd7a","source":{"kind":"arxiv","id":"2510.12035","version":3},"attestation_state":"computed","paper":{"title":"Stranding $\\mathfrak{sl}_n$ webs","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.RT","authors_text":"Heather M. Russell, Julianna Tymoczko","submitted_at":"2025-10-14T00:42:49Z","abstract_excerpt":"Webs are planar directed graphs that encode invariant vectors for tensor products of fundamental $U_q(\\mathfrak{sl}_n)$-representations. For $\\mathfrak{sl}_2$ and $\\mathfrak{sl}_3$, web calculus is governed by effective reduction rules and well-understood reduced-web bases, but these features break down in higher rank. In this paper we develop a global combinatorial framework for untagged $\\mathfrak{sl}_n$ webs, called strandings, which organizes local labeling data into systems of colored directed paths on the web graph.\n  Our main result is an explicit state-sum formula for the invariant vec"},"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":"2510.12035","kind":"arxiv","version":3},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.RT","submitted_at":"2025-10-14T00:42:49Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"84697c250988f5267d2ca2cb6679b5bf1fbaf3cfd7a012d9baaae11f73645b82","abstract_canon_sha256":"ebf9aae5e2279204fb26c2f66943d9a9269c84629ae5edcd5209dce75508d7ce"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-02T01:03:35.350574Z","signature_b64":"pBJwnymKxgU+htIgOCacHviWMJS8pVIJ6E67/rcH8m7sNc+pSpaBOhVBHmoUQC4GiD1dobpU7ue3QP1lwYXyCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c01e8b3ed4d2a2a8ddb4c7850f9f90102bf7697e2c62d72a74a4b67841addd7a","last_reissued_at":"2026-06-02T01:03:35.349726Z","signature_status":"signed_v1","first_computed_at":"2026-06-02T01:03:35.349726Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Stranding $\\mathfrak{sl}_n$ webs","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.RT","authors_text":"Heather M. Russell, Julianna Tymoczko","submitted_at":"2025-10-14T00:42:49Z","abstract_excerpt":"Webs are planar directed graphs that encode invariant vectors for tensor products of fundamental $U_q(\\mathfrak{sl}_n)$-representations. For $\\mathfrak{sl}_2$ and $\\mathfrak{sl}_3$, web calculus is governed by effective reduction rules and well-understood reduced-web bases, but these features break down in higher rank. In this paper we develop a global combinatorial framework for untagged $\\mathfrak{sl}_n$ webs, called strandings, which organizes local labeling data into systems of colored directed paths on the web graph.\n  Our main result is an explicit state-sum formula for the invariant vec"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2510.12035","kind":"arxiv","version":3},"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/2510.12035/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":"2510.12035","created_at":"2026-06-02T01:03:35.349833+00:00"},{"alias_kind":"arxiv_version","alias_value":"2510.12035v3","created_at":"2026-06-02T01:03:35.349833+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2510.12035","created_at":"2026-06-02T01:03:35.349833+00:00"},{"alias_kind":"pith_short_12","alias_value":"YAPIWPWU2KRK","created_at":"2026-06-02T01:03:35.349833+00:00"},{"alias_kind":"pith_short_16","alias_value":"YAPIWPWU2KRKRXNU","created_at":"2026-06-02T01:03:35.349833+00:00"},{"alias_kind":"pith_short_8","alias_value":"YAPIWPWU","created_at":"2026-06-02T01:03:35.349833+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/YAPIWPWU2KRKRXNUY6CQ7H4QCA","json":"https://pith.science/pith/YAPIWPWU2KRKRXNUY6CQ7H4QCA.json","graph_json":"https://pith.science/api/pith-number/YAPIWPWU2KRKRXNUY6CQ7H4QCA/graph.json","events_json":"https://pith.science/api/pith-number/YAPIWPWU2KRKRXNUY6CQ7H4QCA/events.json","paper":"https://pith.science/paper/YAPIWPWU"},"agent_actions":{"view_html":"https://pith.science/pith/YAPIWPWU2KRKRXNUY6CQ7H4QCA","download_json":"https://pith.science/pith/YAPIWPWU2KRKRXNUY6CQ7H4QCA.json","view_paper":"https://pith.science/paper/YAPIWPWU","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2510.12035&json=true","fetch_graph":"https://pith.science/api/pith-number/YAPIWPWU2KRKRXNUY6CQ7H4QCA/graph.json","fetch_events":"https://pith.science/api/pith-number/YAPIWPWU2KRKRXNUY6CQ7H4QCA/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/YAPIWPWU2KRKRXNUY6CQ7H4QCA/action/timestamp_anchor","attest_storage":"https://pith.science/pith/YAPIWPWU2KRKRXNUY6CQ7H4QCA/action/storage_attestation","attest_author":"https://pith.science/pith/YAPIWPWU2KRKRXNUY6CQ7H4QCA/action/author_attestation","sign_citation":"https://pith.science/pith/YAPIWPWU2KRKRXNUY6CQ7H4QCA/action/citation_signature","submit_replication":"https://pith.science/pith/YAPIWPWU2KRKRXNUY6CQ7H4QCA/action/replication_record"}},"created_at":"2026-06-02T01:03:35.349833+00:00","updated_at":"2026-06-02T01:03:35.349833+00:00"}