{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2026:EWUTKUTEP3NTVQ67INIUWXH3HG","short_pith_number":"pith:EWUTKUTE","schema_version":"1.0","canonical_sha256":"25a93552647edb3ac3df43514b5cfb3991e3ac39d17c539867fc49f88a0d6ebd","source":{"kind":"arxiv","id":"2606.19994","version":1},"attestation_state":"computed","paper":{"title":"Two examples of combinatorial relations among relations of $C_{n}\\sp{(1)}$-standard modules for higher levels","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.QA","authors_text":"Tomislav \\v{S}iki\\' c","submitted_at":"2026-06-18T09:32:21Z","abstract_excerpt":"The construction of relations among relations is one ingredient in the Groebner-like basis construction of the maximal ideal of the universal vertex operator algebra $V^k_{\\mathfrak g}$ for affine Lie algebras. For affine Lie algebras of type $C_n^{(1)}$, such combinatorially parametrized relations among relations were constructed in earlier work for level $2$ standard modules \\cite{PS3}, and for $C_2^{(1)}$-standard modules at higher levels \\cite{S}. This article presents two further examples in which the same counting method can be carried out. The first treats $C_n^{(1)}$-standard modules a"},"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":"2606.19994","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2026-06-18T09:32:21Z","cross_cats_sorted":[],"title_canon_sha256":"146a66aeb9e4d82e004c07ab278a1c0a4793bc0653ea1ccfcdb7c1f68b70eb62","abstract_canon_sha256":"ec18524c42eebdb8dd245fc67c06bb65cd80d758c6426e05caf2f48006105d11"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-19T16:13:00.032694Z","signature_b64":"QyJjo8lXhGGI4PxuvZrLHH/ST73krGfEocLOgjYqrphAZVi8Ha3pRduZh2izJ2lePrYKbLgvAvNTceuddy8mBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"25a93552647edb3ac3df43514b5cfb3991e3ac39d17c539867fc49f88a0d6ebd","last_reissued_at":"2026-06-19T16:13:00.032349Z","signature_status":"signed_v1","first_computed_at":"2026-06-19T16:13:00.032349Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Two examples of combinatorial relations among relations of $C_{n}\\sp{(1)}$-standard modules for higher levels","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.QA","authors_text":"Tomislav \\v{S}iki\\' c","submitted_at":"2026-06-18T09:32:21Z","abstract_excerpt":"The construction of relations among relations is one ingredient in the Groebner-like basis construction of the maximal ideal of the universal vertex operator algebra $V^k_{\\mathfrak g}$ for affine Lie algebras. For affine Lie algebras of type $C_n^{(1)}$, such combinatorially parametrized relations among relations were constructed in earlier work for level $2$ standard modules \\cite{PS3}, and for $C_2^{(1)}$-standard modules at higher levels \\cite{S}. This article presents two further examples in which the same counting method can be carried out. The first treats $C_n^{(1)}$-standard modules a"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.19994","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/2606.19994/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":"2606.19994","created_at":"2026-06-19T16:13:00.032412+00:00"},{"alias_kind":"arxiv_version","alias_value":"2606.19994v1","created_at":"2026-06-19T16:13:00.032412+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.19994","created_at":"2026-06-19T16:13:00.032412+00:00"},{"alias_kind":"pith_short_12","alias_value":"EWUTKUTEP3NT","created_at":"2026-06-19T16:13:00.032412+00:00"},{"alias_kind":"pith_short_16","alias_value":"EWUTKUTEP3NTVQ67","created_at":"2026-06-19T16:13:00.032412+00:00"},{"alias_kind":"pith_short_8","alias_value":"EWUTKUTE","created_at":"2026-06-19T16:13:00.032412+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/EWUTKUTEP3NTVQ67INIUWXH3HG","json":"https://pith.science/pith/EWUTKUTEP3NTVQ67INIUWXH3HG.json","graph_json":"https://pith.science/api/pith-number/EWUTKUTEP3NTVQ67INIUWXH3HG/graph.json","events_json":"https://pith.science/api/pith-number/EWUTKUTEP3NTVQ67INIUWXH3HG/events.json","paper":"https://pith.science/paper/EWUTKUTE"},"agent_actions":{"view_html":"https://pith.science/pith/EWUTKUTEP3NTVQ67INIUWXH3HG","download_json":"https://pith.science/pith/EWUTKUTEP3NTVQ67INIUWXH3HG.json","view_paper":"https://pith.science/paper/EWUTKUTE","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2606.19994&json=true","fetch_graph":"https://pith.science/api/pith-number/EWUTKUTEP3NTVQ67INIUWXH3HG/graph.json","fetch_events":"https://pith.science/api/pith-number/EWUTKUTEP3NTVQ67INIUWXH3HG/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/EWUTKUTEP3NTVQ67INIUWXH3HG/action/timestamp_anchor","attest_storage":"https://pith.science/pith/EWUTKUTEP3NTVQ67INIUWXH3HG/action/storage_attestation","attest_author":"https://pith.science/pith/EWUTKUTEP3NTVQ67INIUWXH3HG/action/author_attestation","sign_citation":"https://pith.science/pith/EWUTKUTEP3NTVQ67INIUWXH3HG/action/citation_signature","submit_replication":"https://pith.science/pith/EWUTKUTEP3NTVQ67INIUWXH3HG/action/replication_record"}},"created_at":"2026-06-19T16:13:00.032412+00:00","updated_at":"2026-06-19T16:13:00.032412+00:00"}