{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:EWUTKUTEP3NTVQ67INIUWXH3HG","short_pith_number":"pith:EWUTKUTE","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"},"canonical_sha256":"25a93552647edb3ac3df43514b5cfb3991e3ac39d17c539867fc49f88a0d6ebd","source":{"kind":"arxiv","id":"2606.19994","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2606.19994","created_at":"2026-06-19T16:13:00Z"},{"alias_kind":"arxiv_version","alias_value":"2606.19994v1","created_at":"2026-06-19T16:13:00Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.19994","created_at":"2026-06-19T16:13:00Z"},{"alias_kind":"pith_short_12","alias_value":"EWUTKUTEP3NT","created_at":"2026-06-19T16:13:00Z"},{"alias_kind":"pith_short_16","alias_value":"EWUTKUTEP3NTVQ67","created_at":"2026-06-19T16:13:00Z"},{"alias_kind":"pith_short_8","alias_value":"EWUTKUTE","created_at":"2026-06-19T16:13:00Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:EWUTKUTEP3NTVQ67INIUWXH3HG","target":"record","payload":{"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"},"canonical_sha256":"25a93552647edb3ac3df43514b5cfb3991e3ac39d17c539867fc49f88a0d6ebd","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"},"source_kind":"arxiv","source_id":"2606.19994","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-06-19T16:13:00Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"qIkYLyNOPvx57UXdfMV3kuye795u3Q4tlpLvx9cTIwce6RfDh+1evb7mMbb3hklPUeZu4rcz1DWyFRY424onBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-05T00:31:39.846383Z"},"content_sha256":"8a58b54661338691647a6a511d38a33213aef0cf34fcfdafff449cd544ff6d24","schema_version":"1.0","event_id":"sha256:8a58b54661338691647a6a511d38a33213aef0cf34fcfdafff449cd544ff6d24"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:EWUTKUTEP3NTVQ67INIUWXH3HG","target":"graph","payload":{"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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-06-19T16:13:00Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"nsaxmB8yuDvAN8mvn81IALmTWtQkdBltgTg5iOO2KRIvVjRO2DHNPWjsxKyHr9WtnW79wEFkNTED3CjB+M09CA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-05T00:31:39.846868Z"},"content_sha256":"123e6335ca32b0b2a64e2ba606a30ceff877b27de5e17177d97f95fd1c1b7bc0","schema_version":"1.0","event_id":"sha256:123e6335ca32b0b2a64e2ba606a30ceff877b27de5e17177d97f95fd1c1b7bc0"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/EWUTKUTEP3NTVQ67INIUWXH3HG/bundle.json","state_url":"https://pith.science/pith/EWUTKUTEP3NTVQ67INIUWXH3HG/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/EWUTKUTEP3NTVQ67INIUWXH3HG/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":"2026-08-05T00:31:39Z","links":{"resolver":"https://pith.science/pith/EWUTKUTEP3NTVQ67INIUWXH3HG","bundle":"https://pith.science/pith/EWUTKUTEP3NTVQ67INIUWXH3HG/bundle.json","state":"https://pith.science/pith/EWUTKUTEP3NTVQ67INIUWXH3HG/state.json","well_known_bundle":"https://pith.science/.well-known/pith/EWUTKUTEP3NTVQ67INIUWXH3HG/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:EWUTKUTEP3NTVQ67INIUWXH3HG","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":"ec18524c42eebdb8dd245fc67c06bb65cd80d758c6426e05caf2f48006105d11","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2026-06-18T09:32:21Z","title_canon_sha256":"146a66aeb9e4d82e004c07ab278a1c0a4793bc0653ea1ccfcdb7c1f68b70eb62"},"schema_version":"1.0","source":{"id":"2606.19994","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2606.19994","created_at":"2026-06-19T16:13:00Z"},{"alias_kind":"arxiv_version","alias_value":"2606.19994v1","created_at":"2026-06-19T16:13:00Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.19994","created_at":"2026-06-19T16:13:00Z"},{"alias_kind":"pith_short_12","alias_value":"EWUTKUTEP3NT","created_at":"2026-06-19T16:13:00Z"},{"alias_kind":"pith_short_16","alias_value":"EWUTKUTEP3NTVQ67","created_at":"2026-06-19T16:13:00Z"},{"alias_kind":"pith_short_8","alias_value":"EWUTKUTE","created_at":"2026-06-19T16:13:00Z"}],"graph_snapshots":[{"event_id":"sha256:123e6335ca32b0b2a64e2ba606a30ceff877b27de5e17177d97f95fd1c1b7bc0","target":"graph","created_at":"2026-06-19T16:13:00Z","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/2606.19994/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"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","authors_text":"Tomislav \\v{S}iki\\' c","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2026-06-18T09:32:21Z","title":"Two examples of combinatorial relations among relations of $C_{n}\\sp{(1)}$-standard modules for higher levels"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.19994","kind":"arxiv","version":1},"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":"sha256:8a58b54661338691647a6a511d38a33213aef0cf34fcfdafff449cd544ff6d24","target":"record","created_at":"2026-06-19T16:13:00Z","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":"ec18524c42eebdb8dd245fc67c06bb65cd80d758c6426e05caf2f48006105d11","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2026-06-18T09:32:21Z","title_canon_sha256":"146a66aeb9e4d82e004c07ab278a1c0a4793bc0653ea1ccfcdb7c1f68b70eb62"},"schema_version":"1.0","source":{"id":"2606.19994","kind":"arxiv","version":1}},"canonical_sha256":"25a93552647edb3ac3df43514b5cfb3991e3ac39d17c539867fc49f88a0d6ebd","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"25a93552647edb3ac3df43514b5cfb3991e3ac39d17c539867fc49f88a0d6ebd","first_computed_at":"2026-06-19T16:13:00.032349Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-19T16:13:00.032349Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"QyJjo8lXhGGI4PxuvZrLHH/ST73krGfEocLOgjYqrphAZVi8Ha3pRduZh2izJ2lePrYKbLgvAvNTceuddy8mBg==","signature_status":"signed_v1","signed_at":"2026-06-19T16:13:00.032694Z","signed_message":"canonical_sha256_bytes"},"source_id":"2606.19994","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8a58b54661338691647a6a511d38a33213aef0cf34fcfdafff449cd544ff6d24","sha256:123e6335ca32b0b2a64e2ba606a30ceff877b27de5e17177d97f95fd1c1b7bc0"],"state_sha256":"cd65766792132625ad26c2f4682bf74f4f531d925674321b4bdf84d6036abc9e"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"nE7kfkBsh5eRdJd8QPavQWTCp+1EYsFlHpKC7nUAzv5BGKwXf31geZesKzHKNW+CLf5FpjwAR8s6ksQRDve1DQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-05T00:31:39.850249Z","bundle_sha256":"d74610cc72a7b15375011ef3207d9f601ffcc6db44414ed2111dbc85ff01d377"}}