{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2025:UE5EAQ7BPXDME6A27BVPCGN5DR","short_pith_number":"pith:UE5EAQ7B","schema_version":"1.0","canonical_sha256":"a13a4043e17dc6c2781af86af119bd1c7fb8237a0d5a7cc93b8f5bf42a97d512","source":{"kind":"arxiv","id":"2509.07720","version":1},"attestation_state":"computed","paper":{"title":"Non-Equivalence of Smooth and Nodal Conformal Block Functors in Logarithmic CFT","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.AG","math.MP","math.RT"],"primary_cat":"math.QA","authors_text":"Hao Zhang","submitted_at":"2025-09-09T13:20:15Z","abstract_excerpt":"Let $\\mathbb V$ be an $\\mathbb N$-graded, $C_2$-cofinite vertex operator algebra (VOA) admitting a non-lowest generated module in $\\mathrm{Mod}(\\mathbb V)$ (e.g., the triplet algebras $\\mathcal{W}_p$ for $p\\in \\mathbb{Z}_{\\geq 2}$ or the even symplectic fermion VOAs $SF_d^+$ for $d\\in \\mathbb{Z}_+$). We prove that, unlike in the rational case, the spaces of conformal blocks associated to certain $\\mathbb V$-modules do not form a vector bundle on $\\overline{\\mathcal{M}}_{0,N}$ for $N\\geq 4$ by showing that their dimensions differ between nodal and smooth curves. Consequently, the sheaf of coinv"},"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":"2509.07720","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2025-09-09T13:20:15Z","cross_cats_sorted":["math-ph","math.AG","math.MP","math.RT"],"title_canon_sha256":"5a4980aceb6c1209b0e1d88a020d9ae6f949ddc555727a34460a0ca71e8ae883","abstract_canon_sha256":"d2bcedd6998663debe6fdf0e805c2257b40f7b0284bed3487e50e05e6758b930"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T12:07:26.949407Z","signature_b64":"W/rxhI7Wh1Ni/qz+H5dXG3JgDYxEr43F4gaRHkg8CZuLrWGE2keqglkhDezpYew/UfNaFkXkElMDVjgvP4yzDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a13a4043e17dc6c2781af86af119bd1c7fb8237a0d5a7cc93b8f5bf42a97d512","last_reissued_at":"2026-07-05T12:07:26.948934Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T12:07:26.948934Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Non-Equivalence of Smooth and Nodal Conformal Block Functors in Logarithmic CFT","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.AG","math.MP","math.RT"],"primary_cat":"math.QA","authors_text":"Hao Zhang","submitted_at":"2025-09-09T13:20:15Z","abstract_excerpt":"Let $\\mathbb V$ be an $\\mathbb N$-graded, $C_2$-cofinite vertex operator algebra (VOA) admitting a non-lowest generated module in $\\mathrm{Mod}(\\mathbb V)$ (e.g., the triplet algebras $\\mathcal{W}_p$ for $p\\in \\mathbb{Z}_{\\geq 2}$ or the even symplectic fermion VOAs $SF_d^+$ for $d\\in \\mathbb{Z}_+$). We prove that, unlike in the rational case, the spaces of conformal blocks associated to certain $\\mathbb V$-modules do not form a vector bundle on $\\overline{\\mathcal{M}}_{0,N}$ for $N\\geq 4$ by showing that their dimensions differ between nodal and smooth curves. Consequently, the sheaf of coinv"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2509.07720","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/2509.07720/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":"2509.07720","created_at":"2026-07-05T12:07:26.948988+00:00"},{"alias_kind":"arxiv_version","alias_value":"2509.07720v1","created_at":"2026-07-05T12:07:26.948988+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2509.07720","created_at":"2026-07-05T12:07:26.948988+00:00"},{"alias_kind":"pith_short_12","alias_value":"UE5EAQ7BPXDM","created_at":"2026-07-05T12:07:26.948988+00:00"},{"alias_kind":"pith_short_16","alias_value":"UE5EAQ7BPXDME6A2","created_at":"2026-07-05T12:07:26.948988+00:00"},{"alias_kind":"pith_short_8","alias_value":"UE5EAQ7B","created_at":"2026-07-05T12:07:26.948988+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/UE5EAQ7BPXDME6A27BVPCGN5DR","json":"https://pith.science/pith/UE5EAQ7BPXDME6A27BVPCGN5DR.json","graph_json":"https://pith.science/api/pith-number/UE5EAQ7BPXDME6A27BVPCGN5DR/graph.json","events_json":"https://pith.science/api/pith-number/UE5EAQ7BPXDME6A27BVPCGN5DR/events.json","paper":"https://pith.science/paper/UE5EAQ7B"},"agent_actions":{"view_html":"https://pith.science/pith/UE5EAQ7BPXDME6A27BVPCGN5DR","download_json":"https://pith.science/pith/UE5EAQ7BPXDME6A27BVPCGN5DR.json","view_paper":"https://pith.science/paper/UE5EAQ7B","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2509.07720&json=true","fetch_graph":"https://pith.science/api/pith-number/UE5EAQ7BPXDME6A27BVPCGN5DR/graph.json","fetch_events":"https://pith.science/api/pith-number/UE5EAQ7BPXDME6A27BVPCGN5DR/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/UE5EAQ7BPXDME6A27BVPCGN5DR/action/timestamp_anchor","attest_storage":"https://pith.science/pith/UE5EAQ7BPXDME6A27BVPCGN5DR/action/storage_attestation","attest_author":"https://pith.science/pith/UE5EAQ7BPXDME6A27BVPCGN5DR/action/author_attestation","sign_citation":"https://pith.science/pith/UE5EAQ7BPXDME6A27BVPCGN5DR/action/citation_signature","submit_replication":"https://pith.science/pith/UE5EAQ7BPXDME6A27BVPCGN5DR/action/replication_record"}},"created_at":"2026-07-05T12:07:26.948988+00:00","updated_at":"2026-07-05T12:07:26.948988+00:00"}