{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:KGIEK46AYNNCJCP4TYXP5Q56IT","short_pith_number":"pith:KGIEK46A","schema_version":"1.0","canonical_sha256":"51904573c0c35a2489fc9e2efec3be44ed41c3ef1215df6069aa4a0a8df4c19a","source":{"kind":"arxiv","id":"1312.0038","version":2},"attestation_state":"computed","paper":{"title":"Bounds on Operator Dimensions in 2D Conformal Field Theories","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"hep-th","authors_text":"Alfred D. Shapere, Joshua D. Qualls","submitted_at":"2013-11-29T23:45:42Z","abstract_excerpt":"We extend the work of Hellerman (arxiv:0902.2790) to derive an upper bound on the conformal dimension $\\Delta_2$ of the next-to-lowest nontrival primary operator in unitary two-dimensional conformal field theories without chiral primary operators. The bound we find is of the same form as found for $\\Delta_1$: $\\Delta_2 \\leq c_{tot}/12 + O(1)$. We find a similar bound on the conformal dimension $\\Delta_3$, and present a method for deriving bounds on $\\Delta_n$ for any $n$, under slightly modified assumptions. For asymptotically large $c_{tot}$ and fixed $n$, we show that $\\Delta_n \\leq \\frac{c_"},"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":"1312.0038","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2013-11-29T23:45:42Z","cross_cats_sorted":[],"title_canon_sha256":"f442913b7584d92d3540261dda6d221cb6110b50bbd8da4fcbd4e9803b02886e","abstract_canon_sha256":"414b5333e701e3053f16c46c4e5c0dbdd90732c45ff04f318f47406f8cc91ce7"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:46:04.642962Z","signature_b64":"LZNLtZGph4HWpfbT5ieRf5lbfCRb/CxZ+k01XuhPXnxPIxZwzHkLmkoHBQO2awJ6DCtm2WCac3vkQlusILIBCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"51904573c0c35a2489fc9e2efec3be44ed41c3ef1215df6069aa4a0a8df4c19a","last_reissued_at":"2026-05-18T01:46:04.642559Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:46:04.642559Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Bounds on Operator Dimensions in 2D Conformal Field Theories","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"hep-th","authors_text":"Alfred D. Shapere, Joshua D. Qualls","submitted_at":"2013-11-29T23:45:42Z","abstract_excerpt":"We extend the work of Hellerman (arxiv:0902.2790) to derive an upper bound on the conformal dimension $\\Delta_2$ of the next-to-lowest nontrival primary operator in unitary two-dimensional conformal field theories without chiral primary operators. The bound we find is of the same form as found for $\\Delta_1$: $\\Delta_2 \\leq c_{tot}/12 + O(1)$. We find a similar bound on the conformal dimension $\\Delta_3$, and present a method for deriving bounds on $\\Delta_n$ for any $n$, under slightly modified assumptions. For asymptotically large $c_{tot}$ and fixed $n$, we show that $\\Delta_n \\leq \\frac{c_"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1312.0038","kind":"arxiv","version":2},"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":"1312.0038","created_at":"2026-05-18T01:46:04.642620+00:00"},{"alias_kind":"arxiv_version","alias_value":"1312.0038v2","created_at":"2026-05-18T01:46:04.642620+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1312.0038","created_at":"2026-05-18T01:46:04.642620+00:00"},{"alias_kind":"pith_short_12","alias_value":"KGIEK46AYNNC","created_at":"2026-05-18T12:27:49.015174+00:00"},{"alias_kind":"pith_short_16","alias_value":"KGIEK46AYNNCJCP4","created_at":"2026-05-18T12:27:49.015174+00:00"},{"alias_kind":"pith_short_8","alias_value":"KGIEK46A","created_at":"2026-05-18T12:27:49.015174+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/KGIEK46AYNNCJCP4TYXP5Q56IT","json":"https://pith.science/pith/KGIEK46AYNNCJCP4TYXP5Q56IT.json","graph_json":"https://pith.science/api/pith-number/KGIEK46AYNNCJCP4TYXP5Q56IT/graph.json","events_json":"https://pith.science/api/pith-number/KGIEK46AYNNCJCP4TYXP5Q56IT/events.json","paper":"https://pith.science/paper/KGIEK46A"},"agent_actions":{"view_html":"https://pith.science/pith/KGIEK46AYNNCJCP4TYXP5Q56IT","download_json":"https://pith.science/pith/KGIEK46AYNNCJCP4TYXP5Q56IT.json","view_paper":"https://pith.science/paper/KGIEK46A","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1312.0038&json=true","fetch_graph":"https://pith.science/api/pith-number/KGIEK46AYNNCJCP4TYXP5Q56IT/graph.json","fetch_events":"https://pith.science/api/pith-number/KGIEK46AYNNCJCP4TYXP5Q56IT/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/KGIEK46AYNNCJCP4TYXP5Q56IT/action/timestamp_anchor","attest_storage":"https://pith.science/pith/KGIEK46AYNNCJCP4TYXP5Q56IT/action/storage_attestation","attest_author":"https://pith.science/pith/KGIEK46AYNNCJCP4TYXP5Q56IT/action/author_attestation","sign_citation":"https://pith.science/pith/KGIEK46AYNNCJCP4TYXP5Q56IT/action/citation_signature","submit_replication":"https://pith.science/pith/KGIEK46AYNNCJCP4TYXP5Q56IT/action/replication_record"}},"created_at":"2026-05-18T01:46:04.642620+00:00","updated_at":"2026-05-18T01:46:04.642620+00:00"}