{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2021:A55JRR5WT5WN3R66JT5ZMH4LZP","short_pith_number":"pith:A55JRR5W","schema_version":"1.0","canonical_sha256":"077a98c7b69f6cddc7de4cfb961f8bcbdd495385f2050fa9c61f1bae3af51487","source":{"kind":"arxiv","id":"2107.02816","version":1},"attestation_state":"computed","paper":{"title":"Non-rational Narain CFTs from codes over $F_4$","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.IT","math.IT","quant-ph"],"primary_cat":"hep-th","authors_text":"Adar Sharon, Anatoly Dymarsky","submitted_at":"2021-07-06T18:00:06Z","abstract_excerpt":"We construct a map between a class of codes over $F_4$ and a family of non-rational Narain CFTs. This construction is complementary to a recently introduced relation between quantum stabilizer codes and a class of rational Narain theories. From the modular bootstrap point of view we formulate a polynomial ansatz for the partition function which reduces modular invariance to a handful of algebraic easy-to-solve constraints. For certain small values of central charge our construction yields optimal theories, i.e. those with the largest value of the spectral gap."},"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":"2107.02816","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"hep-th","submitted_at":"2021-07-06T18:00:06Z","cross_cats_sorted":["cs.IT","math.IT","quant-ph"],"title_canon_sha256":"af60f178b59da4b6b0cf644597483755a27ef33340131bc0d97f96225149f39d","abstract_canon_sha256":"824cb085cf98de4ac47c79d6144fe5fcae9ce25796571865123eb1ffb4c33b57"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T03:33:45.728011Z","signature_b64":"nA/+HkaqYCAd5J/DqDrwqxuJNiMs/NrIygrpnGc/GITygGreOmjOVFReG1b3rQoQ6z2aX5SHsQN3HKbPtLkzBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"077a98c7b69f6cddc7de4cfb961f8bcbdd495385f2050fa9c61f1bae3af51487","last_reissued_at":"2026-07-05T03:33:45.727545Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T03:33:45.727545Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Non-rational Narain CFTs from codes over $F_4$","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.IT","math.IT","quant-ph"],"primary_cat":"hep-th","authors_text":"Adar Sharon, Anatoly Dymarsky","submitted_at":"2021-07-06T18:00:06Z","abstract_excerpt":"We construct a map between a class of codes over $F_4$ and a family of non-rational Narain CFTs. This construction is complementary to a recently introduced relation between quantum stabilizer codes and a class of rational Narain theories. From the modular bootstrap point of view we formulate a polynomial ansatz for the partition function which reduces modular invariance to a handful of algebraic easy-to-solve constraints. For certain small values of central charge our construction yields optimal theories, i.e. those with the largest value of the spectral gap."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2107.02816","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/2107.02816/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":"2107.02816","created_at":"2026-07-05T03:33:45.727610+00:00"},{"alias_kind":"arxiv_version","alias_value":"2107.02816v1","created_at":"2026-07-05T03:33:45.727610+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2107.02816","created_at":"2026-07-05T03:33:45.727610+00:00"},{"alias_kind":"pith_short_12","alias_value":"A55JRR5WT5WN","created_at":"2026-07-05T03:33:45.727610+00:00"},{"alias_kind":"pith_short_16","alias_value":"A55JRR5WT5WN3R66","created_at":"2026-07-05T03:33:45.727610+00:00"},{"alias_kind":"pith_short_8","alias_value":"A55JRR5W","created_at":"2026-07-05T03:33:45.727610+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2502.08084","citing_title":"Fermionic CFTs from topological boundaries in abelian Chern-Simons theories","ref_index":26,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/A55JRR5WT5WN3R66JT5ZMH4LZP","json":"https://pith.science/pith/A55JRR5WT5WN3R66JT5ZMH4LZP.json","graph_json":"https://pith.science/api/pith-number/A55JRR5WT5WN3R66JT5ZMH4LZP/graph.json","events_json":"https://pith.science/api/pith-number/A55JRR5WT5WN3R66JT5ZMH4LZP/events.json","paper":"https://pith.science/paper/A55JRR5W"},"agent_actions":{"view_html":"https://pith.science/pith/A55JRR5WT5WN3R66JT5ZMH4LZP","download_json":"https://pith.science/pith/A55JRR5WT5WN3R66JT5ZMH4LZP.json","view_paper":"https://pith.science/paper/A55JRR5W","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2107.02816&json=true","fetch_graph":"https://pith.science/api/pith-number/A55JRR5WT5WN3R66JT5ZMH4LZP/graph.json","fetch_events":"https://pith.science/api/pith-number/A55JRR5WT5WN3R66JT5ZMH4LZP/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/A55JRR5WT5WN3R66JT5ZMH4LZP/action/timestamp_anchor","attest_storage":"https://pith.science/pith/A55JRR5WT5WN3R66JT5ZMH4LZP/action/storage_attestation","attest_author":"https://pith.science/pith/A55JRR5WT5WN3R66JT5ZMH4LZP/action/author_attestation","sign_citation":"https://pith.science/pith/A55JRR5WT5WN3R66JT5ZMH4LZP/action/citation_signature","submit_replication":"https://pith.science/pith/A55JRR5WT5WN3R66JT5ZMH4LZP/action/replication_record"}},"created_at":"2026-07-05T03:33:45.727610+00:00","updated_at":"2026-07-05T03:33:45.727610+00:00"}