{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2020:46LPLFLIMHQZTEOICNNRNTJKAI","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":"7925cca8e18a26f0267f97096506cbff3d2d09e8cf14df38689f55a0e73050ae","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2020-09-02T18:00:00Z","title_canon_sha256":"aee6ea9348c4b0600dc07c377a2f93c81c151873b681a170c69c983ed35081d0"},"schema_version":"1.0","source":{"id":"2009.01236","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2009.01236","created_at":"2026-07-05T02:54:38Z"},{"alias_kind":"arxiv_version","alias_value":"2009.01236v3","created_at":"2026-07-05T02:54:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2009.01236","created_at":"2026-07-05T02:54:38Z"},{"alias_kind":"pith_short_12","alias_value":"46LPLFLIMHQZ","created_at":"2026-07-05T02:54:38Z"},{"alias_kind":"pith_short_16","alias_value":"46LPLFLIMHQZTEOI","created_at":"2026-07-05T02:54:38Z"},{"alias_kind":"pith_short_8","alias_value":"46LPLFLI","created_at":"2026-07-05T02:54:38Z"}],"graph_snapshots":[{"event_id":"sha256:da36bb00c01df4718e8517b2a33362ef6b82e05f3832e7c496fc8ff999ba31ba","target":"graph","created_at":"2026-07-05T02:54:38Z","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/2009.01236/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Modular invariance imposes rigid constrains on the partition functions of two-dimensional conformal field theories. Many fundamental results follow strictly from modular invariance, giving rise to the numerical modular bootstrap program. Here we report a way to assign to a particular family of quantum error correcting codes a family of \"code CFTs\" CFTs\", which forms a subset of the space of Narain CFTs. This correspondence reduces modular invariance of the 2d CFT partition function to a few simple algebraic relations obeyed by a multivariate polynomial characterizing the corresponding code. Us","authors_text":"Alfred Shapere, Anatoly Dymarsky","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2020-09-02T18:00:00Z","title":"Solutions of modular bootstrap constraints from quantum codes"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2009.01236","kind":"arxiv","version":3},"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":"sha256:1d8165258a315c3e11a00ed9c713eca88422b0ba07e0de38f0edd5b382415cdc","target":"record","created_at":"2026-07-05T02:54:38Z","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":"7925cca8e18a26f0267f97096506cbff3d2d09e8cf14df38689f55a0e73050ae","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2020-09-02T18:00:00Z","title_canon_sha256":"aee6ea9348c4b0600dc07c377a2f93c81c151873b681a170c69c983ed35081d0"},"schema_version":"1.0","source":{"id":"2009.01236","kind":"arxiv","version":3}},"canonical_sha256":"e796f5956861e19991c8135b16cd2a023d37b21cea1d89cc62907efcf0adb231","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e796f5956861e19991c8135b16cd2a023d37b21cea1d89cc62907efcf0adb231","first_computed_at":"2026-07-05T02:54:38.935135Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T02:54:38.935135Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"x/1r/j3bihYK2yI5mwx61sZ8tmPcOvGlRpfRpGbnQrnspj3ZFwAS9VqOEey6k/zM1iDJZEoxicEIRqmpExwxAA==","signature_status":"signed_v1","signed_at":"2026-07-05T02:54:38.935515Z","signed_message":"canonical_sha256_bytes"},"source_id":"2009.01236","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1d8165258a315c3e11a00ed9c713eca88422b0ba07e0de38f0edd5b382415cdc","sha256:da36bb00c01df4718e8517b2a33362ef6b82e05f3832e7c496fc8ff999ba31ba"],"state_sha256":"25a23ded5e13f2fcf8de6499f39b0f08eccdc0212394e9e4ec72d77216ed7444"}