{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:J2RVOPZYLLFATYZYC7PGRZVJV4","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":"938fb96a7c31e96952f63cff2a493db56be24bfdea10a3b841d1201803c7ce06","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"hep-th","submitted_at":"2026-07-27T18:00:01Z","title_canon_sha256":"5951d9f42d30e6a9244fe1653dfa0ca5afe4b62fab8d1911c0832bbd697e9fdf"},"schema_version":"1.0","source":{"id":"2607.24913","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2607.24913","created_at":"2026-07-29T00:24:51Z"},{"alias_kind":"arxiv_version","alias_value":"2607.24913v1","created_at":"2026-07-29T00:24:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.24913","created_at":"2026-07-29T00:24:51Z"},{"alias_kind":"pith_short_12","alias_value":"J2RVOPZYLLFA","created_at":"2026-07-29T00:24:51Z"},{"alias_kind":"pith_short_16","alias_value":"J2RVOPZYLLFATYZY","created_at":"2026-07-29T00:24:51Z"},{"alias_kind":"pith_short_8","alias_value":"J2RVOPZY","created_at":"2026-07-29T00:24:51Z"}],"graph_snapshots":[{"event_id":"sha256:6d804f5e3eaa1638824fea6aaae80495f0f087d1856d4f1f3f79a16946f603e4","target":"graph","created_at":"2026-07-29T00:24:51Z","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/2607.24913/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We develop a neural network bootstrap framework for reconstructing partition functions of two-dimensional conformal field theories (CFTs) based on modular invariance and the Cardy condition, which are recast as crossing equations for four-point correlators. For torus partition functions, we use the twist-field representation in the symmetric-orbifold description to map modular S-invariance to four-point crossing and focus on the diagonal kinematics of four insertions on a line. For annulus partition functions, we formulate open/closed channel duality as crossing symmetry for mixed four-point f","authors_text":"Andreas Stergiou, Kausik Ghosh, Sidhaarth Kumar, Vasilis Niarchos","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"hep-th","submitted_at":"2026-07-27T18:00:01Z","title":"Neural Spectral Bias and Conformal Correlators II: Modular and Annulus Bootstrap"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.24913","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":"sha256:25e32608918c7ce56eede13f7db9d2a1171c2a03b2331136f3fcdb2601a7b20b","target":"record","created_at":"2026-07-29T00:24:51Z","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":"938fb96a7c31e96952f63cff2a493db56be24bfdea10a3b841d1201803c7ce06","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"hep-th","submitted_at":"2026-07-27T18:00:01Z","title_canon_sha256":"5951d9f42d30e6a9244fe1653dfa0ca5afe4b62fab8d1911c0832bbd697e9fdf"},"schema_version":"1.0","source":{"id":"2607.24913","kind":"arxiv","version":1}},"canonical_sha256":"4ea3573f385aca09e33817de68e6a9af2008e75a7ff50ecedec76cc2f04ec7f4","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4ea3573f385aca09e33817de68e6a9af2008e75a7ff50ecedec76cc2f04ec7f4","first_computed_at":"2026-07-29T00:24:51.511913Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-29T00:24:51.511913Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"sY4NDiqgWrI7rJxW5lid3gLQ4ozmOhjYyicz6GXifkAmuq0OxBoQ8nYnCOhz/mLZ6rgRroIuYr8zHQ66+byUAw==","signature_status":"signed_v1","signed_at":"2026-07-29T00:24:51.512896Z","signed_message":"canonical_sha256_bytes"},"source_id":"2607.24913","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:25e32608918c7ce56eede13f7db9d2a1171c2a03b2331136f3fcdb2601a7b20b","sha256:6d804f5e3eaa1638824fea6aaae80495f0f087d1856d4f1f3f79a16946f603e4"],"state_sha256":"eeb74fb9b58a8004ade8977082453a2fc2dc587d59d5faf8f86835479d3133d0"}