{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2025:ZLKCVFQBY4MXI5HT3J4L6WSVPU","short_pith_number":"pith:ZLKCVFQB","canonical_record":{"source":{"id":"2503.22798","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2025-03-28T18:00:31Z","cross_cats_sorted":[],"title_canon_sha256":"fd496451aa10e089c8cc6593f558092d7a3d69bb4accf80ecb2cf1bf5e48e69c","abstract_canon_sha256":"ccf9507fb77727c1c681331159404d6284a0dc1a6ff9af42fddd9f80b99d4f32"},"schema_version":"1.0"},"canonical_sha256":"cad42a9601c7197474f3da78bf5a557d2d4f9d974fe88eb3a7138827cc13910e","source":{"kind":"arxiv","id":"2503.22798","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2503.22798","created_at":"2026-07-05T11:53:45Z"},{"alias_kind":"arxiv_version","alias_value":"2503.22798v2","created_at":"2026-07-05T11:53:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2503.22798","created_at":"2026-07-05T11:53:45Z"},{"alias_kind":"pith_short_12","alias_value":"ZLKCVFQBY4MX","created_at":"2026-07-05T11:53:45Z"},{"alias_kind":"pith_short_16","alias_value":"ZLKCVFQBY4MXI5HT","created_at":"2026-07-05T11:53:45Z"},{"alias_kind":"pith_short_8","alias_value":"ZLKCVFQB","created_at":"2026-07-05T11:53:45Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2025:ZLKCVFQBY4MXI5HT3J4L6WSVPU","target":"record","payload":{"canonical_record":{"source":{"id":"2503.22798","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2025-03-28T18:00:31Z","cross_cats_sorted":[],"title_canon_sha256":"fd496451aa10e089c8cc6593f558092d7a3d69bb4accf80ecb2cf1bf5e48e69c","abstract_canon_sha256":"ccf9507fb77727c1c681331159404d6284a0dc1a6ff9af42fddd9f80b99d4f32"},"schema_version":"1.0"},"canonical_sha256":"cad42a9601c7197474f3da78bf5a557d2d4f9d974fe88eb3a7138827cc13910e","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:53:45.139881Z","signature_b64":"qp4l1AmEj8r2c3c+SPscK9kztEcdEKrnaZY+h8nV4Av3kKA3rk0OTN/pA7XBOEVz3R3r947mKTeAJPsKCB7jDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"cad42a9601c7197474f3da78bf5a557d2d4f9d974fe88eb3a7138827cc13910e","last_reissued_at":"2026-07-05T11:53:45.139275Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:53:45.139275Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2503.22798","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T11:53:45Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"FxJRxAC73mrTylNTLzvjqv0sTWLutbKiBjfQlqs3ItCVWMju6hgbqLLO+5f6jiKKJ+Cgn49ZBlnD7DJLrIXaBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-11T03:30:06.252898Z"},"content_sha256":"2ec3a2ff6157274325020cd410d3a0131bca4199039267928644c7cc516da26c","schema_version":"1.0","event_id":"sha256:2ec3a2ff6157274325020cd410d3a0131bca4199039267928644c7cc516da26c"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2025:ZLKCVFQBY4MXI5HT3J4L6WSVPU","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Solving 1D crossing and QFT$_2$/CFT$_1$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"hep-th","authors_text":"Kausik Ghosh, Miguel F. Paulos, No\\'e Suchel","submitted_at":"2025-03-28T18:00:31Z","abstract_excerpt":"We provide an effective solution of the 1D crossing equation. We begin by arguing that crossing constraints can be recast in terms of bases of sum rules associated to special sets of CFT data -- extremal solutions -- which solve these constraints in a minimal way and naturally saturate positivity bounds on the space of CFTs. We conjecture, argue and check extensively that any extremal solution behaves as a generalized free field in the UV. This allows us to reconstruct the entirety of their CFT data using a rapidly convergent ``hybrid bootstrap'' method, which combines numerics and analytics. "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2503.22798","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2503.22798/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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T11:53:45Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"CvZMOKLNeCFfu4CY14dw47fcFk533czIfzvgvRFbLT+y7OHe1JkTFW0A+8VIW1bDPigM2bhnSNzxNz0vtD1dCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-11T03:30:06.253460Z"},"content_sha256":"552ad1b623cc49ba347737e9ed93cae235fe81c2a899f95932d19d17d10193bc","schema_version":"1.0","event_id":"sha256:552ad1b623cc49ba347737e9ed93cae235fe81c2a899f95932d19d17d10193bc"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/ZLKCVFQBY4MXI5HT3J4L6WSVPU/bundle.json","state_url":"https://pith.science/pith/ZLKCVFQBY4MXI5HT3J4L6WSVPU/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/ZLKCVFQBY4MXI5HT3J4L6WSVPU/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-08-11T03:30:06Z","links":{"resolver":"https://pith.science/pith/ZLKCVFQBY4MXI5HT3J4L6WSVPU","bundle":"https://pith.science/pith/ZLKCVFQBY4MXI5HT3J4L6WSVPU/bundle.json","state":"https://pith.science/pith/ZLKCVFQBY4MXI5HT3J4L6WSVPU/state.json","well_known_bundle":"https://pith.science/.well-known/pith/ZLKCVFQBY4MXI5HT3J4L6WSVPU/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:ZLKCVFQBY4MXI5HT3J4L6WSVPU","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":"ccf9507fb77727c1c681331159404d6284a0dc1a6ff9af42fddd9f80b99d4f32","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2025-03-28T18:00:31Z","title_canon_sha256":"fd496451aa10e089c8cc6593f558092d7a3d69bb4accf80ecb2cf1bf5e48e69c"},"schema_version":"1.0","source":{"id":"2503.22798","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2503.22798","created_at":"2026-07-05T11:53:45Z"},{"alias_kind":"arxiv_version","alias_value":"2503.22798v2","created_at":"2026-07-05T11:53:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2503.22798","created_at":"2026-07-05T11:53:45Z"},{"alias_kind":"pith_short_12","alias_value":"ZLKCVFQBY4MX","created_at":"2026-07-05T11:53:45Z"},{"alias_kind":"pith_short_16","alias_value":"ZLKCVFQBY4MXI5HT","created_at":"2026-07-05T11:53:45Z"},{"alias_kind":"pith_short_8","alias_value":"ZLKCVFQB","created_at":"2026-07-05T11:53:45Z"}],"graph_snapshots":[{"event_id":"sha256:552ad1b623cc49ba347737e9ed93cae235fe81c2a899f95932d19d17d10193bc","target":"graph","created_at":"2026-07-05T11:53:45Z","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/2503.22798/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We provide an effective solution of the 1D crossing equation. We begin by arguing that crossing constraints can be recast in terms of bases of sum rules associated to special sets of CFT data -- extremal solutions -- which solve these constraints in a minimal way and naturally saturate positivity bounds on the space of CFTs. We conjecture, argue and check extensively that any extremal solution behaves as a generalized free field in the UV. This allows us to reconstruct the entirety of their CFT data using a rapidly convergent ``hybrid bootstrap'' method, which combines numerics and analytics. ","authors_text":"Kausik Ghosh, Miguel F. Paulos, No\\'e Suchel","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2025-03-28T18:00:31Z","title":"Solving 1D crossing and QFT$_2$/CFT$_1$"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2503.22798","kind":"arxiv","version":2},"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":"sha256:2ec3a2ff6157274325020cd410d3a0131bca4199039267928644c7cc516da26c","target":"record","created_at":"2026-07-05T11:53:45Z","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":"ccf9507fb77727c1c681331159404d6284a0dc1a6ff9af42fddd9f80b99d4f32","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2025-03-28T18:00:31Z","title_canon_sha256":"fd496451aa10e089c8cc6593f558092d7a3d69bb4accf80ecb2cf1bf5e48e69c"},"schema_version":"1.0","source":{"id":"2503.22798","kind":"arxiv","version":2}},"canonical_sha256":"cad42a9601c7197474f3da78bf5a557d2d4f9d974fe88eb3a7138827cc13910e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"cad42a9601c7197474f3da78bf5a557d2d4f9d974fe88eb3a7138827cc13910e","first_computed_at":"2026-07-05T11:53:45.139275Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T11:53:45.139275Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"qp4l1AmEj8r2c3c+SPscK9kztEcdEKrnaZY+h8nV4Av3kKA3rk0OTN/pA7XBOEVz3R3r947mKTeAJPsKCB7jDg==","signature_status":"signed_v1","signed_at":"2026-07-05T11:53:45.139881Z","signed_message":"canonical_sha256_bytes"},"source_id":"2503.22798","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2ec3a2ff6157274325020cd410d3a0131bca4199039267928644c7cc516da26c","sha256:552ad1b623cc49ba347737e9ed93cae235fe81c2a899f95932d19d17d10193bc"],"state_sha256":"3adc8821fb8fbcb5ca40878553ce2648cc154cccbda81ce713f20f1491d7e927"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"yEYSwMaGVg95JLeQBA8WwGddWzYiIBEGFJXrwMG99xEs5HQMqj+SjiLESQW5iyx+keSRkJ59dOMaAeR8pBRfAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-11T03:30:06.260077Z","bundle_sha256":"329c3e321c242a48346680499790efcccef775dfd8ce044a2f5e7815b97d6ae2"}}