{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:PKP5GCTCQLLGSNLCKZ7Y33HDNP","short_pith_number":"pith:PKP5GCTC","canonical_record":{"source":{"id":"1804.10525","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2018-04-27T14:08:41Z","cross_cats_sorted":[],"title_canon_sha256":"18bff5dcf56b51690d9650d6a1bcc03494130222e4985c2a975e9d2501a9ed48","abstract_canon_sha256":"bbeb88cebac343ef9219d11853f386cc3c0320355e415cfa6d19ce6d6f8ac92e"},"schema_version":"1.0"},"canonical_sha256":"7a9fd30a6282d6693562567f8dece36be3fd263629c20324b32abb5da4c8919c","source":{"kind":"arxiv","id":"1804.10525","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1804.10525","created_at":"2026-05-18T00:10:21Z"},{"alias_kind":"arxiv_version","alias_value":"1804.10525v2","created_at":"2026-05-18T00:10:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1804.10525","created_at":"2026-05-18T00:10:21Z"},{"alias_kind":"pith_short_12","alias_value":"PKP5GCTCQLLG","created_at":"2026-05-18T12:32:46Z"},{"alias_kind":"pith_short_16","alias_value":"PKP5GCTCQLLGSNLC","created_at":"2026-05-18T12:32:46Z"},{"alias_kind":"pith_short_8","alias_value":"PKP5GCTC","created_at":"2026-05-18T12:32:46Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:PKP5GCTCQLLGSNLCKZ7Y33HDNP","target":"record","payload":{"canonical_record":{"source":{"id":"1804.10525","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2018-04-27T14:08:41Z","cross_cats_sorted":[],"title_canon_sha256":"18bff5dcf56b51690d9650d6a1bcc03494130222e4985c2a975e9d2501a9ed48","abstract_canon_sha256":"bbeb88cebac343ef9219d11853f386cc3c0320355e415cfa6d19ce6d6f8ac92e"},"schema_version":"1.0"},"canonical_sha256":"7a9fd30a6282d6693562567f8dece36be3fd263629c20324b32abb5da4c8919c","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:10:21.808439Z","signature_b64":"H5dt36M7zErUa8TKbwoX3NGg01yliqH/8/oRIhzGZVoW1Loy4o0bKW8D06EK4jLZwhOERK6nZmmpuRfpES9NBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7a9fd30a6282d6693562567f8dece36be3fd263629c20324b32abb5da4c8919c","last_reissued_at":"2026-05-18T00:10:21.807517Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:10:21.807517Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1804.10525","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":"2026-05-18T00:10:21Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"iogV035JkqBsoPtDellajPU3ko9xDC41ODGHT4XcCzmwym1ZxodNOMA2NbVulTVozm0lT0zSFeJivSpYZlXZDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T16:06:12.780602Z"},"content_sha256":"0f1e061a77a9efcfba7e405f9e04cd9b6af16b424a463cefb0be90169ead2d89","schema_version":"1.0","event_id":"sha256:0f1e061a77a9efcfba7e405f9e04cd9b6af16b424a463cefb0be90169ead2d89"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:PKP5GCTCQLLGSNLCKZ7Y33HDNP","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Bootstrapping holographic warped CFTs or: how I learned to stop worrying and tolerate negative norms","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"hep-th","authors_text":"Luis Apolo, Wei Song","submitted_at":"2018-04-27T14:08:41Z","abstract_excerpt":"We use modular invariance to derive constraints on the spectrum of warped conformal field theories (WCFTs) --- nonrelativistic quantum field theories described by a chiral Virasoro and $U(1)$ Kac-Moody algebra. We focus on holographic WCFTs and interpret our results in the simplest holographic set up: three dimensional gravity with Compere-Song-Strominger boundary conditions. Holographic WCFTs feature a negative $U(1)$ level that is responsible for negative norm descendant states. Despite the violation of unitarity we show that the modular bootstrap is still viable provided the (Virasoro-Kac-M"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1804.10525","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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:10:21Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"qsd/PUG81N/ncPZFkvV32vdV4XVlCNSeDVxuLEd+iiodYOiurra+/kN5xdqY+eZIj+yRvr2jbiB6lE6TKDB7AQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T16:06:12.781313Z"},"content_sha256":"9ad2b09b77c451b2b6233d6dda76fb6867230339c727acb40b6b93797c938290","schema_version":"1.0","event_id":"sha256:9ad2b09b77c451b2b6233d6dda76fb6867230339c727acb40b6b93797c938290"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/PKP5GCTCQLLGSNLCKZ7Y33HDNP/bundle.json","state_url":"https://pith.science/pith/PKP5GCTCQLLGSNLCKZ7Y33HDNP/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/PKP5GCTCQLLGSNLCKZ7Y33HDNP/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":"2026-05-31T16:06:12Z","links":{"resolver":"https://pith.science/pith/PKP5GCTCQLLGSNLCKZ7Y33HDNP","bundle":"https://pith.science/pith/PKP5GCTCQLLGSNLCKZ7Y33HDNP/bundle.json","state":"https://pith.science/pith/PKP5GCTCQLLGSNLCKZ7Y33HDNP/state.json","well_known_bundle":"https://pith.science/.well-known/pith/PKP5GCTCQLLGSNLCKZ7Y33HDNP/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:PKP5GCTCQLLGSNLCKZ7Y33HDNP","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":"bbeb88cebac343ef9219d11853f386cc3c0320355e415cfa6d19ce6d6f8ac92e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2018-04-27T14:08:41Z","title_canon_sha256":"18bff5dcf56b51690d9650d6a1bcc03494130222e4985c2a975e9d2501a9ed48"},"schema_version":"1.0","source":{"id":"1804.10525","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1804.10525","created_at":"2026-05-18T00:10:21Z"},{"alias_kind":"arxiv_version","alias_value":"1804.10525v2","created_at":"2026-05-18T00:10:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1804.10525","created_at":"2026-05-18T00:10:21Z"},{"alias_kind":"pith_short_12","alias_value":"PKP5GCTCQLLG","created_at":"2026-05-18T12:32:46Z"},{"alias_kind":"pith_short_16","alias_value":"PKP5GCTCQLLGSNLC","created_at":"2026-05-18T12:32:46Z"},{"alias_kind":"pith_short_8","alias_value":"PKP5GCTC","created_at":"2026-05-18T12:32:46Z"}],"graph_snapshots":[{"event_id":"sha256:9ad2b09b77c451b2b6233d6dda76fb6867230339c727acb40b6b93797c938290","target":"graph","created_at":"2026-05-18T00:10:21Z","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"},"paper":{"abstract_excerpt":"We use modular invariance to derive constraints on the spectrum of warped conformal field theories (WCFTs) --- nonrelativistic quantum field theories described by a chiral Virasoro and $U(1)$ Kac-Moody algebra. We focus on holographic WCFTs and interpret our results in the simplest holographic set up: three dimensional gravity with Compere-Song-Strominger boundary conditions. Holographic WCFTs feature a negative $U(1)$ level that is responsible for negative norm descendant states. Despite the violation of unitarity we show that the modular bootstrap is still viable provided the (Virasoro-Kac-M","authors_text":"Luis Apolo, Wei Song","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2018-04-27T14:08:41Z","title":"Bootstrapping holographic warped CFTs or: how I learned to stop worrying and tolerate negative norms"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1804.10525","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":"sha256:0f1e061a77a9efcfba7e405f9e04cd9b6af16b424a463cefb0be90169ead2d89","target":"record","created_at":"2026-05-18T00:10:21Z","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":"bbeb88cebac343ef9219d11853f386cc3c0320355e415cfa6d19ce6d6f8ac92e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2018-04-27T14:08:41Z","title_canon_sha256":"18bff5dcf56b51690d9650d6a1bcc03494130222e4985c2a975e9d2501a9ed48"},"schema_version":"1.0","source":{"id":"1804.10525","kind":"arxiv","version":2}},"canonical_sha256":"7a9fd30a6282d6693562567f8dece36be3fd263629c20324b32abb5da4c8919c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7a9fd30a6282d6693562567f8dece36be3fd263629c20324b32abb5da4c8919c","first_computed_at":"2026-05-18T00:10:21.807517Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:10:21.807517Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"H5dt36M7zErUa8TKbwoX3NGg01yliqH/8/oRIhzGZVoW1Loy4o0bKW8D06EK4jLZwhOERK6nZmmpuRfpES9NBg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:10:21.808439Z","signed_message":"canonical_sha256_bytes"},"source_id":"1804.10525","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0f1e061a77a9efcfba7e405f9e04cd9b6af16b424a463cefb0be90169ead2d89","sha256:9ad2b09b77c451b2b6233d6dda76fb6867230339c727acb40b6b93797c938290"],"state_sha256":"022c46af4ee71d6592370c70bbfb1d1327c5c07c329895434e057b440895bf1e"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"721kGEvhbawKkrYN4mJeq1H7tayh2bEd74Vz3/5sFupfJQwA5DedSomzkNDb7jFhCfne5Cd6kLP7vOJtWvINAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-31T16:06:12.784714Z","bundle_sha256":"bce0bc4931c3c380eae57102456cc3e7b1b737bb0ff9847a34a5d7394f91b5e4"}}