{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2021:LBJS5W74CM3L7NPN2XGNZYDEXB","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":"b265d3c4436687931e0d3f11789007c7d38e91524899b18af99b480c8bb72877","cross_cats_sorted":["math.DG","math.SP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2021-07-20T18:00:00Z","title_canon_sha256":"f5d6690eb60ff1b8c9a098a5b7a9f3a729066d3a10c4161d0f877f5355ca484a"},"schema_version":"1.0","source":{"id":"2107.09674","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2107.09674","created_at":"2026-07-05T03:58:51Z"},{"alias_kind":"arxiv_version","alias_value":"2107.09674v1","created_at":"2026-07-05T03:58:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2107.09674","created_at":"2026-07-05T03:58:51Z"},{"alias_kind":"pith_short_12","alias_value":"LBJS5W74CM3L","created_at":"2026-07-05T03:58:51Z"},{"alias_kind":"pith_short_16","alias_value":"LBJS5W74CM3L7NPN","created_at":"2026-07-05T03:58:51Z"},{"alias_kind":"pith_short_8","alias_value":"LBJS5W74","created_at":"2026-07-05T03:58:51Z"}],"graph_snapshots":[{"event_id":"sha256:24aac77a97e808e69e27b3763b6555b2aebb0920ecc7ac623b7b45a403af7ee2","target":"graph","created_at":"2026-07-05T03:58:51Z","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/2107.09674/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"The eigenvalues of the Laplace-Beltrami operator and the integrals of products of eigenfunctions must satisfy certain consistency conditions on compact Riemannian manifolds. These consistency conditions are derived by using spectral decompositions to write quadruple overlap integrals in terms of products of triple overlap integrals in multiple ways. In this paper, we show how these consistency conditions imply bounds on the Laplacian eigenvalues and triple overlap integrals of closed hyperbolic manifolds, in analogy to the conformal bootstrap bounds on conformal field theories. We find an uppe","authors_text":"James Bonifacio","cross_cats":["math.DG","math.SP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2021-07-20T18:00:00Z","title":"Bootstrap Bounds on Closed Hyperbolic Manifolds"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2107.09674","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":"sha256:4c333686f43726fafb382acc56747a861e539eea9bd3b8c1fbe294f60b8ecf3d","target":"record","created_at":"2026-07-05T03:58:51Z","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":"b265d3c4436687931e0d3f11789007c7d38e91524899b18af99b480c8bb72877","cross_cats_sorted":["math.DG","math.SP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2021-07-20T18:00:00Z","title_canon_sha256":"f5d6690eb60ff1b8c9a098a5b7a9f3a729066d3a10c4161d0f877f5355ca484a"},"schema_version":"1.0","source":{"id":"2107.09674","kind":"arxiv","version":1}},"canonical_sha256":"58532edbfc1336bfb5edd5ccdce064b877ad43c6d63432cf9cad0b572778490b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"58532edbfc1336bfb5edd5ccdce064b877ad43c6d63432cf9cad0b572778490b","first_computed_at":"2026-07-05T03:58:51.589212Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T03:58:51.589212Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"0zYt7jgMftekgriW8bKSyGHIB0YMRa2ev/0HKTUi4r752EO3Tv6SMwJwXVNA4aw1ld/xHBOxeoUAhXnEcRX3BQ==","signature_status":"signed_v1","signed_at":"2026-07-05T03:58:51.589689Z","signed_message":"canonical_sha256_bytes"},"source_id":"2107.09674","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4c333686f43726fafb382acc56747a861e539eea9bd3b8c1fbe294f60b8ecf3d","sha256:24aac77a97e808e69e27b3763b6555b2aebb0920ecc7ac623b7b45a403af7ee2"],"state_sha256":"bb0d920b72b7fb52a1046c5bd991c443351b65147fe0e42a760cf9597a632674"}