{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2021:L72XYQSISTZWGIRXZ6C6DT36QF","short_pith_number":"pith:L72XYQSI","canonical_record":{"source":{"id":"2112.11411","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2021-12-21T18:15:45Z","cross_cats_sorted":["gr-qc","math-ph","math.MP"],"title_canon_sha256":"869db1f6f2c27505c3f0d1fde023d299865914de55fe61a5674c0faa4b3135a2","abstract_canon_sha256":"60c2f03a75d7e3358178524bb6a8fda1372cc90d2790e0a49ded28056553a7cd"},"schema_version":"1.0"},"canonical_sha256":"5ff57c424894f3632237cf85e1cf7e8175fc7699dcd9b24d9bfa7b6632e4a362","source":{"kind":"arxiv","id":"2112.11411","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2112.11411","created_at":"2026-07-05T04:27:50Z"},{"alias_kind":"arxiv_version","alias_value":"2112.11411v2","created_at":"2026-07-05T04:27:50Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2112.11411","created_at":"2026-07-05T04:27:50Z"},{"alias_kind":"pith_short_12","alias_value":"L72XYQSISTZW","created_at":"2026-07-05T04:27:50Z"},{"alias_kind":"pith_short_16","alias_value":"L72XYQSISTZWGIRX","created_at":"2026-07-05T04:27:50Z"},{"alias_kind":"pith_short_8","alias_value":"L72XYQSI","created_at":"2026-07-05T04:27:50Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2021:L72XYQSISTZWGIRXZ6C6DT36QF","target":"record","payload":{"canonical_record":{"source":{"id":"2112.11411","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2021-12-21T18:15:45Z","cross_cats_sorted":["gr-qc","math-ph","math.MP"],"title_canon_sha256":"869db1f6f2c27505c3f0d1fde023d299865914de55fe61a5674c0faa4b3135a2","abstract_canon_sha256":"60c2f03a75d7e3358178524bb6a8fda1372cc90d2790e0a49ded28056553a7cd"},"schema_version":"1.0"},"canonical_sha256":"5ff57c424894f3632237cf85e1cf7e8175fc7699dcd9b24d9bfa7b6632e4a362","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T04:27:50.228461Z","signature_b64":"2xyMMXBQXfTDhiFhgx3+Pshqrd3zCWhiM3kMrexTNSIhWuYoCxC1tfl0ayu14j7/4k7qOgKkBTYG18ORKfDgCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5ff57c424894f3632237cf85e1cf7e8175fc7699dcd9b24d9bfa7b6632e4a362","last_reissued_at":"2026-07-05T04:27:50.227987Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T04:27:50.227987Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2112.11411","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":"2026-07-05T04:27:50Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"mhboJGGoskHKffw2VGpJGH9ehKK1KvGB5x77W0xlfPN2BVY5KmGviJrnNBh6Gao06uWtXW3H+ce3+CavSca/Bg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-03T16:47:20.314417Z"},"content_sha256":"e5db077b178eb89b762f9e2f1d98917cf30315750ec1905d168a99ac93e95aba","schema_version":"1.0","event_id":"sha256:e5db077b178eb89b762f9e2f1d98917cf30315750ec1905d168a99ac93e95aba"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2021:L72XYQSISTZWGIRXZ6C6DT36QF","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Spectral Geometry of Nuts and Bolts","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["gr-qc","math-ph","math.MP"],"primary_cat":"hep-th","authors_text":"Bernd Schroers, Kim Smedley-Williams, Lyonell Boulton","submitted_at":"2021-12-21T18:15:45Z","abstract_excerpt":"We study the spectrum of Laplace operators on a one-parameter family of gravitational instantons of bi-axial Bianchi IX type coupled to an abelian connection with self-dual curvature. The family of geometries includes the Taub-NUT, Taub-bolt and Euclidean Schwarzschild geometries and interpolates between them. The interpolating geometries have conical singularities along a submanifold of co-dimension two, but we prove that the associated Laplace operators have natural self-adjoint extensions and study their spectra. In particular, we determine the essential spectrum and prove that its compleme"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2112.11411","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/2112.11411/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":"2026-07-05T04:27:50Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"xnh9zrrkeOeltkUJa66iSnST1DVyH4Ze01icZse7Wsds6IEK+z51T7YiNAVlMBSuJIoGK3J/P66LBLnpH3IcDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-03T16:47:20.314996Z"},"content_sha256":"43e1da11f6f02e8b5f5c12d418bbc80becd6c533d2e38b73c950a8d366f3d3ac","schema_version":"1.0","event_id":"sha256:43e1da11f6f02e8b5f5c12d418bbc80becd6c533d2e38b73c950a8d366f3d3ac"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/L72XYQSISTZWGIRXZ6C6DT36QF/bundle.json","state_url":"https://pith.science/pith/L72XYQSISTZWGIRXZ6C6DT36QF/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/L72XYQSISTZWGIRXZ6C6DT36QF/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":"2026-08-03T16:47:20Z","links":{"resolver":"https://pith.science/pith/L72XYQSISTZWGIRXZ6C6DT36QF","bundle":"https://pith.science/pith/L72XYQSISTZWGIRXZ6C6DT36QF/bundle.json","state":"https://pith.science/pith/L72XYQSISTZWGIRXZ6C6DT36QF/state.json","well_known_bundle":"https://pith.science/.well-known/pith/L72XYQSISTZWGIRXZ6C6DT36QF/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2021:L72XYQSISTZWGIRXZ6C6DT36QF","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":"60c2f03a75d7e3358178524bb6a8fda1372cc90d2790e0a49ded28056553a7cd","cross_cats_sorted":["gr-qc","math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2021-12-21T18:15:45Z","title_canon_sha256":"869db1f6f2c27505c3f0d1fde023d299865914de55fe61a5674c0faa4b3135a2"},"schema_version":"1.0","source":{"id":"2112.11411","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2112.11411","created_at":"2026-07-05T04:27:50Z"},{"alias_kind":"arxiv_version","alias_value":"2112.11411v2","created_at":"2026-07-05T04:27:50Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2112.11411","created_at":"2026-07-05T04:27:50Z"},{"alias_kind":"pith_short_12","alias_value":"L72XYQSISTZW","created_at":"2026-07-05T04:27:50Z"},{"alias_kind":"pith_short_16","alias_value":"L72XYQSISTZWGIRX","created_at":"2026-07-05T04:27:50Z"},{"alias_kind":"pith_short_8","alias_value":"L72XYQSI","created_at":"2026-07-05T04:27:50Z"}],"graph_snapshots":[{"event_id":"sha256:43e1da11f6f02e8b5f5c12d418bbc80becd6c533d2e38b73c950a8d366f3d3ac","target":"graph","created_at":"2026-07-05T04:27:50Z","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/2112.11411/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We study the spectrum of Laplace operators on a one-parameter family of gravitational instantons of bi-axial Bianchi IX type coupled to an abelian connection with self-dual curvature. The family of geometries includes the Taub-NUT, Taub-bolt and Euclidean Schwarzschild geometries and interpolates between them. The interpolating geometries have conical singularities along a submanifold of co-dimension two, but we prove that the associated Laplace operators have natural self-adjoint extensions and study their spectra. In particular, we determine the essential spectrum and prove that its compleme","authors_text":"Bernd Schroers, Kim Smedley-Williams, Lyonell Boulton","cross_cats":["gr-qc","math-ph","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2021-12-21T18:15:45Z","title":"Spectral Geometry of Nuts and Bolts"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2112.11411","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:e5db077b178eb89b762f9e2f1d98917cf30315750ec1905d168a99ac93e95aba","target":"record","created_at":"2026-07-05T04:27:50Z","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":"60c2f03a75d7e3358178524bb6a8fda1372cc90d2790e0a49ded28056553a7cd","cross_cats_sorted":["gr-qc","math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2021-12-21T18:15:45Z","title_canon_sha256":"869db1f6f2c27505c3f0d1fde023d299865914de55fe61a5674c0faa4b3135a2"},"schema_version":"1.0","source":{"id":"2112.11411","kind":"arxiv","version":2}},"canonical_sha256":"5ff57c424894f3632237cf85e1cf7e8175fc7699dcd9b24d9bfa7b6632e4a362","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5ff57c424894f3632237cf85e1cf7e8175fc7699dcd9b24d9bfa7b6632e4a362","first_computed_at":"2026-07-05T04:27:50.227987Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T04:27:50.227987Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"2xyMMXBQXfTDhiFhgx3+Pshqrd3zCWhiM3kMrexTNSIhWuYoCxC1tfl0ayu14j7/4k7qOgKkBTYG18ORKfDgCQ==","signature_status":"signed_v1","signed_at":"2026-07-05T04:27:50.228461Z","signed_message":"canonical_sha256_bytes"},"source_id":"2112.11411","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e5db077b178eb89b762f9e2f1d98917cf30315750ec1905d168a99ac93e95aba","sha256:43e1da11f6f02e8b5f5c12d418bbc80becd6c533d2e38b73c950a8d366f3d3ac"],"state_sha256":"dad603a0e3bcdae975603391c5e32d59819bcf6f891111457cca774b581577ad"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"gPS3KgYOWSuwOS/aZRdjwRtGzNwJaOSQtk6+PgaFTwXDonoPTEWzJE4A6RDQfoUYDZMWpolDUCfC/GnQfNP7AA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-03T16:47:20.319841Z","bundle_sha256":"78a6ab4a8d7dd610f6301c0e004cdeae1f1a5a80c265c7900b6b3cee2b35c7f7"}}