{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2023:A7E2YPIQ3EYSDT4C7PJKEH3TSA","short_pith_number":"pith:A7E2YPIQ","canonical_record":{"source":{"id":"2303.04780","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2023-03-08T18:24:51Z","cross_cats_sorted":["math.DG","math.RT"],"title_canon_sha256":"e75f1119619ccc9cea266fa5242902390635f96efe4ed994d40d045b55efbaf8","abstract_canon_sha256":"18e4f5b5babac992bde19d484f317c9520e005bdae7d7893691debf89fb823a8"},"schema_version":"1.0"},"canonical_sha256":"07c9ac3d10d93121cf82fbd2a21f73902bf1e80319c40e229c4edb10da6c1fe7","source":{"kind":"arxiv","id":"2303.04780","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2303.04780","created_at":"2026-07-05T06:42:19Z"},{"alias_kind":"arxiv_version","alias_value":"2303.04780v2","created_at":"2026-07-05T06:42:19Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2303.04780","created_at":"2026-07-05T06:42:19Z"},{"alias_kind":"pith_short_12","alias_value":"A7E2YPIQ3EYS","created_at":"2026-07-05T06:42:19Z"},{"alias_kind":"pith_short_16","alias_value":"A7E2YPIQ3EYSDT4C","created_at":"2026-07-05T06:42:19Z"},{"alias_kind":"pith_short_8","alias_value":"A7E2YPIQ","created_at":"2026-07-05T06:42:19Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2023:A7E2YPIQ3EYSDT4C7PJKEH3TSA","target":"record","payload":{"canonical_record":{"source":{"id":"2303.04780","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2023-03-08T18:24:51Z","cross_cats_sorted":["math.DG","math.RT"],"title_canon_sha256":"e75f1119619ccc9cea266fa5242902390635f96efe4ed994d40d045b55efbaf8","abstract_canon_sha256":"18e4f5b5babac992bde19d484f317c9520e005bdae7d7893691debf89fb823a8"},"schema_version":"1.0"},"canonical_sha256":"07c9ac3d10d93121cf82fbd2a21f73902bf1e80319c40e229c4edb10da6c1fe7","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T06:42:19.928527Z","signature_b64":"7NDXKG4sXvzoMDBIHOlT+T5Fz7HTw17/WyR0/cK4Vq3cPyeWga7xKO8kw1qvEzwx/0cxidXdt4m9Yh8CW6XMDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"07c9ac3d10d93121cf82fbd2a21f73902bf1e80319c40e229c4edb10da6c1fe7","last_reissued_at":"2026-07-05T06:42:19.928080Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T06:42:19.928080Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2303.04780","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":"2026-07-05T06:42:19Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"RxN+LfhvIGz4hHU5/gIjPv/GcbtccBiOJiPYctHnMmsEZ45r/CTcxfSsv/S8miaLiDTWOiF0JOGAVwX9rsmSDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-06T01:44:53.027506Z"},"content_sha256":"335f80d2a907e7f3793a44af772e8280491328f171312949b70a36f8204c575f","schema_version":"1.0","event_id":"sha256:335f80d2a907e7f3793a44af772e8280491328f171312949b70a36f8204c575f"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2023:A7E2YPIQ3EYSDT4C7PJKEH3TSA","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Resonances and residue operators for pseudo-Riemannian hyperbolic spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DG","math.RT"],"primary_cat":"math.SP","authors_text":"Jan Frahm, Polyxeni Spilioti","submitted_at":"2023-03-08T18:24:51Z","abstract_excerpt":"For any pseudo-Riemannian hyperbolic space $X$ over $\\mathbb{R},\\mathbb{C},\\mathbb{H}$ or $\\mathbb{O}$, we show that the resolvent $R(z)=(\\Box-z\\operatorname{Id})^{-1}$ of the Laplace-Beltrami operator $-\\Box$ on $X$ can be extended meromorphically across the spectrum of $\\Box$ as a family of operators $C_c^\\infty(X)\\to \\mathcal{D}'(X)$. Its poles are called resonances and we determine them explicitly in all cases. For each resonance, the image of the corresponding residue operator in $\\mathcal{D}'(X)$ forms a representation of the isometry group of $X$, which we identify with a subrepresentat"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2303.04780","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/2303.04780/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":"2026-07-05T06:42:19Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"43F18KJBioYuf53M8TrvKzXjkSEgnVCldsFqJkMc5xBGmA4mAZJzN0uGYx5ZPD5pX5UYJymgtO/dTBae2nZnBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-06T01:44:53.028654Z"},"content_sha256":"4419957ccf75006d7f914a29ebcac054f6fca9039ae08f370db8d96f6cd04fe2","schema_version":"1.0","event_id":"sha256:4419957ccf75006d7f914a29ebcac054f6fca9039ae08f370db8d96f6cd04fe2"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/A7E2YPIQ3EYSDT4C7PJKEH3TSA/bundle.json","state_url":"https://pith.science/pith/A7E2YPIQ3EYSDT4C7PJKEH3TSA/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/A7E2YPIQ3EYSDT4C7PJKEH3TSA/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":"2026-08-06T01:44:53Z","links":{"resolver":"https://pith.science/pith/A7E2YPIQ3EYSDT4C7PJKEH3TSA","bundle":"https://pith.science/pith/A7E2YPIQ3EYSDT4C7PJKEH3TSA/bundle.json","state":"https://pith.science/pith/A7E2YPIQ3EYSDT4C7PJKEH3TSA/state.json","well_known_bundle":"https://pith.science/.well-known/pith/A7E2YPIQ3EYSDT4C7PJKEH3TSA/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2023:A7E2YPIQ3EYSDT4C7PJKEH3TSA","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":"18e4f5b5babac992bde19d484f317c9520e005bdae7d7893691debf89fb823a8","cross_cats_sorted":["math.DG","math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2023-03-08T18:24:51Z","title_canon_sha256":"e75f1119619ccc9cea266fa5242902390635f96efe4ed994d40d045b55efbaf8"},"schema_version":"1.0","source":{"id":"2303.04780","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2303.04780","created_at":"2026-07-05T06:42:19Z"},{"alias_kind":"arxiv_version","alias_value":"2303.04780v2","created_at":"2026-07-05T06:42:19Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2303.04780","created_at":"2026-07-05T06:42:19Z"},{"alias_kind":"pith_short_12","alias_value":"A7E2YPIQ3EYS","created_at":"2026-07-05T06:42:19Z"},{"alias_kind":"pith_short_16","alias_value":"A7E2YPIQ3EYSDT4C","created_at":"2026-07-05T06:42:19Z"},{"alias_kind":"pith_short_8","alias_value":"A7E2YPIQ","created_at":"2026-07-05T06:42:19Z"}],"graph_snapshots":[{"event_id":"sha256:4419957ccf75006d7f914a29ebcac054f6fca9039ae08f370db8d96f6cd04fe2","target":"graph","created_at":"2026-07-05T06:42:19Z","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/2303.04780/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"For any pseudo-Riemannian hyperbolic space $X$ over $\\mathbb{R},\\mathbb{C},\\mathbb{H}$ or $\\mathbb{O}$, we show that the resolvent $R(z)=(\\Box-z\\operatorname{Id})^{-1}$ of the Laplace-Beltrami operator $-\\Box$ on $X$ can be extended meromorphically across the spectrum of $\\Box$ as a family of operators $C_c^\\infty(X)\\to \\mathcal{D}'(X)$. Its poles are called resonances and we determine them explicitly in all cases. For each resonance, the image of the corresponding residue operator in $\\mathcal{D}'(X)$ forms a representation of the isometry group of $X$, which we identify with a subrepresentat","authors_text":"Jan Frahm, Polyxeni Spilioti","cross_cats":["math.DG","math.RT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2023-03-08T18:24:51Z","title":"Resonances and residue operators for pseudo-Riemannian hyperbolic spaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2303.04780","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":"sha256:335f80d2a907e7f3793a44af772e8280491328f171312949b70a36f8204c575f","target":"record","created_at":"2026-07-05T06:42:19Z","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":"18e4f5b5babac992bde19d484f317c9520e005bdae7d7893691debf89fb823a8","cross_cats_sorted":["math.DG","math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2023-03-08T18:24:51Z","title_canon_sha256":"e75f1119619ccc9cea266fa5242902390635f96efe4ed994d40d045b55efbaf8"},"schema_version":"1.0","source":{"id":"2303.04780","kind":"arxiv","version":2}},"canonical_sha256":"07c9ac3d10d93121cf82fbd2a21f73902bf1e80319c40e229c4edb10da6c1fe7","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"07c9ac3d10d93121cf82fbd2a21f73902bf1e80319c40e229c4edb10da6c1fe7","first_computed_at":"2026-07-05T06:42:19.928080Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T06:42:19.928080Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"7NDXKG4sXvzoMDBIHOlT+T5Fz7HTw17/WyR0/cK4Vq3cPyeWga7xKO8kw1qvEzwx/0cxidXdt4m9Yh8CW6XMDQ==","signature_status":"signed_v1","signed_at":"2026-07-05T06:42:19.928527Z","signed_message":"canonical_sha256_bytes"},"source_id":"2303.04780","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:335f80d2a907e7f3793a44af772e8280491328f171312949b70a36f8204c575f","sha256:4419957ccf75006d7f914a29ebcac054f6fca9039ae08f370db8d96f6cd04fe2"],"state_sha256":"c39ad80977a79ac4db465054d06b00ea8d2f12a38ab0f553e32f81960b5b2eba"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Uv55uopRhgt4P1M0tVsuxELfC7HvJjHrPnUQT3vE1aV3yCnDE9E+h/N1ht2ZUnN7WwlCFy3vM+m2Vx5WgaREAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-06T01:44:53.036562Z","bundle_sha256":"4c2e17a941859f07d154d42386363f1597e058028da42f94d1859d107c681bd6"}}