{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:WKZFZ7DPNE5ETKRIAEU5JPK3K4","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":"c5414d0131248c9515bd9f991fbd69e343cf505e6b3c1c6c2fee1b214c51da9d","cross_cats_sorted":["gr-qc","math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2011-12-28T22:18:34Z","title_canon_sha256":"2e86181a7beabbd7faf3a6bc778547affabf3b40cd08c535128e4a867be8e152"},"schema_version":"1.0","source":{"id":"1112.6192","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1112.6192","created_at":"2026-05-18T04:05:36Z"},{"alias_kind":"arxiv_version","alias_value":"1112.6192v1","created_at":"2026-05-18T04:05:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1112.6192","created_at":"2026-05-18T04:05:36Z"},{"alias_kind":"pith_short_12","alias_value":"WKZFZ7DPNE5E","created_at":"2026-05-18T12:26:44Z"},{"alias_kind":"pith_short_16","alias_value":"WKZFZ7DPNE5ETKRI","created_at":"2026-05-18T12:26:44Z"},{"alias_kind":"pith_short_8","alias_value":"WKZFZ7DP","created_at":"2026-05-18T12:26:44Z"}],"graph_snapshots":[{"event_id":"sha256:45b15c6b5c18f6e5efe522442aa0860de9845d738b4fab95c86127b287964e91","target":"graph","created_at":"2026-05-18T04:05:36Z","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":"Using methods in the theory of semisimple Lie algebras, we can obtain all smooth solutions of the Klein-Gordon equation on the 4-dimensional de Sitter spacetime (dS^4). The mass of a Klein-Gordon scalar on dS^4 is related to an eigenvalue of the Casimir operator of so(1,4). Thus it is discrete, or quantized. Furthermore, the mass m of a Klein-Gordon scalar on dS^4 is imaginary: m^2 being proportional to -N(N+3), with N >= 0 an integer.","authors_text":"Bin Zhou, Zhen-Hua Zhou","cross_cats":["gr-qc","math-ph","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2011-12-28T22:18:34Z","title":"Smooth Solutions and Discrete Imaginary Mass of the Klein-Gordon Equation in the de Sitter Background"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1112.6192","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:a86eb4cad78fa4fcb1437346839815fa4a7869791c3877573e0ac6acd70d4a20","target":"record","created_at":"2026-05-18T04:05:36Z","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":"c5414d0131248c9515bd9f991fbd69e343cf505e6b3c1c6c2fee1b214c51da9d","cross_cats_sorted":["gr-qc","math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2011-12-28T22:18:34Z","title_canon_sha256":"2e86181a7beabbd7faf3a6bc778547affabf3b40cd08c535128e4a867be8e152"},"schema_version":"1.0","source":{"id":"1112.6192","kind":"arxiv","version":1}},"canonical_sha256":"b2b25cfc6f693a49aa280129d4bd5b5703602427e7fe08ebaf21d844878dfefa","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b2b25cfc6f693a49aa280129d4bd5b5703602427e7fe08ebaf21d844878dfefa","first_computed_at":"2026-05-18T04:05:36.551422Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:05:36.551422Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"bM47AWxdKTRNIYNvJQBtrnfxI08WSLoZ+nr+rIFf8dtDv+CrlXf966DZ+HJF0DEjVngBlnyC+/8dfCkDfZNMCw==","signature_status":"signed_v1","signed_at":"2026-05-18T04:05:36.551881Z","signed_message":"canonical_sha256_bytes"},"source_id":"1112.6192","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a86eb4cad78fa4fcb1437346839815fa4a7869791c3877573e0ac6acd70d4a20","sha256:45b15c6b5c18f6e5efe522442aa0860de9845d738b4fab95c86127b287964e91"],"state_sha256":"e04d12ed68c74b6a4c5607a8f844bac89c5992d403013d07b2cd70c0b716e305"}