{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2021:GGG5KYG66A7M7COEHVUPIUQRMY","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":"2ad545becea989d4684e77f244289194d82cdf3d87bb46128392bda1411c0b42","cross_cats_sorted":["hep-th","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2021-07-19T11:05:08Z","title_canon_sha256":"72229c5e11eb0dda0addc33472895ef0809ae570ecbcf79a3467f72129236639"},"schema_version":"1.0","source":{"id":"2107.08754","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2107.08754","created_at":"2026-07-05T05:32:20Z"},{"alias_kind":"arxiv_version","alias_value":"2107.08754v3","created_at":"2026-07-05T05:32:20Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2107.08754","created_at":"2026-07-05T05:32:20Z"},{"alias_kind":"pith_short_12","alias_value":"GGG5KYG66A7M","created_at":"2026-07-05T05:32:20Z"},{"alias_kind":"pith_short_16","alias_value":"GGG5KYG66A7M7COE","created_at":"2026-07-05T05:32:20Z"},{"alias_kind":"pith_short_8","alias_value":"GGG5KYG6","created_at":"2026-07-05T05:32:20Z"}],"graph_snapshots":[{"event_id":"sha256:ec4a983900916700e5bb457d7fef14af985f464c5df1e0f05ba57095cbb54f84","target":"graph","created_at":"2026-07-05T05:32:20Z","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/2107.08754/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We study the solutions to the Klein-Gordon equation for the massive scalar field in the universal covering space of two-dimensional anti-de Sitter space. For certain values of the mass parameter, we impose a suitable set of boundary conditions which make the spatial component of the Klein-Gordon operator self-adjoint. This makes the time-evolution of the classical field well defined. Then, we use the transformation properties of the scalar field under the isometry group of the theory, namely, the universal covering group of $\\mathrm{SL}(2,\\mathbb{R})$, in order to determine which self-adjoint ","authors_text":"Atsushi Higuchi, David Serrano Blanco, Lasse Schmieding","cross_cats":["hep-th","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2021-07-19T11:05:08Z","title":"Scalar field in $\\mathrm{AdS}_2$ and representations of $\\widetilde{\\mathrm{SL}}(2,\\mathbb{R})$"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2107.08754","kind":"arxiv","version":3},"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":"sha256:65601c5c98edfea72d772434779528f62fc45fcfd4a5cd49fddcb04b27a0c522","target":"record","created_at":"2026-07-05T05:32:20Z","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":"2ad545becea989d4684e77f244289194d82cdf3d87bb46128392bda1411c0b42","cross_cats_sorted":["hep-th","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2021-07-19T11:05:08Z","title_canon_sha256":"72229c5e11eb0dda0addc33472895ef0809ae570ecbcf79a3467f72129236639"},"schema_version":"1.0","source":{"id":"2107.08754","kind":"arxiv","version":3}},"canonical_sha256":"318dd560def03ecf89c43d68f452116608de5413c7d631e701cf099fdd82fe31","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"318dd560def03ecf89c43d68f452116608de5413c7d631e701cf099fdd82fe31","first_computed_at":"2026-07-05T05:32:20.052731Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T05:32:20.052731Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"veYJDJ9tnDGuYQu4VrcG++yaDo3t7U4C4ot1GEYEu8Gn9FmFXJ85AZXu1FkcC7+Zszagq0shBqCo0KYXgRUjDw==","signature_status":"signed_v1","signed_at":"2026-07-05T05:32:20.053160Z","signed_message":"canonical_sha256_bytes"},"source_id":"2107.08754","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:65601c5c98edfea72d772434779528f62fc45fcfd4a5cd49fddcb04b27a0c522","sha256:ec4a983900916700e5bb457d7fef14af985f464c5df1e0f05ba57095cbb54f84"],"state_sha256":"3957a51f5525f6382ee19c759290e59837aa49896c9d6b2e1928d5752011eef5"}