{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2009:EKUIR4AZ3I3XFMJQV5Y6IC2FEY","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":"943a68d92d28792824efa1e127fa7841bc401e86bd99038a5735c46060155ce3","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2009-12-01T14:32:58Z","title_canon_sha256":"5e479862fb7be888d98089ac95ff6534924b18421288935331d080337716994f"},"schema_version":"1.0","source":{"id":"0912.0162","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0912.0162","created_at":"2026-07-04T17:28:13Z"},{"alias_kind":"arxiv_version","alias_value":"0912.0162v1","created_at":"2026-07-04T17:28:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0912.0162","created_at":"2026-07-04T17:28:13Z"},{"alias_kind":"pith_short_12","alias_value":"EKUIR4AZ3I3X","created_at":"2026-07-04T17:28:13Z"},{"alias_kind":"pith_short_16","alias_value":"EKUIR4AZ3I3XFMJQ","created_at":"2026-07-04T17:28:13Z"},{"alias_kind":"pith_short_8","alias_value":"EKUIR4AZ","created_at":"2026-07-04T17:28:13Z"}],"graph_snapshots":[{"event_id":"sha256:1724f16cd736c0282c931a468740ca84ee95d3da0ead762fa0c1c5728ff3d959","target":"graph","created_at":"2026-07-04T17:28:13Z","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/0912.0162/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"The self-adjointness of an evolution operator $\\Theta_{\\Lambda}$ corresponding to the model of flat FRW universe with massless scalar field and cosmological constant quantized in the framework of Loop Quantum Cosmology is studied in the case $\\Lambda>0$. It is shown, that for $\\Lambda<\\Lambda_c\\approx 10.3 \\lPl^{-2}$ the operator admits many self-adjoint extensions, each of the purely discrete spectrum. On the other hand for $\\Lambda\\geq\\Lambda_c$ the operator is essentially self-adjoint, however the physical Hilbert space of the model does not contain any physically interesting states.","authors_text":"Tomasz Pawlowski, Wojciech Kaminski","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2009-12-01T14:32:58Z","title":"The LQC evolution operator of FRW universe with positive cosmological constant"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0912.0162","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":"sha256:52bd6fecbdbd34a34ae5764a0fc30dae3d6dd4779aada90b0653cf6b126b110b","target":"record","created_at":"2026-07-04T17:28:13Z","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":"943a68d92d28792824efa1e127fa7841bc401e86bd99038a5735c46060155ce3","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2009-12-01T14:32:58Z","title_canon_sha256":"5e479862fb7be888d98089ac95ff6534924b18421288935331d080337716994f"},"schema_version":"1.0","source":{"id":"0912.0162","kind":"arxiv","version":1}},"canonical_sha256":"22a888f019da3772b130af71e40b45263f99856a99f36a92e4f024f91a4a8561","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"22a888f019da3772b130af71e40b45263f99856a99f36a92e4f024f91a4a8561","first_computed_at":"2026-07-04T17:28:13.520341Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-04T17:28:13.520341Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"DyuBezpzApysuEUIhmqPq7PWQrnzfTxsubkCpkLciWgwHfEGq/RF4aPMVJudhhhH947/NY2RWvQ5IiejfFVRCg==","signature_status":"signed_v1","signed_at":"2026-07-04T17:28:13.520781Z","signed_message":"canonical_sha256_bytes"},"source_id":"0912.0162","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:52bd6fecbdbd34a34ae5764a0fc30dae3d6dd4779aada90b0653cf6b126b110b","sha256:1724f16cd736c0282c931a468740ca84ee95d3da0ead762fa0c1c5728ff3d959"],"state_sha256":"f2686882d96b611b73eed5322780ae6fcd322a1c7502694c58f83f92f8a87eea"}