{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2006:CTENYMISJW4KJ3BGFV5SIDHFV2","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":"5e2937bbb5ae9b70b773204bb4da1cd2a3f155f0178a8937f43a7c3680d8b3a7","cross_cats_sorted":[],"license":"","primary_cat":"gr-qc","submitted_at":"2006-12-12T14:28:20Z","title_canon_sha256":"ff119ecfd53cf558f7a669903d4916f252b6470e526e2ac66e415615bd5ca6c8"},"schema_version":"1.0","source":{"id":"gr-qc/0612070","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"gr-qc/0612070","created_at":"2026-07-04T15:18:49Z"},{"alias_kind":"arxiv_version","alias_value":"gr-qc/0612070v2","created_at":"2026-07-04T15:18:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.gr-qc/0612070","created_at":"2026-07-04T15:18:49Z"},{"alias_kind":"pith_short_12","alias_value":"CTENYMISJW4K","created_at":"2026-07-04T15:18:49Z"},{"alias_kind":"pith_short_16","alias_value":"CTENYMISJW4KJ3BG","created_at":"2026-07-04T15:18:49Z"},{"alias_kind":"pith_short_8","alias_value":"CTENYMIS","created_at":"2026-07-04T15:18:49Z"}],"graph_snapshots":[{"event_id":"sha256:fa2cf255d4d8577e8e77d8d9c57f8ec523f599fbf2fa25ec599c803eb9c5ee0d","target":"graph","created_at":"2026-07-04T15:18:49Z","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/gr-qc/0612070/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"The loop quantization of the negatively curved k=-1 RW model poses several technical challenges. We show that the issues can be overcome and a successful quantization is possible that extends the results of the k=0,+1 models in a natural fashion. We discuss the resulting dynamics and show that for a universe consisting of a massless scalar field, a bounce is predicted in the backward evolution in accordance with the results of the k=0,+1 models. We also show that the model predicts a vacuum repulsion in the high curvature regime that would lead to a bounce even for matter with vanishing energy","authors_text":"Kevin Vandersloot","cross_cats":[],"headline":"","license":"","primary_cat":"gr-qc","submitted_at":"2006-12-12T14:28:20Z","title":"Loop quantum cosmology and the k = - 1 RW model"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"gr-qc/0612070","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":"sha256:4c569bdf5d5466229b88d2924200426a887efb91e9e8f064a9953e770669ae87","target":"record","created_at":"2026-07-04T15:18:49Z","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":"5e2937bbb5ae9b70b773204bb4da1cd2a3f155f0178a8937f43a7c3680d8b3a7","cross_cats_sorted":[],"license":"","primary_cat":"gr-qc","submitted_at":"2006-12-12T14:28:20Z","title_canon_sha256":"ff119ecfd53cf558f7a669903d4916f252b6470e526e2ac66e415615bd5ca6c8"},"schema_version":"1.0","source":{"id":"gr-qc/0612070","kind":"arxiv","version":2}},"canonical_sha256":"14c8dc31124db8a4ec262d7b240ce5aebc95b4d453b99838ef88b354f4eab2b5","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"14c8dc31124db8a4ec262d7b240ce5aebc95b4d453b99838ef88b354f4eab2b5","first_computed_at":"2026-07-04T15:18:49.217517Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-04T15:18:49.217517Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"jZI+Qwf+jfMtZMaVpUWadUlH7AzvYS2PvIxqjts9JUW/951/oy7KyTik0WowWWso80CVwUBORoqobGl4sg7oCg==","signature_status":"signed_v1","signed_at":"2026-07-04T15:18:49.217913Z","signed_message":"canonical_sha256_bytes"},"source_id":"gr-qc/0612070","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4c569bdf5d5466229b88d2924200426a887efb91e9e8f064a9953e770669ae87","sha256:fa2cf255d4d8577e8e77d8d9c57f8ec523f599fbf2fa25ec599c803eb9c5ee0d"],"state_sha256":"28a8c2007d3b3739aa58afe9199330cb5bc6afaa1fd5d508907e5a9728499bc5"}