{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2006:CTENYMISJW4KJ3BGFV5SIDHFV2","short_pith_number":"pith:CTENYMIS","schema_version":"1.0","canonical_sha256":"14c8dc31124db8a4ec262d7b240ce5aebc95b4d453b99838ef88b354f4eab2b5","source":{"kind":"arxiv","id":"gr-qc/0612070","version":2},"attestation_state":"computed","paper":{"title":"Loop quantum cosmology and the k = - 1 RW model","license":"","headline":"","cross_cats":[],"primary_cat":"gr-qc","authors_text":"Kevin Vandersloot","submitted_at":"2006-12-12T14:28:20Z","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"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"gr-qc/0612070","kind":"arxiv","version":2},"metadata":{"license":"","primary_cat":"gr-qc","submitted_at":"2006-12-12T14:28:20Z","cross_cats_sorted":[],"title_canon_sha256":"ff119ecfd53cf558f7a669903d4916f252b6470e526e2ac66e415615bd5ca6c8","abstract_canon_sha256":"5e2937bbb5ae9b70b773204bb4da1cd2a3f155f0178a8937f43a7c3680d8b3a7"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-04T15:18:49.217913Z","signature_b64":"jZI+Qwf+jfMtZMaVpUWadUlH7AzvYS2PvIxqjts9JUW/951/oy7KyTik0WowWWso80CVwUBORoqobGl4sg7oCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"14c8dc31124db8a4ec262d7b240ce5aebc95b4d453b99838ef88b354f4eab2b5","last_reissued_at":"2026-07-04T15:18:49.217517Z","signature_status":"signed_v1","first_computed_at":"2026-07-04T15:18:49.217517Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Loop quantum cosmology and the k = - 1 RW model","license":"","headline":"","cross_cats":[],"primary_cat":"gr-qc","authors_text":"Kevin Vandersloot","submitted_at":"2006-12-12T14:28:20Z","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"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"gr-qc/0612070","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/gr-qc/0612070/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"},"aliases":[{"alias_kind":"arxiv","alias_value":"gr-qc/0612070","created_at":"2026-07-04T15:18:49.217581+00:00"},{"alias_kind":"arxiv_version","alias_value":"gr-qc/0612070v2","created_at":"2026-07-04T15:18:49.217581+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.gr-qc/0612070","created_at":"2026-07-04T15:18:49.217581+00:00"},{"alias_kind":"pith_short_12","alias_value":"CTENYMISJW4K","created_at":"2026-07-04T15:18:49.217581+00:00"},{"alias_kind":"pith_short_16","alias_value":"CTENYMISJW4KJ3BG","created_at":"2026-07-04T15:18:49.217581+00:00"},{"alias_kind":"pith_short_8","alias_value":"CTENYMIS","created_at":"2026-07-04T15:18:49.217581+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/CTENYMISJW4KJ3BGFV5SIDHFV2","json":"https://pith.science/pith/CTENYMISJW4KJ3BGFV5SIDHFV2.json","graph_json":"https://pith.science/api/pith-number/CTENYMISJW4KJ3BGFV5SIDHFV2/graph.json","events_json":"https://pith.science/api/pith-number/CTENYMISJW4KJ3BGFV5SIDHFV2/events.json","paper":"https://pith.science/paper/CTENYMIS"},"agent_actions":{"view_html":"https://pith.science/pith/CTENYMISJW4KJ3BGFV5SIDHFV2","download_json":"https://pith.science/pith/CTENYMISJW4KJ3BGFV5SIDHFV2.json","view_paper":"https://pith.science/paper/CTENYMIS","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=gr-qc/0612070&json=true","fetch_graph":"https://pith.science/api/pith-number/CTENYMISJW4KJ3BGFV5SIDHFV2/graph.json","fetch_events":"https://pith.science/api/pith-number/CTENYMISJW4KJ3BGFV5SIDHFV2/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/CTENYMISJW4KJ3BGFV5SIDHFV2/action/timestamp_anchor","attest_storage":"https://pith.science/pith/CTENYMISJW4KJ3BGFV5SIDHFV2/action/storage_attestation","attest_author":"https://pith.science/pith/CTENYMISJW4KJ3BGFV5SIDHFV2/action/author_attestation","sign_citation":"https://pith.science/pith/CTENYMISJW4KJ3BGFV5SIDHFV2/action/citation_signature","submit_replication":"https://pith.science/pith/CTENYMISJW4KJ3BGFV5SIDHFV2/action/replication_record"}},"created_at":"2026-07-04T15:18:49.217581+00:00","updated_at":"2026-07-04T15:18:49.217581+00:00"}