{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:3LD4DWB7FVKL6WKFVRINJWUAJ4","short_pith_number":"pith:3LD4DWB7","canonical_record":{"source":{"id":"1401.1485","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2014-01-07T19:58:22Z","cross_cats_sorted":[],"title_canon_sha256":"0081b268987134e8f884af38e50bf8de813d5a2345ef7a455f0c4b1db473a16b","abstract_canon_sha256":"48e78e24c6362625075b73c5f93f1e4a64cd6dfe8bdb186a2b103116474df369"},"schema_version":"1.0"},"canonical_sha256":"dac7c1d83f2d54bf5945ac50d4da804f205ecadcf5e4f57dbdb717340d82f3fc","source":{"kind":"arxiv","id":"1401.1485","version":4},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1401.1485","created_at":"2026-05-18T01:15:39Z"},{"alias_kind":"arxiv_version","alias_value":"1401.1485v4","created_at":"2026-05-18T01:15:39Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1401.1485","created_at":"2026-05-18T01:15:39Z"},{"alias_kind":"pith_short_12","alias_value":"3LD4DWB7FVKL","created_at":"2026-05-18T12:28:11Z"},{"alias_kind":"pith_short_16","alias_value":"3LD4DWB7FVKL6WKF","created_at":"2026-05-18T12:28:11Z"},{"alias_kind":"pith_short_8","alias_value":"3LD4DWB7","created_at":"2026-05-18T12:28:11Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:3LD4DWB7FVKL6WKFVRINJWUAJ4","target":"record","payload":{"canonical_record":{"source":{"id":"1401.1485","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2014-01-07T19:58:22Z","cross_cats_sorted":[],"title_canon_sha256":"0081b268987134e8f884af38e50bf8de813d5a2345ef7a455f0c4b1db473a16b","abstract_canon_sha256":"48e78e24c6362625075b73c5f93f1e4a64cd6dfe8bdb186a2b103116474df369"},"schema_version":"1.0"},"canonical_sha256":"dac7c1d83f2d54bf5945ac50d4da804f205ecadcf5e4f57dbdb717340d82f3fc","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:15:39.202674Z","signature_b64":"YMbTKSqUa6l+Akfr1dUOvoiD/K1ZMgASnGUtPr35EnZXAY3dzFwyK5LQZRrLK1Y/LEpPA2CDqQ48ink2+7wwDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"dac7c1d83f2d54bf5945ac50d4da804f205ecadcf5e4f57dbdb717340d82f3fc","last_reissued_at":"2026-05-18T01:15:39.201945Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:15:39.201945Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1401.1485","source_version":4,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:15:39Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"WizttPLg3eI6brcZmi0aTT6XUf2sricd+oNfFGeAncAyDf8saTKE2//Lo4rH1ukB2AY1smaZI3q4ELP0cJGZBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T10:46:13.165263Z"},"content_sha256":"2b59624f93b32ea6e83db43f941828c5f81c79e15e86f535ecf7af24bab8f8ac","schema_version":"1.0","event_id":"sha256:2b59624f93b32ea6e83db43f941828c5f81c79e15e86f535ecf7af24bab8f8ac"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:3LD4DWB7FVKL6WKFVRINJWUAJ4","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Noncommutativity in the early Universe","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"gr-qc","authors_text":"E. V. Corr\\^ea Silva, G. A. Monerat, G. Oliveira-Neto, M. Silva de Oliveira","submitted_at":"2014-01-07T19:58:22Z","abstract_excerpt":"In the present work, we study the noncommutative version of a quantum cosmology model. The model has a Friedmann-Robertson-Walker geometry, the matter content is a radiative perfect fluid and the spatial sections have zero constant curvature. In this model the scale factor takes values in a bounded domain. Therefore, its quantum mechanical version has a discrete energy spectrum. We compute the discrete energy spectrum and the corresponding eigenfunctions. The energies depend on a noncommutative parameter $\\beta$. We compute the scale factor expected value ($\\left<a\\right>$) for several values "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1401.1485","kind":"arxiv","version":4},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:15:39Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"6xo7zV1e6veIsEgikfD3iaZkm0sQP9VFLX3JIk0uB4Um9ZzzvvTM4NpkfwqatdRzq4+XlYH0B6aLGHG/YI9KCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T10:46:13.165926Z"},"content_sha256":"75aa71ec5f3b7e046a277bf766b61001992a76bcc04ac17c9162b6fc5f21333f","schema_version":"1.0","event_id":"sha256:75aa71ec5f3b7e046a277bf766b61001992a76bcc04ac17c9162b6fc5f21333f"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/3LD4DWB7FVKL6WKFVRINJWUAJ4/bundle.json","state_url":"https://pith.science/pith/3LD4DWB7FVKL6WKFVRINJWUAJ4/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/3LD4DWB7FVKL6WKFVRINJWUAJ4/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-05-30T10:46:13Z","links":{"resolver":"https://pith.science/pith/3LD4DWB7FVKL6WKFVRINJWUAJ4","bundle":"https://pith.science/pith/3LD4DWB7FVKL6WKFVRINJWUAJ4/bundle.json","state":"https://pith.science/pith/3LD4DWB7FVKL6WKFVRINJWUAJ4/state.json","well_known_bundle":"https://pith.science/.well-known/pith/3LD4DWB7FVKL6WKFVRINJWUAJ4/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:3LD4DWB7FVKL6WKFVRINJWUAJ4","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":"48e78e24c6362625075b73c5f93f1e4a64cd6dfe8bdb186a2b103116474df369","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2014-01-07T19:58:22Z","title_canon_sha256":"0081b268987134e8f884af38e50bf8de813d5a2345ef7a455f0c4b1db473a16b"},"schema_version":"1.0","source":{"id":"1401.1485","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1401.1485","created_at":"2026-05-18T01:15:39Z"},{"alias_kind":"arxiv_version","alias_value":"1401.1485v4","created_at":"2026-05-18T01:15:39Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1401.1485","created_at":"2026-05-18T01:15:39Z"},{"alias_kind":"pith_short_12","alias_value":"3LD4DWB7FVKL","created_at":"2026-05-18T12:28:11Z"},{"alias_kind":"pith_short_16","alias_value":"3LD4DWB7FVKL6WKF","created_at":"2026-05-18T12:28:11Z"},{"alias_kind":"pith_short_8","alias_value":"3LD4DWB7","created_at":"2026-05-18T12:28:11Z"}],"graph_snapshots":[{"event_id":"sha256:75aa71ec5f3b7e046a277bf766b61001992a76bcc04ac17c9162b6fc5f21333f","target":"graph","created_at":"2026-05-18T01:15:39Z","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":"In the present work, we study the noncommutative version of a quantum cosmology model. The model has a Friedmann-Robertson-Walker geometry, the matter content is a radiative perfect fluid and the spatial sections have zero constant curvature. In this model the scale factor takes values in a bounded domain. Therefore, its quantum mechanical version has a discrete energy spectrum. We compute the discrete energy spectrum and the corresponding eigenfunctions. The energies depend on a noncommutative parameter $\\beta$. We compute the scale factor expected value ($\\left<a\\right>$) for several values ","authors_text":"E. V. Corr\\^ea Silva, G. A. Monerat, G. Oliveira-Neto, M. Silva de Oliveira","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2014-01-07T19:58:22Z","title":"Noncommutativity in the early Universe"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1401.1485","kind":"arxiv","version":4},"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":"sha256:2b59624f93b32ea6e83db43f941828c5f81c79e15e86f535ecf7af24bab8f8ac","target":"record","created_at":"2026-05-18T01:15:39Z","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":"48e78e24c6362625075b73c5f93f1e4a64cd6dfe8bdb186a2b103116474df369","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2014-01-07T19:58:22Z","title_canon_sha256":"0081b268987134e8f884af38e50bf8de813d5a2345ef7a455f0c4b1db473a16b"},"schema_version":"1.0","source":{"id":"1401.1485","kind":"arxiv","version":4}},"canonical_sha256":"dac7c1d83f2d54bf5945ac50d4da804f205ecadcf5e4f57dbdb717340d82f3fc","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"dac7c1d83f2d54bf5945ac50d4da804f205ecadcf5e4f57dbdb717340d82f3fc","first_computed_at":"2026-05-18T01:15:39.201945Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:15:39.201945Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"YMbTKSqUa6l+Akfr1dUOvoiD/K1ZMgASnGUtPr35EnZXAY3dzFwyK5LQZRrLK1Y/LEpPA2CDqQ48ink2+7wwDg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:15:39.202674Z","signed_message":"canonical_sha256_bytes"},"source_id":"1401.1485","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2b59624f93b32ea6e83db43f941828c5f81c79e15e86f535ecf7af24bab8f8ac","sha256:75aa71ec5f3b7e046a277bf766b61001992a76bcc04ac17c9162b6fc5f21333f"],"state_sha256":"01a489d84164a752294dc5fe491d1dcff747b8d0441aaef2273b9f686739eb7e"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"m7v78DQs1RWJlPc16c8mVrKa/AvbtBKIA8lSLMzJK00fFuPCqz7VpBXPvKfO0E+CSaxh+WQrmb/mRRcfpWU6CQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-30T10:46:13.169278Z","bundle_sha256":"37f1a25ccf6a2eb709c26062b0b7a9b2fea386bec1316938618ac0a6c287d758"}}