{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2010:U4UIGL3SFTZF36EBWMAFVHLLRM","short_pith_number":"pith:U4UIGL3S","canonical_record":{"source":{"id":"1011.3418","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2010-11-15T15:20:33Z","cross_cats_sorted":["astro-ph.CO","hep-th"],"title_canon_sha256":"0d4f42074ca00b6be87fe31ff2431d4bc3c5a4078aadd02b639f6dc12cc783cf","abstract_canon_sha256":"ef9909f30f9e210ef28375bc5555cf0e57d8b21940f41d401614acfaf34a6d2e"},"schema_version":"1.0"},"canonical_sha256":"a728832f722cf25df881b3005a9d6b8b0b97a41d87f913b16ccbe6d27f918fcf","source":{"kind":"arxiv","id":"1011.3418","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1011.3418","created_at":"2026-05-18T04:22:29Z"},{"alias_kind":"arxiv_version","alias_value":"1011.3418v2","created_at":"2026-05-18T04:22:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1011.3418","created_at":"2026-05-18T04:22:29Z"},{"alias_kind":"pith_short_12","alias_value":"U4UIGL3SFTZF","created_at":"2026-05-18T12:26:15Z"},{"alias_kind":"pith_short_16","alias_value":"U4UIGL3SFTZF36EB","created_at":"2026-05-18T12:26:15Z"},{"alias_kind":"pith_short_8","alias_value":"U4UIGL3S","created_at":"2026-05-18T12:26:15Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2010:U4UIGL3SFTZF36EBWMAFVHLLRM","target":"record","payload":{"canonical_record":{"source":{"id":"1011.3418","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2010-11-15T15:20:33Z","cross_cats_sorted":["astro-ph.CO","hep-th"],"title_canon_sha256":"0d4f42074ca00b6be87fe31ff2431d4bc3c5a4078aadd02b639f6dc12cc783cf","abstract_canon_sha256":"ef9909f30f9e210ef28375bc5555cf0e57d8b21940f41d401614acfaf34a6d2e"},"schema_version":"1.0"},"canonical_sha256":"a728832f722cf25df881b3005a9d6b8b0b97a41d87f913b16ccbe6d27f918fcf","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:22:29.473529Z","signature_b64":"gVTHlklscofZwWdVLdBNX/XiDatewG7RV8Js7BaO2+IJyRribR9ZJJRzs6LSTsvs6gRqvU2HSxM1cDRRHzHGCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a728832f722cf25df881b3005a9d6b8b0b97a41d87f913b16ccbe6d27f918fcf","last_reissued_at":"2026-05-18T04:22:29.473106Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:22:29.473106Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1011.3418","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T04:22:29Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"F+5+CCP5dRXFp4VPOEV0HtyRSb+7gDiuVKqTIANZw2TgUR8jX3eLU344yCjXHGLrIheESYolxlPbpJ9Xt5jlDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T15:25:08.789362Z"},"content_sha256":"6ba5a03d918b42f16c8b3e1469c6a210c646878869876983e14abaa6cea7bee8","schema_version":"1.0","event_id":"sha256:6ba5a03d918b42f16c8b3e1469c6a210c646878869876983e14abaa6cea7bee8"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2010:U4UIGL3SFTZF36EBWMAFVHLLRM","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Quantum of volume in de Sitter space","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["astro-ph.CO","hep-th"],"primary_cat":"gr-qc","authors_text":"Jakub Mielczarek, Wlodzimierz Piechocki","submitted_at":"2010-11-15T15:20:33Z","abstract_excerpt":"We apply the nonstandard loop quantum cosmology method to quantize a flat Friedmann-Robertson-Walker cosmological model with a free scalar field and the cosmological constant $\\Lambda>0$. Modification of the Hamiltonian in terms of loop geometry parametrized by a length $\\lambda$ introduces a scale dependence of the model. The spectrum of the volume operator is discrete and depends on $\\Lambda$. Relating quantum of the volume with an elementary lattice cell leads to an explicit dependence of $\\Lambda$ on $\\lambda$. Based on this assumption, we investigate the possibility of interpreting $\\Lamb"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1011.3418","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":""},"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":"2026-05-18T04:22:29Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"NvsT2lUx+VpiI4ale3tB8eXkDF8F+P1agGEDQtF5kGf9aUlaKnVWHVUKR93spv70QfigygB76+CtpwlFBrE8Cw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T15:25:08.790051Z"},"content_sha256":"4582f0c4a7fcd87fcd74337f8be03094c66a968f1f537a572a5ab73cfff48408","schema_version":"1.0","event_id":"sha256:4582f0c4a7fcd87fcd74337f8be03094c66a968f1f537a572a5ab73cfff48408"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/U4UIGL3SFTZF36EBWMAFVHLLRM/bundle.json","state_url":"https://pith.science/pith/U4UIGL3SFTZF36EBWMAFVHLLRM/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/U4UIGL3SFTZF36EBWMAFVHLLRM/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":"2026-05-28T15:25:08Z","links":{"resolver":"https://pith.science/pith/U4UIGL3SFTZF36EBWMAFVHLLRM","bundle":"https://pith.science/pith/U4UIGL3SFTZF36EBWMAFVHLLRM/bundle.json","state":"https://pith.science/pith/U4UIGL3SFTZF36EBWMAFVHLLRM/state.json","well_known_bundle":"https://pith.science/.well-known/pith/U4UIGL3SFTZF36EBWMAFVHLLRM/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:U4UIGL3SFTZF36EBWMAFVHLLRM","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":"ef9909f30f9e210ef28375bc5555cf0e57d8b21940f41d401614acfaf34a6d2e","cross_cats_sorted":["astro-ph.CO","hep-th"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2010-11-15T15:20:33Z","title_canon_sha256":"0d4f42074ca00b6be87fe31ff2431d4bc3c5a4078aadd02b639f6dc12cc783cf"},"schema_version":"1.0","source":{"id":"1011.3418","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1011.3418","created_at":"2026-05-18T04:22:29Z"},{"alias_kind":"arxiv_version","alias_value":"1011.3418v2","created_at":"2026-05-18T04:22:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1011.3418","created_at":"2026-05-18T04:22:29Z"},{"alias_kind":"pith_short_12","alias_value":"U4UIGL3SFTZF","created_at":"2026-05-18T12:26:15Z"},{"alias_kind":"pith_short_16","alias_value":"U4UIGL3SFTZF36EB","created_at":"2026-05-18T12:26:15Z"},{"alias_kind":"pith_short_8","alias_value":"U4UIGL3S","created_at":"2026-05-18T12:26:15Z"}],"graph_snapshots":[{"event_id":"sha256:4582f0c4a7fcd87fcd74337f8be03094c66a968f1f537a572a5ab73cfff48408","target":"graph","created_at":"2026-05-18T04:22:29Z","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":"We apply the nonstandard loop quantum cosmology method to quantize a flat Friedmann-Robertson-Walker cosmological model with a free scalar field and the cosmological constant $\\Lambda>0$. Modification of the Hamiltonian in terms of loop geometry parametrized by a length $\\lambda$ introduces a scale dependence of the model. The spectrum of the volume operator is discrete and depends on $\\Lambda$. Relating quantum of the volume with an elementary lattice cell leads to an explicit dependence of $\\Lambda$ on $\\lambda$. Based on this assumption, we investigate the possibility of interpreting $\\Lamb","authors_text":"Jakub Mielczarek, Wlodzimierz Piechocki","cross_cats":["astro-ph.CO","hep-th"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2010-11-15T15:20:33Z","title":"Quantum of volume in de Sitter space"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1011.3418","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":"sha256:6ba5a03d918b42f16c8b3e1469c6a210c646878869876983e14abaa6cea7bee8","target":"record","created_at":"2026-05-18T04:22:29Z","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":"ef9909f30f9e210ef28375bc5555cf0e57d8b21940f41d401614acfaf34a6d2e","cross_cats_sorted":["astro-ph.CO","hep-th"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2010-11-15T15:20:33Z","title_canon_sha256":"0d4f42074ca00b6be87fe31ff2431d4bc3c5a4078aadd02b639f6dc12cc783cf"},"schema_version":"1.0","source":{"id":"1011.3418","kind":"arxiv","version":2}},"canonical_sha256":"a728832f722cf25df881b3005a9d6b8b0b97a41d87f913b16ccbe6d27f918fcf","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a728832f722cf25df881b3005a9d6b8b0b97a41d87f913b16ccbe6d27f918fcf","first_computed_at":"2026-05-18T04:22:29.473106Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:22:29.473106Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"gVTHlklscofZwWdVLdBNX/XiDatewG7RV8Js7BaO2+IJyRribR9ZJJRzs6LSTsvs6gRqvU2HSxM1cDRRHzHGCA==","signature_status":"signed_v1","signed_at":"2026-05-18T04:22:29.473529Z","signed_message":"canonical_sha256_bytes"},"source_id":"1011.3418","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6ba5a03d918b42f16c8b3e1469c6a210c646878869876983e14abaa6cea7bee8","sha256:4582f0c4a7fcd87fcd74337f8be03094c66a968f1f537a572a5ab73cfff48408"],"state_sha256":"d3e47e3866f395964adc7bb32aa42e8b2a55d73ee5c23003acf453909bd06101"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"VzEqqDA9DFn4rkIL0XMZY/J6ZpZp52iJGBibzcBOHQHj8hPqNXInGyxw8vk8YBtbzo7/nunQhv8JFjUfPU+tBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-28T15:25:08.793617Z","bundle_sha256":"7fb7bbfbda857f6ad091eb9d986d7852ad8834d17446de93a9d2cb8f62a1ac7a"}}