{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:2XDO7X53PRKOLRLDVZLX7R2D3K","short_pith_number":"pith:2XDO7X53","canonical_record":{"source":{"id":"1303.5813","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2013-03-23T02:07:52Z","cross_cats_sorted":["gr-qc"],"title_canon_sha256":"2245d21d0c3b1c27904edb61ecceb5b2091277b7852463afb659fd5756728a0d","abstract_canon_sha256":"540f687ac09b1c01370759610aa659ff0dc5111454d45fb554fb0a452ed3cb59"},"schema_version":"1.0"},"canonical_sha256":"d5c6efdfbb7c54e5c563ae577fc743da912fc9e7bdd304fb082b9a62c9690494","source":{"kind":"arxiv","id":"1303.5813","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1303.5813","created_at":"2026-05-18T01:50:59Z"},{"alias_kind":"arxiv_version","alias_value":"1303.5813v2","created_at":"2026-05-18T01:50:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1303.5813","created_at":"2026-05-18T01:50:59Z"},{"alias_kind":"pith_short_12","alias_value":"2XDO7X53PRKO","created_at":"2026-05-18T12:27:32Z"},{"alias_kind":"pith_short_16","alias_value":"2XDO7X53PRKOLRLD","created_at":"2026-05-18T12:27:32Z"},{"alias_kind":"pith_short_8","alias_value":"2XDO7X53","created_at":"2026-05-18T12:27:32Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:2XDO7X53PRKOLRLDVZLX7R2D3K","target":"record","payload":{"canonical_record":{"source":{"id":"1303.5813","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2013-03-23T02:07:52Z","cross_cats_sorted":["gr-qc"],"title_canon_sha256":"2245d21d0c3b1c27904edb61ecceb5b2091277b7852463afb659fd5756728a0d","abstract_canon_sha256":"540f687ac09b1c01370759610aa659ff0dc5111454d45fb554fb0a452ed3cb59"},"schema_version":"1.0"},"canonical_sha256":"d5c6efdfbb7c54e5c563ae577fc743da912fc9e7bdd304fb082b9a62c9690494","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:50:59.329816Z","signature_b64":"6Act2zMS559qrrk67Oe9SWHtGLCkpt7QlXtvoH3K3mRJaT12rf53kT+ZkSECtKuapFw4hDuwLCiDkHRtl7blBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d5c6efdfbb7c54e5c563ae577fc743da912fc9e7bdd304fb082b9a62c9690494","last_reissued_at":"2026-05-18T01:50:59.329476Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:50:59.329476Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1303.5813","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":"2026-05-18T01:50:59Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"qWfQVBwmbya+OUCdfQ0Y0Y4YS62wEr8Dk+0Wj6TYcm36UPGmiRURMaJo+6MKzdryfCm3ccz+dxXk6nbOKvFuDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T15:21:28.955900Z"},"content_sha256":"aabdeecfd8bd8e42d5b2d6a0cfeba18f82c9706cea2bbe3dc93d388a2956d5be","schema_version":"1.0","event_id":"sha256:aabdeecfd8bd8e42d5b2d6a0cfeba18f82c9706cea2bbe3dc93d388a2956d5be"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:2XDO7X53PRKOLRLDVZLX7R2D3K","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Emergence of spaces and the dynamic equations of FRW universes in the $f(R)$ theory and deformed Ho\\v{r}ava-Lifshitz theory","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["gr-qc"],"primary_cat":"hep-th","authors_text":"Fei-Quan Tu, Yi-Xin Chen","submitted_at":"2013-03-23T02:07:52Z","abstract_excerpt":"It has been shown that Friedmann equation of FRW universe can be derived from the idea which says cosmic space is emergent as cosmic time progresses and our universe is expanding towards the state with the holographic equipartition by Padmanabhan. In this note, we give a general relationship between the horizon entropy and the number of the degrees of freedom on the surface, we also obtain the corresponding dynamic equations by using the idea of emergence of space in the $f(R)$ theory and deformed Ho\\v{r}ava-Lifshitz (HL) theory."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1303.5813","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":"2026-05-18T01:50:59Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"1Qztsu4aFm3+iEdFEXLfgnDHw9RkldyT6cQzU3ZRVh9uxJZ5EX5bUKn2RZAWkATZyB9eugUnkJLc7R+9AsCoAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T15:21:28.956625Z"},"content_sha256":"0517948f6a8a5038d9d14c5f610cf5256ed7055a092a2dc0aabbce02eeb3a506","schema_version":"1.0","event_id":"sha256:0517948f6a8a5038d9d14c5f610cf5256ed7055a092a2dc0aabbce02eeb3a506"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/2XDO7X53PRKOLRLDVZLX7R2D3K/bundle.json","state_url":"https://pith.science/pith/2XDO7X53PRKOLRLDVZLX7R2D3K/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/2XDO7X53PRKOLRLDVZLX7R2D3K/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":"2026-05-25T15:21:28Z","links":{"resolver":"https://pith.science/pith/2XDO7X53PRKOLRLDVZLX7R2D3K","bundle":"https://pith.science/pith/2XDO7X53PRKOLRLDVZLX7R2D3K/bundle.json","state":"https://pith.science/pith/2XDO7X53PRKOLRLDVZLX7R2D3K/state.json","well_known_bundle":"https://pith.science/.well-known/pith/2XDO7X53PRKOLRLDVZLX7R2D3K/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:2XDO7X53PRKOLRLDVZLX7R2D3K","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":"540f687ac09b1c01370759610aa659ff0dc5111454d45fb554fb0a452ed3cb59","cross_cats_sorted":["gr-qc"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2013-03-23T02:07:52Z","title_canon_sha256":"2245d21d0c3b1c27904edb61ecceb5b2091277b7852463afb659fd5756728a0d"},"schema_version":"1.0","source":{"id":"1303.5813","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1303.5813","created_at":"2026-05-18T01:50:59Z"},{"alias_kind":"arxiv_version","alias_value":"1303.5813v2","created_at":"2026-05-18T01:50:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1303.5813","created_at":"2026-05-18T01:50:59Z"},{"alias_kind":"pith_short_12","alias_value":"2XDO7X53PRKO","created_at":"2026-05-18T12:27:32Z"},{"alias_kind":"pith_short_16","alias_value":"2XDO7X53PRKOLRLD","created_at":"2026-05-18T12:27:32Z"},{"alias_kind":"pith_short_8","alias_value":"2XDO7X53","created_at":"2026-05-18T12:27:32Z"}],"graph_snapshots":[{"event_id":"sha256:0517948f6a8a5038d9d14c5f610cf5256ed7055a092a2dc0aabbce02eeb3a506","target":"graph","created_at":"2026-05-18T01:50:59Z","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":"It has been shown that Friedmann equation of FRW universe can be derived from the idea which says cosmic space is emergent as cosmic time progresses and our universe is expanding towards the state with the holographic equipartition by Padmanabhan. In this note, we give a general relationship between the horizon entropy and the number of the degrees of freedom on the surface, we also obtain the corresponding dynamic equations by using the idea of emergence of space in the $f(R)$ theory and deformed Ho\\v{r}ava-Lifshitz (HL) theory.","authors_text":"Fei-Quan Tu, Yi-Xin Chen","cross_cats":["gr-qc"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2013-03-23T02:07:52Z","title":"Emergence of spaces and the dynamic equations of FRW universes in the $f(R)$ theory and deformed Ho\\v{r}ava-Lifshitz theory"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1303.5813","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:aabdeecfd8bd8e42d5b2d6a0cfeba18f82c9706cea2bbe3dc93d388a2956d5be","target":"record","created_at":"2026-05-18T01:50:59Z","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":"540f687ac09b1c01370759610aa659ff0dc5111454d45fb554fb0a452ed3cb59","cross_cats_sorted":["gr-qc"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2013-03-23T02:07:52Z","title_canon_sha256":"2245d21d0c3b1c27904edb61ecceb5b2091277b7852463afb659fd5756728a0d"},"schema_version":"1.0","source":{"id":"1303.5813","kind":"arxiv","version":2}},"canonical_sha256":"d5c6efdfbb7c54e5c563ae577fc743da912fc9e7bdd304fb082b9a62c9690494","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d5c6efdfbb7c54e5c563ae577fc743da912fc9e7bdd304fb082b9a62c9690494","first_computed_at":"2026-05-18T01:50:59.329476Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:50:59.329476Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"6Act2zMS559qrrk67Oe9SWHtGLCkpt7QlXtvoH3K3mRJaT12rf53kT+ZkSECtKuapFw4hDuwLCiDkHRtl7blBA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:50:59.329816Z","signed_message":"canonical_sha256_bytes"},"source_id":"1303.5813","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:aabdeecfd8bd8e42d5b2d6a0cfeba18f82c9706cea2bbe3dc93d388a2956d5be","sha256:0517948f6a8a5038d9d14c5f610cf5256ed7055a092a2dc0aabbce02eeb3a506"],"state_sha256":"9494ec8facc0b581b3155918c5977597a9c95c2032c19baf8d3dd6011d008884"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"i2U/nDjbrqw+ejjNX2Z3DS1k0m8SDvcnZFJ+UGqQ02JpL8wa+AlLBaP4Aov5rjV6C1SZCIMx/AEAU40tcO0QAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-25T15:21:28.960716Z","bundle_sha256":"3182a138c54e910ef4ff28450018e3bee46f3f6a10310bfd922cc622966814c2"}}