{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2024:6OU3RJOBYEIIF3FB33L7SDAEQG","short_pith_number":"pith:6OU3RJOB","canonical_record":{"source":{"id":"2404.17624","kind":"arxiv","version":3},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"gr-qc","submitted_at":"2024-04-26T14:47:39Z","cross_cats_sorted":[],"title_canon_sha256":"fc5e59260fae11450eff01ebfab9472945819488ea59e3d0717e6db9c987704e","abstract_canon_sha256":"b18eda18151abd6bf3befdb4888f57e707e062fecfa1eb36e6f42adf67aa6bc7"},"schema_version":"1.0"},"canonical_sha256":"f3a9b8a5c1c11082eca1ded7f90c0481bb310c52b95a4b3438b61cafadf57034","source":{"kind":"arxiv","id":"2404.17624","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2404.17624","created_at":"2026-07-05T09:36:40Z"},{"alias_kind":"arxiv_version","alias_value":"2404.17624v3","created_at":"2026-07-05T09:36:40Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2404.17624","created_at":"2026-07-05T09:36:40Z"},{"alias_kind":"pith_short_12","alias_value":"6OU3RJOBYEII","created_at":"2026-07-05T09:36:40Z"},{"alias_kind":"pith_short_16","alias_value":"6OU3RJOBYEIIF3FB","created_at":"2026-07-05T09:36:40Z"},{"alias_kind":"pith_short_8","alias_value":"6OU3RJOB","created_at":"2026-07-05T09:36:40Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2024:6OU3RJOBYEIIF3FB33L7SDAEQG","target":"record","payload":{"canonical_record":{"source":{"id":"2404.17624","kind":"arxiv","version":3},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"gr-qc","submitted_at":"2024-04-26T14:47:39Z","cross_cats_sorted":[],"title_canon_sha256":"fc5e59260fae11450eff01ebfab9472945819488ea59e3d0717e6db9c987704e","abstract_canon_sha256":"b18eda18151abd6bf3befdb4888f57e707e062fecfa1eb36e6f42adf67aa6bc7"},"schema_version":"1.0"},"canonical_sha256":"f3a9b8a5c1c11082eca1ded7f90c0481bb310c52b95a4b3438b61cafadf57034","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T09:36:40.439165Z","signature_b64":"asnUi1ig6ORYhqPxa8/jN+ei6DCLYZqD9pPi0SAnVnvO9ceeNEiNLkw3L1zyfG3CRozcr0b2Sq6iptrmtblpAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f3a9b8a5c1c11082eca1ded7f90c0481bb310c52b95a4b3438b61cafadf57034","last_reissued_at":"2026-07-05T09:36:40.438667Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T09:36:40.438667Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2404.17624","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T09:36:40Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"L+8605sF7drhBZSVDs5SHfnyLhYkha6g6WVvRjMnc2q+U+UNOSkUv5//nuF+CaOlbLtBq6uMXvZ5CdPf+pT3BA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-17T20:16:40.145292Z"},"content_sha256":"393e72546156c5310d0d2419f4e3be2e650eea4d9761800c42f6895188f7ca1c","schema_version":"1.0","event_id":"sha256:393e72546156c5310d0d2419f4e3be2e650eea4d9761800c42f6895188f7ca1c"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2024:6OU3RJOBYEIIF3FB33L7SDAEQG","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Phase transitions, critical behavior and microstructure of the FRW universe in the framework of higher order GUP","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"gr-qc","authors_text":"Haximjan Abdusattar, Shi-Yu Li, Xia Zhou, Zhong-Wen Feng","submitted_at":"2024-04-26T14:47:39Z","abstract_excerpt":"In this paper, we explore the the phase transition, critical behavior and microstructure of the FRW in the framework of a new higher order generalized uncertainty principle. Our initial step involves deriving the equation of state by defining the work density $W$ from GUP-corrected Friedmann equations as the thermodynamic pressure $P$. Based on the modified equation of state, we conduct an analysis of the $P-V$ phase transition in the FRW universe. Subsequently, we obtain the critical exponents and coexistence curves for the small and large phases of the FRW universe around the critical point."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2404.17624","kind":"arxiv","version":3},"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/2404.17624/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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T09:36:40Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"n6r6Y7yJ8RU52SZsgLPj+4+F/C+nts9L8F9dfEpboMGUDwofsd2lKYBKOQgwXMmpqV2JPG3bzvsbEcjPB3zyAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-17T20:16:40.145675Z"},"content_sha256":"99d0dda63ff9163f1f3a1f7364ed0013d4b6922961892315f917061388b17b56","schema_version":"1.0","event_id":"sha256:99d0dda63ff9163f1f3a1f7364ed0013d4b6922961892315f917061388b17b56"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/6OU3RJOBYEIIF3FB33L7SDAEQG/bundle.json","state_url":"https://pith.science/pith/6OU3RJOBYEIIF3FB33L7SDAEQG/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/6OU3RJOBYEIIF3FB33L7SDAEQG/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":"2026-07-17T20:16:40Z","links":{"resolver":"https://pith.science/pith/6OU3RJOBYEIIF3FB33L7SDAEQG","bundle":"https://pith.science/pith/6OU3RJOBYEIIF3FB33L7SDAEQG/bundle.json","state":"https://pith.science/pith/6OU3RJOBYEIIF3FB33L7SDAEQG/state.json","well_known_bundle":"https://pith.science/.well-known/pith/6OU3RJOBYEIIF3FB33L7SDAEQG/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:6OU3RJOBYEIIF3FB33L7SDAEQG","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":"b18eda18151abd6bf3befdb4888f57e707e062fecfa1eb36e6f42adf67aa6bc7","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"gr-qc","submitted_at":"2024-04-26T14:47:39Z","title_canon_sha256":"fc5e59260fae11450eff01ebfab9472945819488ea59e3d0717e6db9c987704e"},"schema_version":"1.0","source":{"id":"2404.17624","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2404.17624","created_at":"2026-07-05T09:36:40Z"},{"alias_kind":"arxiv_version","alias_value":"2404.17624v3","created_at":"2026-07-05T09:36:40Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2404.17624","created_at":"2026-07-05T09:36:40Z"},{"alias_kind":"pith_short_12","alias_value":"6OU3RJOBYEII","created_at":"2026-07-05T09:36:40Z"},{"alias_kind":"pith_short_16","alias_value":"6OU3RJOBYEIIF3FB","created_at":"2026-07-05T09:36:40Z"},{"alias_kind":"pith_short_8","alias_value":"6OU3RJOB","created_at":"2026-07-05T09:36:40Z"}],"graph_snapshots":[{"event_id":"sha256:99d0dda63ff9163f1f3a1f7364ed0013d4b6922961892315f917061388b17b56","target":"graph","created_at":"2026-07-05T09:36:40Z","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/2404.17624/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In this paper, we explore the the phase transition, critical behavior and microstructure of the FRW in the framework of a new higher order generalized uncertainty principle. Our initial step involves deriving the equation of state by defining the work density $W$ from GUP-corrected Friedmann equations as the thermodynamic pressure $P$. Based on the modified equation of state, we conduct an analysis of the $P-V$ phase transition in the FRW universe. Subsequently, we obtain the critical exponents and coexistence curves for the small and large phases of the FRW universe around the critical point.","authors_text":"Haximjan Abdusattar, Shi-Yu Li, Xia Zhou, Zhong-Wen Feng","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"gr-qc","submitted_at":"2024-04-26T14:47:39Z","title":"Phase transitions, critical behavior and microstructure of the FRW universe in the framework of higher order GUP"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2404.17624","kind":"arxiv","version":3},"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":"sha256:393e72546156c5310d0d2419f4e3be2e650eea4d9761800c42f6895188f7ca1c","target":"record","created_at":"2026-07-05T09:36:40Z","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":"b18eda18151abd6bf3befdb4888f57e707e062fecfa1eb36e6f42adf67aa6bc7","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"gr-qc","submitted_at":"2024-04-26T14:47:39Z","title_canon_sha256":"fc5e59260fae11450eff01ebfab9472945819488ea59e3d0717e6db9c987704e"},"schema_version":"1.0","source":{"id":"2404.17624","kind":"arxiv","version":3}},"canonical_sha256":"f3a9b8a5c1c11082eca1ded7f90c0481bb310c52b95a4b3438b61cafadf57034","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f3a9b8a5c1c11082eca1ded7f90c0481bb310c52b95a4b3438b61cafadf57034","first_computed_at":"2026-07-05T09:36:40.438667Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T09:36:40.438667Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"asnUi1ig6ORYhqPxa8/jN+ei6DCLYZqD9pPi0SAnVnvO9ceeNEiNLkw3L1zyfG3CRozcr0b2Sq6iptrmtblpAQ==","signature_status":"signed_v1","signed_at":"2026-07-05T09:36:40.439165Z","signed_message":"canonical_sha256_bytes"},"source_id":"2404.17624","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:393e72546156c5310d0d2419f4e3be2e650eea4d9761800c42f6895188f7ca1c","sha256:99d0dda63ff9163f1f3a1f7364ed0013d4b6922961892315f917061388b17b56"],"state_sha256":"d52025f30a189cab6688c9146459296a0d182c2b05be54e8f1d54cbf0905afff"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"3IiMHfXBicKoVI3l4GuAPJ8AdK0NYmly21Yd+NI9HcTQqjOgWqR0GA8b2nZyYpyGHlAkGtWSYLgiNtnqlOn9Ag==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-17T20:16:40.148261Z","bundle_sha256":"889c39e5d9b28cabe8f2c0ff4aa40ad15bb54526df64336d0765b72284196a1f"}}