{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2021:LH5HVO4ZRPJX6DYUCYQD3L5MC3","short_pith_number":"pith:LH5HVO4Z","canonical_record":{"source":{"id":"2108.09411","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2021-08-21T01:13:00Z","cross_cats_sorted":["astro-ph.CO","hep-th"],"title_canon_sha256":"580c4ce07a5ca0d926be3982cb9d5db163e56a0d9d028ff84bf2177d2256c128","abstract_canon_sha256":"2e33de6ea181adce2171c3bfd196793c261c5f8cca5a72ee70d97ee612dd016d"},"schema_version":"1.0"},"canonical_sha256":"59fa7abb998bd37f0f1416203dafac16f47989e1d0f662f2dea933989a2394ed","source":{"kind":"arxiv","id":"2108.09411","version":4},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2108.09411","created_at":"2026-07-05T05:19:11Z"},{"alias_kind":"arxiv_version","alias_value":"2108.09411v4","created_at":"2026-07-05T05:19:11Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2108.09411","created_at":"2026-07-05T05:19:11Z"},{"alias_kind":"pith_short_12","alias_value":"LH5HVO4ZRPJX","created_at":"2026-07-05T05:19:11Z"},{"alias_kind":"pith_short_16","alias_value":"LH5HVO4ZRPJX6DYU","created_at":"2026-07-05T05:19:11Z"},{"alias_kind":"pith_short_8","alias_value":"LH5HVO4Z","created_at":"2026-07-05T05:19:11Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2021:LH5HVO4ZRPJX6DYUCYQD3L5MC3","target":"record","payload":{"canonical_record":{"source":{"id":"2108.09411","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2021-08-21T01:13:00Z","cross_cats_sorted":["astro-ph.CO","hep-th"],"title_canon_sha256":"580c4ce07a5ca0d926be3982cb9d5db163e56a0d9d028ff84bf2177d2256c128","abstract_canon_sha256":"2e33de6ea181adce2171c3bfd196793c261c5f8cca5a72ee70d97ee612dd016d"},"schema_version":"1.0"},"canonical_sha256":"59fa7abb998bd37f0f1416203dafac16f47989e1d0f662f2dea933989a2394ed","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T05:19:11.220993Z","signature_b64":"1+SgqyKfk9vlTaUKu5IN64WFnbGTdLtOzKrRrif3UBOrbDSHGEzuVwghprndSTUiTBMGFSvhPGbSatUoRjs6BA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"59fa7abb998bd37f0f1416203dafac16f47989e1d0f662f2dea933989a2394ed","last_reissued_at":"2026-07-05T05:19:11.220515Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T05:19:11.220515Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2108.09411","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":"2026-07-05T05:19:11Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"NSWbVryYDbRFJ8EBuzPayvqwNpRDhuWn1mLH4SjqdNFDDjgp+l7me3BJdvXkD1lzHobUA5GqV/LmabqB46vmCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-14T08:26:32.501810Z"},"content_sha256":"959773ad8b46e811c882c6e5a0c3abb0c0c19a0cf51e8e1097ba56326fa462b7","schema_version":"1.0","event_id":"sha256:959773ad8b46e811c882c6e5a0c3abb0c0c19a0cf51e8e1097ba56326fa462b7"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2021:LH5HVO4ZRPJX6DYUCYQD3L5MC3","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The P-V Phase Transition of the FRW Universe","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["astro-ph.CO","hep-th"],"primary_cat":"gr-qc","authors_text":"Haximjan Abdusattar, Hongsheng Zhang, Shi-Bei Kong, Ya-Peng Hu, Yihao Yin","submitted_at":"2021-08-21T01:13:00Z","abstract_excerpt":"We define thermodynamic pressure $P$ by work density $W$ as the conjugate quantity of thermodynamic volume $V$ from field equation. We derive the equations of state $P$=$P(V, T)$ for the Friedmann-Robertson-Walker (FRW) universe in Einstein gravity and a modified gravity respectively. We find that the equation of state from Einstein gravity shows no $P$-$V$ phase transition, while the equation of state from the modified gravity does, where the critical exponents are the same as those in mean field theory."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2108.09411","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2108.09411/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":"2026-07-05T05:19:11Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ljp0eg/jx3OXM0dci1CbSBCOu1IfVtqvvc9Iv+ggabgqiBdtl7dBmPoxX0GtKIasd6jB2jSKxcUIeQm/q1a1DA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-14T08:26:32.502333Z"},"content_sha256":"32aa2fafc6504d53c3d5217f2a06362dd20af1bc93fbfc1bfcd6949be73b2dc9","schema_version":"1.0","event_id":"sha256:32aa2fafc6504d53c3d5217f2a06362dd20af1bc93fbfc1bfcd6949be73b2dc9"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/LH5HVO4ZRPJX6DYUCYQD3L5MC3/bundle.json","state_url":"https://pith.science/pith/LH5HVO4ZRPJX6DYUCYQD3L5MC3/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/LH5HVO4ZRPJX6DYUCYQD3L5MC3/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":"2026-08-14T08:26:32Z","links":{"resolver":"https://pith.science/pith/LH5HVO4ZRPJX6DYUCYQD3L5MC3","bundle":"https://pith.science/pith/LH5HVO4ZRPJX6DYUCYQD3L5MC3/bundle.json","state":"https://pith.science/pith/LH5HVO4ZRPJX6DYUCYQD3L5MC3/state.json","well_known_bundle":"https://pith.science/.well-known/pith/LH5HVO4ZRPJX6DYUCYQD3L5MC3/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2021:LH5HVO4ZRPJX6DYUCYQD3L5MC3","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":"2e33de6ea181adce2171c3bfd196793c261c5f8cca5a72ee70d97ee612dd016d","cross_cats_sorted":["astro-ph.CO","hep-th"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2021-08-21T01:13:00Z","title_canon_sha256":"580c4ce07a5ca0d926be3982cb9d5db163e56a0d9d028ff84bf2177d2256c128"},"schema_version":"1.0","source":{"id":"2108.09411","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2108.09411","created_at":"2026-07-05T05:19:11Z"},{"alias_kind":"arxiv_version","alias_value":"2108.09411v4","created_at":"2026-07-05T05:19:11Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2108.09411","created_at":"2026-07-05T05:19:11Z"},{"alias_kind":"pith_short_12","alias_value":"LH5HVO4ZRPJX","created_at":"2026-07-05T05:19:11Z"},{"alias_kind":"pith_short_16","alias_value":"LH5HVO4ZRPJX6DYU","created_at":"2026-07-05T05:19:11Z"},{"alias_kind":"pith_short_8","alias_value":"LH5HVO4Z","created_at":"2026-07-05T05:19:11Z"}],"graph_snapshots":[{"event_id":"sha256:32aa2fafc6504d53c3d5217f2a06362dd20af1bc93fbfc1bfcd6949be73b2dc9","target":"graph","created_at":"2026-07-05T05:19:11Z","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/2108.09411/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We define thermodynamic pressure $P$ by work density $W$ as the conjugate quantity of thermodynamic volume $V$ from field equation. We derive the equations of state $P$=$P(V, T)$ for the Friedmann-Robertson-Walker (FRW) universe in Einstein gravity and a modified gravity respectively. We find that the equation of state from Einstein gravity shows no $P$-$V$ phase transition, while the equation of state from the modified gravity does, where the critical exponents are the same as those in mean field theory.","authors_text":"Haximjan Abdusattar, Hongsheng Zhang, Shi-Bei Kong, Ya-Peng Hu, Yihao Yin","cross_cats":["astro-ph.CO","hep-th"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2021-08-21T01:13:00Z","title":"The P-V Phase Transition of the FRW Universe"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2108.09411","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":"sha256:959773ad8b46e811c882c6e5a0c3abb0c0c19a0cf51e8e1097ba56326fa462b7","target":"record","created_at":"2026-07-05T05:19:11Z","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":"2e33de6ea181adce2171c3bfd196793c261c5f8cca5a72ee70d97ee612dd016d","cross_cats_sorted":["astro-ph.CO","hep-th"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2021-08-21T01:13:00Z","title_canon_sha256":"580c4ce07a5ca0d926be3982cb9d5db163e56a0d9d028ff84bf2177d2256c128"},"schema_version":"1.0","source":{"id":"2108.09411","kind":"arxiv","version":4}},"canonical_sha256":"59fa7abb998bd37f0f1416203dafac16f47989e1d0f662f2dea933989a2394ed","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"59fa7abb998bd37f0f1416203dafac16f47989e1d0f662f2dea933989a2394ed","first_computed_at":"2026-07-05T05:19:11.220515Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T05:19:11.220515Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"1+SgqyKfk9vlTaUKu5IN64WFnbGTdLtOzKrRrif3UBOrbDSHGEzuVwghprndSTUiTBMGFSvhPGbSatUoRjs6BA==","signature_status":"signed_v1","signed_at":"2026-07-05T05:19:11.220993Z","signed_message":"canonical_sha256_bytes"},"source_id":"2108.09411","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:959773ad8b46e811c882c6e5a0c3abb0c0c19a0cf51e8e1097ba56326fa462b7","sha256:32aa2fafc6504d53c3d5217f2a06362dd20af1bc93fbfc1bfcd6949be73b2dc9"],"state_sha256":"ce626fffde2506e618606ad5fcd049748e3f36126cb61387a37854e7c7a0ae5f"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"P5csR8Yk46Q+9unPIkXAADuH61QHS0hxLPSxLuZrF/fTRKdSzDwnGqyc4bewNSN1KCJDvOPfJVw/tohDQFswDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-14T08:26:32.507499Z","bundle_sha256":"b6287edf4cecd6e2d19d67f05c258f2611880396dbd18111886a5738f42d0aba"}}