{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:PSXXOUMOMVDMNCH4Q6I5PFWX5M","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":"83a3345c473131ea67ebbc112711dcecaa4b90e440c4346a6b92c0b64d9e8c0f","cross_cats_sorted":["gr-qc"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2015-08-26T12:52:27Z","title_canon_sha256":"d3e440b5d148c12ebeaaf38b921a0c9b5af1c790173112d8a4d4bed1085d7a75"},"schema_version":"1.0","source":{"id":"1508.06475","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1508.06475","created_at":"2026-05-18T01:02:56Z"},{"alias_kind":"arxiv_version","alias_value":"1508.06475v3","created_at":"2026-05-18T01:02:56Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1508.06475","created_at":"2026-05-18T01:02:56Z"},{"alias_kind":"pith_short_12","alias_value":"PSXXOUMOMVDM","created_at":"2026-05-18T12:29:37Z"},{"alias_kind":"pith_short_16","alias_value":"PSXXOUMOMVDMNCH4","created_at":"2026-05-18T12:29:37Z"},{"alias_kind":"pith_short_8","alias_value":"PSXXOUMO","created_at":"2026-05-18T12:29:37Z"}],"graph_snapshots":[{"event_id":"sha256:9c2f09d79a2e053409c41b42b332996da38dfa665ec99643b09cab3546d2aa4d","target":"graph","created_at":"2026-05-18T01:02:56Z","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 this paper, employing the modified dispersion relation, we have derived the general modified Friedmann equations and the corresponding modified entropy relations for the Friedmann-Robertson-Walker (FRW) Universe. In this setup, we find that when the big bounce happens, its energy scale and its corresponding modified entropy behavior are sensitive to the value of $k$. In contrast to the previous work with $k=0$, our work mainly demonstrates that the bouncing behavior for the closed Universe with $k=1$ appears at the normal energy limit of the modified dispersion relation introduced, and when","authors_text":"Wen-Jian Pan, Yong-Chang Huang","cross_cats":["gr-qc"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2015-08-26T12:52:27Z","title":"Bouncing universe with modified dispersion relation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1508.06475","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:ac439874443d6c448153d0b166cd65fa205947d721f7ce0efb7ddc4ed6856114","target":"record","created_at":"2026-05-18T01:02:56Z","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":"83a3345c473131ea67ebbc112711dcecaa4b90e440c4346a6b92c0b64d9e8c0f","cross_cats_sorted":["gr-qc"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2015-08-26T12:52:27Z","title_canon_sha256":"d3e440b5d148c12ebeaaf38b921a0c9b5af1c790173112d8a4d4bed1085d7a75"},"schema_version":"1.0","source":{"id":"1508.06475","kind":"arxiv","version":3}},"canonical_sha256":"7caf77518e6546c688fc8791d796d7eb091dceb02403c396e9d2f90e1e3707df","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7caf77518e6546c688fc8791d796d7eb091dceb02403c396e9d2f90e1e3707df","first_computed_at":"2026-05-18T01:02:56.864733Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:02:56.864733Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Xldl63zi11xM7G4R7DpaU8reO+7Z2ZJgdSe2J8GttObUUVQ9wvrdEvx4tXrBBJuDowQmAtS3yfwxwxBr0dzOCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:02:56.865300Z","signed_message":"canonical_sha256_bytes"},"source_id":"1508.06475","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ac439874443d6c448153d0b166cd65fa205947d721f7ce0efb7ddc4ed6856114","sha256:9c2f09d79a2e053409c41b42b332996da38dfa665ec99643b09cab3546d2aa4d"],"state_sha256":"7b0bddeac77b5e00f273ec04702ecf55d200810b7c619e9b63d07927d3d04113"}