{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:5JIJILJW7ULGASSA5MPDIQY3ZF","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":"d662342d11f969657b5baee43d2ab5c6d497079c68889ea790381f4208acadd0","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"hep-th","submitted_at":"2018-04-25T13:28:44Z","title_canon_sha256":"93006619433463991c27248c73d8edd67ad03a0424ffefacf820f0d97e60fdee"},"schema_version":"1.0","source":{"id":"1805.00368","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1805.00368","created_at":"2026-05-18T00:00:19Z"},{"alias_kind":"arxiv_version","alias_value":"1805.00368v2","created_at":"2026-05-18T00:00:19Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1805.00368","created_at":"2026-05-18T00:00:19Z"},{"alias_kind":"pith_short_12","alias_value":"5JIJILJW7ULG","created_at":"2026-05-18T12:32:08Z"},{"alias_kind":"pith_short_16","alias_value":"5JIJILJW7ULGASSA","created_at":"2026-05-18T12:32:08Z"},{"alias_kind":"pith_short_8","alias_value":"5JIJILJW","created_at":"2026-05-18T12:32:08Z"}],"graph_snapshots":[{"event_id":"sha256:1e4eeadc2dede932bfbc3f83c937b5cc8ba6c3b59a85facda49c3a7f04ceff30","target":"graph","created_at":"2026-05-18T00:00:19Z","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":"Till now, critical behaviour of Lifshitz black holes, in an extended $P-v$ space, has not been studied, because it is impossible to find an analytical equation of state, $P=P(v,T)$, for an arbitrary Lifshitz exponent $z$. In this paper, we adopt a new approach toward thermodynamic phase space and successfully explore the critical behaviour of $(n+1)$-dimensional Lifshitz dilaton black holes. For this purpose, we write down the equation of state as $Q^s=Q^s(T,\\Psi)$ with $\\Psi=\\left({\\partial M}/{\\partial Q^{s} }\\right)_{S,P}$ is the conjugate of $Q^s$ and construct Smarr relation based on this","authors_text":"Ahmad Sheykhi, Zeinab Dayyani","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"hep-th","submitted_at":"2018-04-25T13:28:44Z","title":"Critical behaviour of Lifshitz dilaton black holes"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1805.00368","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":"sha256:8b7742d5d3ee4746523861f9f3bb0438375f5e28c04d6dfceca4bc8884f344ee","target":"record","created_at":"2026-05-18T00:00:19Z","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":"d662342d11f969657b5baee43d2ab5c6d497079c68889ea790381f4208acadd0","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"hep-th","submitted_at":"2018-04-25T13:28:44Z","title_canon_sha256":"93006619433463991c27248c73d8edd67ad03a0424ffefacf820f0d97e60fdee"},"schema_version":"1.0","source":{"id":"1805.00368","kind":"arxiv","version":2}},"canonical_sha256":"ea50942d36fd16604a40eb1e34431bc952f52224030c197be20713d5132ee2c7","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ea50942d36fd16604a40eb1e34431bc952f52224030c197be20713d5132ee2c7","first_computed_at":"2026-05-18T00:00:19.623671Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:00:19.623671Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"TxIwh3WfIAlqVm8N2vhnyqOPCckN+kypsSFivlNRCLURVNxsPqPPwVW65R86R/xI3uDvZcK1vY1LZAgEf8+1CQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:00:19.624188Z","signed_message":"canonical_sha256_bytes"},"source_id":"1805.00368","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8b7742d5d3ee4746523861f9f3bb0438375f5e28c04d6dfceca4bc8884f344ee","sha256:1e4eeadc2dede932bfbc3f83c937b5cc8ba6c3b59a85facda49c3a7f04ceff30"],"state_sha256":"90270354687ab330190bc4acb258db2f654b0adbcaa53562c9118f863a0b087e"}