{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:XFWFT5KDLGCAQ2NUBU2SOEWSVP","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":"16ff54cff69f6bb93204178c64f06d52ecc1da29285e29ab116b95a38c75e921","cross_cats_sorted":["gr-qc","math-ph","math.MP","math.NT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2018-08-13T01:31:05Z","title_canon_sha256":"b6b2088c8319ecf4b46846dc131fffd9119bd1027ac816519d91ab78e9e36033"},"schema_version":"1.0","source":{"id":"1808.04034","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1808.04034","created_at":"2026-05-17T23:43:17Z"},{"alias_kind":"arxiv_version","alias_value":"1808.04034v2","created_at":"2026-05-17T23:43:17Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1808.04034","created_at":"2026-05-17T23:43:17Z"},{"alias_kind":"pith_short_12","alias_value":"XFWFT5KDLGCA","created_at":"2026-05-18T12:33:01Z"},{"alias_kind":"pith_short_16","alias_value":"XFWFT5KDLGCAQ2NU","created_at":"2026-05-18T12:33:01Z"},{"alias_kind":"pith_short_8","alias_value":"XFWFT5KD","created_at":"2026-05-18T12:33:01Z"}],"graph_snapshots":[{"event_id":"sha256:f845d2480d2737e1e63f2779560abbfb5b86e5a37e25e66e7c3384916ad896c5","target":"graph","created_at":"2026-05-17T23:43:17Z","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":"Non-relativistic field theories with anisotropic scale invariance in (1+1)-d are typically characterized by a dispersion relation $E\\sim k^{z}$ and dynamical exponent $z>1$. The asymptotic growth of the number of states of these theories can be described by an extension of Cardy formula that depends on $z$. We show that this result can be recovered by counting the partitions of an integer into $z$-th powers, as proposed by Hardy and Ramanujan a century ago. This gives a novel relationship between the characteristic energy of the dispersion relation with the cylinder radius and the ground state","authors_text":"Alfredo P\\'erez, Dmitry Melnikov, F\\'abio Novaes, Ricardo Troncoso","cross_cats":["gr-qc","math-ph","math.MP","math.NT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2018-08-13T01:31:05Z","title":"Lifshitz Scaling, Microstate Counting from Number Theory and Black Hole Entropy"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1808.04034","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:dfc20a29443b76cf985a29ccdc1f58dbae46b08e64c94a86a6b22c099a5bb2cd","target":"record","created_at":"2026-05-17T23:43:17Z","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":"16ff54cff69f6bb93204178c64f06d52ecc1da29285e29ab116b95a38c75e921","cross_cats_sorted":["gr-qc","math-ph","math.MP","math.NT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2018-08-13T01:31:05Z","title_canon_sha256":"b6b2088c8319ecf4b46846dc131fffd9119bd1027ac816519d91ab78e9e36033"},"schema_version":"1.0","source":{"id":"1808.04034","kind":"arxiv","version":2}},"canonical_sha256":"b96c59f54359840869b40d352712d2abfbec16cb54221efc53af815dd9a3f756","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b96c59f54359840869b40d352712d2abfbec16cb54221efc53af815dd9a3f756","first_computed_at":"2026-05-17T23:43:17.711341Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:43:17.711341Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"/957VV5013z/iKLIqcD49s0+T+IXocxiKe336mgCkNH8rfSciCRn1Ji0Tz7lQub/YPZQdXJolPFC28XQJltKBg==","signature_status":"signed_v1","signed_at":"2026-05-17T23:43:17.711892Z","signed_message":"canonical_sha256_bytes"},"source_id":"1808.04034","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:dfc20a29443b76cf985a29ccdc1f58dbae46b08e64c94a86a6b22c099a5bb2cd","sha256:f845d2480d2737e1e63f2779560abbfb5b86e5a37e25e66e7c3384916ad896c5"],"state_sha256":"79ee4c2a5e5ae9db1cc27e0bc3d8da0097a6c65982660413ceae1a2e0dff62ad"}