{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:1993:SX4H64KE7FVP6GRSTQHLYNSE6K","short_pith_number":"pith:SX4H64KE","schema_version":"1.0","canonical_sha256":"95f87f7144f96aff1a329c0ebc3644f29035a281a64295bb12bb040aa47fed65","source":{"kind":"arxiv","id":"hep-th/9304088","version":2},"attestation_state":"computed","paper":{"title":"Critical and Topological Properties of Cluster Boundaries in the $3d$ Ising Model","license":"","headline":"","cross_cats":["cond-mat","hep-lat"],"primary_cat":"hep-th","authors_text":"E. Marinari, E. Martinec, G. Harris, M. Picco, P. Windey, V. Dotsenko","submitted_at":"1993-04-21T01:57:38Z","abstract_excerpt":"We analyze the behavior of the ensemble of surface boundaries of the critical clusters at $T=T_c$ in the $3d$ Ising model. We find that $N_g(A)$, the number of surfaces of given genus $g$ and fixed area $A$, behaves as $A^{-x(g)}$ $e^{-\\mu A}$. We show that $\\mu$ is a constant independent of $g$ and $x(g)$ is approximately a linear function of $g$. The sum of $N_g(A)$ over genus scales as a power of $A$. We also observe that the volume of the clusters is proportional to its surface area. We argue that this behavior is typical of a branching instability for the surfaces, similar to the ones fou"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"hep-th/9304088","kind":"arxiv","version":2},"metadata":{"license":"","primary_cat":"hep-th","submitted_at":"1993-04-21T01:57:38Z","cross_cats_sorted":["cond-mat","hep-lat"],"title_canon_sha256":"9184c08d904966cc32615f97e629f2a202e1dc10a3d338fd77d16c59c76f9f4c","abstract_canon_sha256":"5cbec80d7d12e438ff0d57a04113fe98bad6ec9874e91564db66669d75f443a8"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-04T15:56:12.542843Z","signature_b64":"SOqYLP9RkcopaenvtOdEJ1RKiM/w6/jvXtYaloOan6bTBoM9s8io/dQpVRNxiK8+/Sm61pMglCuHRIL2cTCsCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"95f87f7144f96aff1a329c0ebc3644f29035a281a64295bb12bb040aa47fed65","last_reissued_at":"2026-07-04T15:56:12.542427Z","signature_status":"signed_v1","first_computed_at":"2026-07-04T15:56:12.542427Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Critical and Topological Properties of Cluster Boundaries in the $3d$ Ising Model","license":"","headline":"","cross_cats":["cond-mat","hep-lat"],"primary_cat":"hep-th","authors_text":"E. Marinari, E. Martinec, G. Harris, M. Picco, P. Windey, V. Dotsenko","submitted_at":"1993-04-21T01:57:38Z","abstract_excerpt":"We analyze the behavior of the ensemble of surface boundaries of the critical clusters at $T=T_c$ in the $3d$ Ising model. We find that $N_g(A)$, the number of surfaces of given genus $g$ and fixed area $A$, behaves as $A^{-x(g)}$ $e^{-\\mu A}$. We show that $\\mu$ is a constant independent of $g$ and $x(g)$ is approximately a linear function of $g$. The sum of $N_g(A)$ over genus scales as a power of $A$. We also observe that the volume of the clusters is proportional to its surface area. We argue that this behavior is typical of a branching instability for the surfaces, similar to the ones fou"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"hep-th/9304088","kind":"arxiv","version":2},"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/hep-th/9304088/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"},"aliases":[{"alias_kind":"arxiv","alias_value":"hep-th/9304088","created_at":"2026-07-04T15:56:12.542492+00:00"},{"alias_kind":"arxiv_version","alias_value":"hep-th/9304088v2","created_at":"2026-07-04T15:56:12.542492+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.hep-th/9304088","created_at":"2026-07-04T15:56:12.542492+00:00"},{"alias_kind":"pith_short_12","alias_value":"SX4H64KE7FVP","created_at":"2026-07-04T15:56:12.542492+00:00"},{"alias_kind":"pith_short_16","alias_value":"SX4H64KE7FVP6GRS","created_at":"2026-07-04T15:56:12.542492+00:00"},{"alias_kind":"pith_short_8","alias_value":"SX4H64KE","created_at":"2026-07-04T15:56:12.542492+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/SX4H64KE7FVP6GRSTQHLYNSE6K","json":"https://pith.science/pith/SX4H64KE7FVP6GRSTQHLYNSE6K.json","graph_json":"https://pith.science/api/pith-number/SX4H64KE7FVP6GRSTQHLYNSE6K/graph.json","events_json":"https://pith.science/api/pith-number/SX4H64KE7FVP6GRSTQHLYNSE6K/events.json","paper":"https://pith.science/paper/SX4H64KE"},"agent_actions":{"view_html":"https://pith.science/pith/SX4H64KE7FVP6GRSTQHLYNSE6K","download_json":"https://pith.science/pith/SX4H64KE7FVP6GRSTQHLYNSE6K.json","view_paper":"https://pith.science/paper/SX4H64KE","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=hep-th/9304088&json=true","fetch_graph":"https://pith.science/api/pith-number/SX4H64KE7FVP6GRSTQHLYNSE6K/graph.json","fetch_events":"https://pith.science/api/pith-number/SX4H64KE7FVP6GRSTQHLYNSE6K/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/SX4H64KE7FVP6GRSTQHLYNSE6K/action/timestamp_anchor","attest_storage":"https://pith.science/pith/SX4H64KE7FVP6GRSTQHLYNSE6K/action/storage_attestation","attest_author":"https://pith.science/pith/SX4H64KE7FVP6GRSTQHLYNSE6K/action/author_attestation","sign_citation":"https://pith.science/pith/SX4H64KE7FVP6GRSTQHLYNSE6K/action/citation_signature","submit_replication":"https://pith.science/pith/SX4H64KE7FVP6GRSTQHLYNSE6K/action/replication_record"}},"created_at":"2026-07-04T15:56:12.542492+00:00","updated_at":"2026-07-04T15:56:12.542492+00:00"}