{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2026:5U4XC45CQSSFPRYJ6QJG6J27GU","short_pith_number":"pith:5U4XC45C","schema_version":"1.0","canonical_sha256":"ed397173a284a457c709f4126f275f3528641ddcc269e8bc55d8ddcfa86dac11","source":{"kind":"arxiv","id":"2606.31424","version":1},"attestation_state":"computed","paper":{"title":"Critical Lin-Lunin-Maldacena geometries","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"hep-th","authors_text":"Lev Senchukov, Prokopii Anempodistov, Vladimir Kazakov","submitted_at":"2026-06-30T09:48:25Z","abstract_excerpt":"We study the critical behavior of the Lin-Lunin-Maldacena (LLM) geometry in the case when a droplet in the LLM base space develops a cusp. This cusp is a generic feature of the density of complex eigenvalues in the dual complex matrix model (CMM) computing the correlation functions of huge 1/2-BPS operators in $\\mathcal{N}=4$ SYM theory. It is also related to the criticality in CMM describing the pure $2D$ quantum gravity behavior. The supergravity dual -- LLM metric in the vicinity of the tip of the cusp -- acquires a universal $ISO(1,3)\\times SO(5)$ symmetric form, with a naked singularity a"},"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":"2606.31424","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"hep-th","submitted_at":"2026-06-30T09:48:25Z","cross_cats_sorted":[],"title_canon_sha256":"afc64ad25732859dbaebbee57f9d1ba9ef14ba2fdbfd3103d05319222eec4f83","abstract_canon_sha256":"7971dcb848c0e90ba7eb329f3c30162fd51075d2b54a3445ba1f087870eb35f4"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-01T01:18:02.832237Z","signature_b64":"6GC6GJPptHqBH1xVrs9f87pX10cHl3xMgKaZ1Wuk2idvFk/hdXjNU79x0CcvS93wypAiHb428HTy/5OV9HeHCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ed397173a284a457c709f4126f275f3528641ddcc269e8bc55d8ddcfa86dac11","last_reissued_at":"2026-07-01T01:18:02.831792Z","signature_status":"signed_v1","first_computed_at":"2026-07-01T01:18:02.831792Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Critical Lin-Lunin-Maldacena geometries","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"hep-th","authors_text":"Lev Senchukov, Prokopii Anempodistov, Vladimir Kazakov","submitted_at":"2026-06-30T09:48:25Z","abstract_excerpt":"We study the critical behavior of the Lin-Lunin-Maldacena (LLM) geometry in the case when a droplet in the LLM base space develops a cusp. This cusp is a generic feature of the density of complex eigenvalues in the dual complex matrix model (CMM) computing the correlation functions of huge 1/2-BPS operators in $\\mathcal{N}=4$ SYM theory. It is also related to the criticality in CMM describing the pure $2D$ quantum gravity behavior. The supergravity dual -- LLM metric in the vicinity of the tip of the cusp -- acquires a universal $ISO(1,3)\\times SO(5)$ symmetric form, with a naked singularity a"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.31424","kind":"arxiv","version":1},"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/2606.31424/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":"2606.31424","created_at":"2026-07-01T01:18:02.831864+00:00"},{"alias_kind":"arxiv_version","alias_value":"2606.31424v1","created_at":"2026-07-01T01:18:02.831864+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.31424","created_at":"2026-07-01T01:18:02.831864+00:00"},{"alias_kind":"pith_short_12","alias_value":"5U4XC45CQSSF","created_at":"2026-07-01T01:18:02.831864+00:00"},{"alias_kind":"pith_short_16","alias_value":"5U4XC45CQSSFPRYJ","created_at":"2026-07-01T01:18:02.831864+00:00"},{"alias_kind":"pith_short_8","alias_value":"5U4XC45C","created_at":"2026-07-01T01:18:02.831864+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/5U4XC45CQSSFPRYJ6QJG6J27GU","json":"https://pith.science/pith/5U4XC45CQSSFPRYJ6QJG6J27GU.json","graph_json":"https://pith.science/api/pith-number/5U4XC45CQSSFPRYJ6QJG6J27GU/graph.json","events_json":"https://pith.science/api/pith-number/5U4XC45CQSSFPRYJ6QJG6J27GU/events.json","paper":"https://pith.science/paper/5U4XC45C"},"agent_actions":{"view_html":"https://pith.science/pith/5U4XC45CQSSFPRYJ6QJG6J27GU","download_json":"https://pith.science/pith/5U4XC45CQSSFPRYJ6QJG6J27GU.json","view_paper":"https://pith.science/paper/5U4XC45C","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2606.31424&json=true","fetch_graph":"https://pith.science/api/pith-number/5U4XC45CQSSFPRYJ6QJG6J27GU/graph.json","fetch_events":"https://pith.science/api/pith-number/5U4XC45CQSSFPRYJ6QJG6J27GU/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/5U4XC45CQSSFPRYJ6QJG6J27GU/action/timestamp_anchor","attest_storage":"https://pith.science/pith/5U4XC45CQSSFPRYJ6QJG6J27GU/action/storage_attestation","attest_author":"https://pith.science/pith/5U4XC45CQSSFPRYJ6QJG6J27GU/action/author_attestation","sign_citation":"https://pith.science/pith/5U4XC45CQSSFPRYJ6QJG6J27GU/action/citation_signature","submit_replication":"https://pith.science/pith/5U4XC45CQSSFPRYJ6QJG6J27GU/action/replication_record"}},"created_at":"2026-07-01T01:18:02.831864+00:00","updated_at":"2026-07-01T01:18:02.831864+00:00"}