{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:GQK6J5SHTZD6KNJII2FEGVQGYD","short_pith_number":"pith:GQK6J5SH","canonical_record":{"source":{"id":"1606.04303","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2016-06-14T10:55:35Z","cross_cats_sorted":["math.CA","math.MP"],"title_canon_sha256":"c80845cc0d002091724b9bf5ac9fd735ce8531a75877c8986203b6d6e0a910e7","abstract_canon_sha256":"01244ccc2086f5a1b86888eabeef6f7afe40c961c3163d0411ea895af5340eab"},"schema_version":"1.0"},"canonical_sha256":"3415e4f6479e47e53528468a435606c0f3ea7ccd74e16f1869ebe746156f8a55","source":{"kind":"arxiv","id":"1606.04303","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1606.04303","created_at":"2026-05-18T00:42:44Z"},{"alias_kind":"arxiv_version","alias_value":"1606.04303v1","created_at":"2026-05-18T00:42:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1606.04303","created_at":"2026-05-18T00:42:44Z"},{"alias_kind":"pith_short_12","alias_value":"GQK6J5SHTZD6","created_at":"2026-05-18T12:30:19Z"},{"alias_kind":"pith_short_16","alias_value":"GQK6J5SHTZD6KNJI","created_at":"2026-05-18T12:30:19Z"},{"alias_kind":"pith_short_8","alias_value":"GQK6J5SH","created_at":"2026-05-18T12:30:19Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:GQK6J5SHTZD6KNJII2FEGVQGYD","target":"record","payload":{"canonical_record":{"source":{"id":"1606.04303","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2016-06-14T10:55:35Z","cross_cats_sorted":["math.CA","math.MP"],"title_canon_sha256":"c80845cc0d002091724b9bf5ac9fd735ce8531a75877c8986203b6d6e0a910e7","abstract_canon_sha256":"01244ccc2086f5a1b86888eabeef6f7afe40c961c3163d0411ea895af5340eab"},"schema_version":"1.0"},"canonical_sha256":"3415e4f6479e47e53528468a435606c0f3ea7ccd74e16f1869ebe746156f8a55","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:42:44.360940Z","signature_b64":"a4t/c4eiP/dpBsAnTZC2nZ3D+SQ3Vp4vJ0mj3CrFvoDCKz0uW2m9BB8NRGv3bLDqOk/cAIYU2ZUFNsMv1AovAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3415e4f6479e47e53528468a435606c0f3ea7ccd74e16f1869ebe746156f8a55","last_reissued_at":"2026-05-18T00:42:44.360259Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:42:44.360259Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1606.04303","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:42:44Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"WAuMekGkCVOBvqc4aVAP0tThNPHMpk0VinngSr5Bv+z6zn3GKfk3FfouXSKsMZiNO+U+tPGFhWf7IJ5q6QFLAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T07:53:57.897486Z"},"content_sha256":"a08838fac3a6999d55adac7732a371dfb20e08d87bd25297cb5ddbb54c67f69e","schema_version":"1.0","event_id":"sha256:a08838fac3a6999d55adac7732a371dfb20e08d87bd25297cb5ddbb54c67f69e"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:GQK6J5SHTZD6KNJII2FEGVQGYD","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Topological Expansion in the Complex Cubic Log-Gas Model. One-Cut Case","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CA","math.MP"],"primary_cat":"math-ph","authors_text":"Alfredo Dea\\~no, Maxim Yattselev, Pavel M. Bleher","submitted_at":"2016-06-14T10:55:35Z","abstract_excerpt":"We prove the topological expansion for the cubic log-gas partition function \\[ Z_N(t)= \\int_\\Gamma\\cdots\\int_\\Gamma\\prod_{1\\leq j<k\\leq N}(z_j-z_k)^2 \\prod_{k=1}^Ne^{-N\\left(-\\frac{z^3}{3}+tz\\right)}\\mathrm dz_1\\cdots \\mathrm dz_N, \\] where $t$ is a complex parameter and $\\Gamma$ is an unbounded contour on the complex plane extending from $e^{\\pi \\mathrm i}\\infty$ to $e^{\\pi \\mathrm i/3}\\infty$. The complex cubic log-gas model exhibits two phase regions on the complex $t$-plane, with one cut and two cuts, separated by analytic critical arcs of the two types of phase transition: split of a cut "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1606.04303","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":""},"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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:42:44Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ICbZi42Zf0uutlOD3UIWMA5E9hK8hWd+VhshcqKocB5XyF+sF1XUV7Us5UpkJpC+r/YizgW+AnhZnT4wsWNBAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T07:53:57.898484Z"},"content_sha256":"8c9b64d066b516d981945974c77d79c7de745127b878713868e60a46d3892acb","schema_version":"1.0","event_id":"sha256:8c9b64d066b516d981945974c77d79c7de745127b878713868e60a46d3892acb"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/GQK6J5SHTZD6KNJII2FEGVQGYD/bundle.json","state_url":"https://pith.science/pith/GQK6J5SHTZD6KNJII2FEGVQGYD/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/GQK6J5SHTZD6KNJII2FEGVQGYD/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-05-31T07:53:57Z","links":{"resolver":"https://pith.science/pith/GQK6J5SHTZD6KNJII2FEGVQGYD","bundle":"https://pith.science/pith/GQK6J5SHTZD6KNJII2FEGVQGYD/bundle.json","state":"https://pith.science/pith/GQK6J5SHTZD6KNJII2FEGVQGYD/state.json","well_known_bundle":"https://pith.science/.well-known/pith/GQK6J5SHTZD6KNJII2FEGVQGYD/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:GQK6J5SHTZD6KNJII2FEGVQGYD","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":"01244ccc2086f5a1b86888eabeef6f7afe40c961c3163d0411ea895af5340eab","cross_cats_sorted":["math.CA","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2016-06-14T10:55:35Z","title_canon_sha256":"c80845cc0d002091724b9bf5ac9fd735ce8531a75877c8986203b6d6e0a910e7"},"schema_version":"1.0","source":{"id":"1606.04303","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1606.04303","created_at":"2026-05-18T00:42:44Z"},{"alias_kind":"arxiv_version","alias_value":"1606.04303v1","created_at":"2026-05-18T00:42:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1606.04303","created_at":"2026-05-18T00:42:44Z"},{"alias_kind":"pith_short_12","alias_value":"GQK6J5SHTZD6","created_at":"2026-05-18T12:30:19Z"},{"alias_kind":"pith_short_16","alias_value":"GQK6J5SHTZD6KNJI","created_at":"2026-05-18T12:30:19Z"},{"alias_kind":"pith_short_8","alias_value":"GQK6J5SH","created_at":"2026-05-18T12:30:19Z"}],"graph_snapshots":[{"event_id":"sha256:8c9b64d066b516d981945974c77d79c7de745127b878713868e60a46d3892acb","target":"graph","created_at":"2026-05-18T00:42:44Z","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":"We prove the topological expansion for the cubic log-gas partition function \\[ Z_N(t)= \\int_\\Gamma\\cdots\\int_\\Gamma\\prod_{1\\leq j<k\\leq N}(z_j-z_k)^2 \\prod_{k=1}^Ne^{-N\\left(-\\frac{z^3}{3}+tz\\right)}\\mathrm dz_1\\cdots \\mathrm dz_N, \\] where $t$ is a complex parameter and $\\Gamma$ is an unbounded contour on the complex plane extending from $e^{\\pi \\mathrm i}\\infty$ to $e^{\\pi \\mathrm i/3}\\infty$. The complex cubic log-gas model exhibits two phase regions on the complex $t$-plane, with one cut and two cuts, separated by analytic critical arcs of the two types of phase transition: split of a cut ","authors_text":"Alfredo Dea\\~no, Maxim Yattselev, Pavel M. Bleher","cross_cats":["math.CA","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2016-06-14T10:55:35Z","title":"Topological Expansion in the Complex Cubic Log-Gas Model. One-Cut Case"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1606.04303","kind":"arxiv","version":1},"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:a08838fac3a6999d55adac7732a371dfb20e08d87bd25297cb5ddbb54c67f69e","target":"record","created_at":"2026-05-18T00:42:44Z","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":"01244ccc2086f5a1b86888eabeef6f7afe40c961c3163d0411ea895af5340eab","cross_cats_sorted":["math.CA","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2016-06-14T10:55:35Z","title_canon_sha256":"c80845cc0d002091724b9bf5ac9fd735ce8531a75877c8986203b6d6e0a910e7"},"schema_version":"1.0","source":{"id":"1606.04303","kind":"arxiv","version":1}},"canonical_sha256":"3415e4f6479e47e53528468a435606c0f3ea7ccd74e16f1869ebe746156f8a55","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3415e4f6479e47e53528468a435606c0f3ea7ccd74e16f1869ebe746156f8a55","first_computed_at":"2026-05-18T00:42:44.360259Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:42:44.360259Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"a4t/c4eiP/dpBsAnTZC2nZ3D+SQ3Vp4vJ0mj3CrFvoDCKz0uW2m9BB8NRGv3bLDqOk/cAIYU2ZUFNsMv1AovAg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:42:44.360940Z","signed_message":"canonical_sha256_bytes"},"source_id":"1606.04303","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a08838fac3a6999d55adac7732a371dfb20e08d87bd25297cb5ddbb54c67f69e","sha256:8c9b64d066b516d981945974c77d79c7de745127b878713868e60a46d3892acb"],"state_sha256":"62305bf0b42d0c3e03ad59618d831be0ace644673bef4bebceb51b91aae32d02"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"NRNtc5xnJNA0hBLV1d8MVJTtmOrZZZxJbVU3qzzOzBPjK+5gPmEUWsz9TFKqg//5WSlq916mnh8soi+JfN3GDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-31T07:53:57.904508Z","bundle_sha256":"5be40bab592632ac5e60e3c9bada8d9e0fc33a9f72cbd5ebc23fec3252130417"}}