{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2025:7AODY5SAOTEXERSRWTDWIDXT4Q","short_pith_number":"pith:7AODY5SA","canonical_record":{"source":{"id":"2507.05406","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2025-07-07T18:45:57Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"678d744d7b7e0c1364925bfe0c851c61594760d981b9044ade64a58d9a5535c8","abstract_canon_sha256":"739ddb871a83f597f599448bbaae600d26104c996a620e33cd19a5bc076f5934"},"schema_version":"1.0"},"canonical_sha256":"f81c3c764074c9724651b4c7640ef3e43c79cead1d5be57f1d1e3c83e7c7b571","source":{"kind":"arxiv","id":"2507.05406","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2507.05406","created_at":"2026-07-05T12:03:49Z"},{"alias_kind":"arxiv_version","alias_value":"2507.05406v1","created_at":"2026-07-05T12:03:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2507.05406","created_at":"2026-07-05T12:03:49Z"},{"alias_kind":"pith_short_12","alias_value":"7AODY5SAOTEX","created_at":"2026-07-05T12:03:49Z"},{"alias_kind":"pith_short_16","alias_value":"7AODY5SAOTEXERSR","created_at":"2026-07-05T12:03:49Z"},{"alias_kind":"pith_short_8","alias_value":"7AODY5SA","created_at":"2026-07-05T12:03:49Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2025:7AODY5SAOTEXERSRWTDWIDXT4Q","target":"record","payload":{"canonical_record":{"source":{"id":"2507.05406","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2025-07-07T18:45:57Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"678d744d7b7e0c1364925bfe0c851c61594760d981b9044ade64a58d9a5535c8","abstract_canon_sha256":"739ddb871a83f597f599448bbaae600d26104c996a620e33cd19a5bc076f5934"},"schema_version":"1.0"},"canonical_sha256":"f81c3c764074c9724651b4c7640ef3e43c79cead1d5be57f1d1e3c83e7c7b571","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T12:03:49.801019Z","signature_b64":"U73qNHhdglM0om54TZaLD8cLJnb4nuApF01QA6MowAevGWuwsWi+F+1TLRMOMoqAzUb+jHRjEiYE41YPIwGQAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f81c3c764074c9724651b4c7640ef3e43c79cead1d5be57f1d1e3c83e7c7b571","last_reissued_at":"2026-07-05T12:03:49.800489Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T12:03:49.800489Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2507.05406","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":"2026-07-05T12:03:49Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"0lPWMWVvj4S04z3WUPyK67VZKkPYxVUmEsEA0SgeGQbOs6aFhTzq9UNnana6b/M4OYQIXL1xTlRcnVXHELkgDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-07T05:40:27.466214Z"},"content_sha256":"a25c591882f545a8ed5f03c12483e3e58bf0e3a555b29518239a430fdd7bae65","schema_version":"1.0","event_id":"sha256:a25c591882f545a8ed5f03c12483e3e58bf0e3a555b29518239a430fdd7bae65"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2025:7AODY5SAOTEXERSRWTDWIDXT4Q","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Phases in WLZZ Matrix Models","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"hep-th","authors_text":"A. Mironov, A. Oreshina, A. Popolitov","submitted_at":"2025-07-07T18:45:57Z","abstract_excerpt":"We discuss the space of solutions to the Ward identities associated with the WLZZ models. We mostly concentrate on the case of these models described by a two-matrix model with the cubic potential in one of the matrices. We study how this space of solutions can be described by the freedom in choosing integration contours in the matrix integral."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2507.05406","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/2507.05406/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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T12:03:49Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"goAI6z4AydhrUkrNa+a9ERRxQT6sJ8TTtRVIF7+lan3KuXEvC+KNvsAMvuXtG701J4EAqF7CqfKvMNpBnpgtCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-07T05:40:27.466726Z"},"content_sha256":"1e4425c8b5ea2900cd6bec15e962061d7cae4c0c19222f8e26810de58131641d","schema_version":"1.0","event_id":"sha256:1e4425c8b5ea2900cd6bec15e962061d7cae4c0c19222f8e26810de58131641d"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/7AODY5SAOTEXERSRWTDWIDXT4Q/bundle.json","state_url":"https://pith.science/pith/7AODY5SAOTEXERSRWTDWIDXT4Q/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/7AODY5SAOTEXERSRWTDWIDXT4Q/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":"2026-08-07T05:40:27Z","links":{"resolver":"https://pith.science/pith/7AODY5SAOTEXERSRWTDWIDXT4Q","bundle":"https://pith.science/pith/7AODY5SAOTEXERSRWTDWIDXT4Q/bundle.json","state":"https://pith.science/pith/7AODY5SAOTEXERSRWTDWIDXT4Q/state.json","well_known_bundle":"https://pith.science/.well-known/pith/7AODY5SAOTEXERSRWTDWIDXT4Q/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:7AODY5SAOTEXERSRWTDWIDXT4Q","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":"739ddb871a83f597f599448bbaae600d26104c996a620e33cd19a5bc076f5934","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2025-07-07T18:45:57Z","title_canon_sha256":"678d744d7b7e0c1364925bfe0c851c61594760d981b9044ade64a58d9a5535c8"},"schema_version":"1.0","source":{"id":"2507.05406","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2507.05406","created_at":"2026-07-05T12:03:49Z"},{"alias_kind":"arxiv_version","alias_value":"2507.05406v1","created_at":"2026-07-05T12:03:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2507.05406","created_at":"2026-07-05T12:03:49Z"},{"alias_kind":"pith_short_12","alias_value":"7AODY5SAOTEX","created_at":"2026-07-05T12:03:49Z"},{"alias_kind":"pith_short_16","alias_value":"7AODY5SAOTEXERSR","created_at":"2026-07-05T12:03:49Z"},{"alias_kind":"pith_short_8","alias_value":"7AODY5SA","created_at":"2026-07-05T12:03:49Z"}],"graph_snapshots":[{"event_id":"sha256:1e4425c8b5ea2900cd6bec15e962061d7cae4c0c19222f8e26810de58131641d","target":"graph","created_at":"2026-07-05T12:03:49Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2507.05406/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We discuss the space of solutions to the Ward identities associated with the WLZZ models. We mostly concentrate on the case of these models described by a two-matrix model with the cubic potential in one of the matrices. We study how this space of solutions can be described by the freedom in choosing integration contours in the matrix integral.","authors_text":"A. Mironov, A. Oreshina, A. Popolitov","cross_cats":["math-ph","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2025-07-07T18:45:57Z","title":"Phases in WLZZ Matrix Models"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2507.05406","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:a25c591882f545a8ed5f03c12483e3e58bf0e3a555b29518239a430fdd7bae65","target":"record","created_at":"2026-07-05T12:03:49Z","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":"739ddb871a83f597f599448bbaae600d26104c996a620e33cd19a5bc076f5934","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2025-07-07T18:45:57Z","title_canon_sha256":"678d744d7b7e0c1364925bfe0c851c61594760d981b9044ade64a58d9a5535c8"},"schema_version":"1.0","source":{"id":"2507.05406","kind":"arxiv","version":1}},"canonical_sha256":"f81c3c764074c9724651b4c7640ef3e43c79cead1d5be57f1d1e3c83e7c7b571","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f81c3c764074c9724651b4c7640ef3e43c79cead1d5be57f1d1e3c83e7c7b571","first_computed_at":"2026-07-05T12:03:49.800489Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T12:03:49.800489Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"U73qNHhdglM0om54TZaLD8cLJnb4nuApF01QA6MowAevGWuwsWi+F+1TLRMOMoqAzUb+jHRjEiYE41YPIwGQAg==","signature_status":"signed_v1","signed_at":"2026-07-05T12:03:49.801019Z","signed_message":"canonical_sha256_bytes"},"source_id":"2507.05406","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a25c591882f545a8ed5f03c12483e3e58bf0e3a555b29518239a430fdd7bae65","sha256:1e4425c8b5ea2900cd6bec15e962061d7cae4c0c19222f8e26810de58131641d"],"state_sha256":"e0bb66c87617dc08a60e68bbe2b757e3d7dd0038b8fed3a1f77b28b18e37aac2"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"oDKAMd/IpbKNQbKLo+PX6V+NTKHJVlGs32UIUUDVqQlMge3yI7krakcq7Z5hApCNOMc4+zYgVvH0E+U2RzcgDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-07T05:40:27.471838Z","bundle_sha256":"0278e87198cc7b54cf45dbd9de56d95936847c6fc37de2658265bb933bad31a9"}}