{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:ZQ6S3WX44DY3GQGRFIKE7FETMA","short_pith_number":"pith:ZQ6S3WX4","canonical_record":{"source":{"id":"2608.03366","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"hep-th","submitted_at":"2026-08-04T09:17:08Z","cross_cats_sorted":[],"title_canon_sha256":"a3987c243812016ec4b5e933b2bf511944b63076087a6e87cf2666a967ff6533","abstract_canon_sha256":"d5e3bcd7c9b9cb59c9001b293972582e44d0039b5236f9e4a39510eb4000b674"},"schema_version":"1.0"},"canonical_sha256":"cc3d2ddafce0f1b340d12a144f94936002662ffb671de663d6d07a2fafa2778b","source":{"kind":"arxiv","id":"2608.03366","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2608.03366","created_at":"2026-08-05T01:35:37Z"},{"alias_kind":"arxiv_version","alias_value":"2608.03366v1","created_at":"2026-08-05T01:35:37Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2608.03366","created_at":"2026-08-05T01:35:37Z"},{"alias_kind":"pith_short_12","alias_value":"ZQ6S3WX44DY3","created_at":"2026-08-05T01:35:37Z"},{"alias_kind":"pith_short_16","alias_value":"ZQ6S3WX44DY3GQGR","created_at":"2026-08-05T01:35:37Z"},{"alias_kind":"pith_short_8","alias_value":"ZQ6S3WX4","created_at":"2026-08-05T01:35:37Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:ZQ6S3WX44DY3GQGRFIKE7FETMA","target":"record","payload":{"canonical_record":{"source":{"id":"2608.03366","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"hep-th","submitted_at":"2026-08-04T09:17:08Z","cross_cats_sorted":[],"title_canon_sha256":"a3987c243812016ec4b5e933b2bf511944b63076087a6e87cf2666a967ff6533","abstract_canon_sha256":"d5e3bcd7c9b9cb59c9001b293972582e44d0039b5236f9e4a39510eb4000b674"},"schema_version":"1.0"},"canonical_sha256":"cc3d2ddafce0f1b340d12a144f94936002662ffb671de663d6d07a2fafa2778b","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-08-05T01:35:37.525410Z","signature_b64":"unbCamndFopxd9kY6eUyo6jRiqtw4u/TwsyoBewwP0wcPI+tLCWLEpRso0QNUFxiUcD2KX40u0GD02c56GlmDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"cc3d2ddafce0f1b340d12a144f94936002662ffb671de663d6d07a2fafa2778b","last_reissued_at":"2026-08-05T01:35:37.523908Z","signature_status":"signed_v1","first_computed_at":"2026-08-05T01:35:37.523908Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2608.03366","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":"2026-08-05T01:35:37Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"r1rxn4bNBuyB3x5l6BokEs+jHKRWK6V2DfS1uRZ63x+tn5R8B5kqUQXlVZCpSFZs8DeZ1XTZ7n264pG5HBcUBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-18T04:42:35.506827Z"},"content_sha256":"172e6adcf119641050412ad607b6a031a4f0d2b69eb55884740d61b60619157b","schema_version":"1.0","event_id":"sha256:172e6adcf119641050412ad607b6a031a4f0d2b69eb55884740d61b60619157b"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:ZQ6S3WX44DY3GQGRFIKE7FETMA","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Notes on phase structure and non-vanishing $\\beta$ functions of one-unitary matrix model","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"hep-th","authors_text":"Hiroshi Itoyama, Reiji Yoshioka","submitted_at":"2026-08-04T09:17:08Z","abstract_excerpt":"Unitary matrix models, among other things, play an important role in representing the irregular conformal block and hence LEEA of some asymptotically free susy gauge theories. Here, we develop a method of how to determine the qualitative structure of phase diagram by the deformation of classical potential, and illustrate this by the examples that contain term up to $\\cos n\\alpha$, $n \\leq 3$. We point out that a set of $\\beta$ functions on critical ``lines\" is nowhere a vanishing vector. This generalizes the $n =1$ GWW case and tells us the third order (rather than second order) phase transiti"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2608.03366","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/2608.03366/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":"2026-08-05T01:35:37Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"YQH07JUInd0YxKqLlRfoHAtC/I51wT17D+s3QNOUWxIUXWX02LF5WXg231fVhKoCtnTpPPZIU+dYHAlYJ5TkDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-18T04:42:35.507354Z"},"content_sha256":"41a3aba5549cd95f72cc5ff8087e74b125f614ff6cb0b8974aab5c7ba8989c5d","schema_version":"1.0","event_id":"sha256:41a3aba5549cd95f72cc5ff8087e74b125f614ff6cb0b8974aab5c7ba8989c5d"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/ZQ6S3WX44DY3GQGRFIKE7FETMA/bundle.json","state_url":"https://pith.science/pith/ZQ6S3WX44DY3GQGRFIKE7FETMA/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/ZQ6S3WX44DY3GQGRFIKE7FETMA/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":"2026-08-18T04:42:35Z","links":{"resolver":"https://pith.science/pith/ZQ6S3WX44DY3GQGRFIKE7FETMA","bundle":"https://pith.science/pith/ZQ6S3WX44DY3GQGRFIKE7FETMA/bundle.json","state":"https://pith.science/pith/ZQ6S3WX44DY3GQGRFIKE7FETMA/state.json","well_known_bundle":"https://pith.science/.well-known/pith/ZQ6S3WX44DY3GQGRFIKE7FETMA/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:ZQ6S3WX44DY3GQGRFIKE7FETMA","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":"d5e3bcd7c9b9cb59c9001b293972582e44d0039b5236f9e4a39510eb4000b674","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"hep-th","submitted_at":"2026-08-04T09:17:08Z","title_canon_sha256":"a3987c243812016ec4b5e933b2bf511944b63076087a6e87cf2666a967ff6533"},"schema_version":"1.0","source":{"id":"2608.03366","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2608.03366","created_at":"2026-08-05T01:35:37Z"},{"alias_kind":"arxiv_version","alias_value":"2608.03366v1","created_at":"2026-08-05T01:35:37Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2608.03366","created_at":"2026-08-05T01:35:37Z"},{"alias_kind":"pith_short_12","alias_value":"ZQ6S3WX44DY3","created_at":"2026-08-05T01:35:37Z"},{"alias_kind":"pith_short_16","alias_value":"ZQ6S3WX44DY3GQGR","created_at":"2026-08-05T01:35:37Z"},{"alias_kind":"pith_short_8","alias_value":"ZQ6S3WX4","created_at":"2026-08-05T01:35:37Z"}],"graph_snapshots":[{"event_id":"sha256:41a3aba5549cd95f72cc5ff8087e74b125f614ff6cb0b8974aab5c7ba8989c5d","target":"graph","created_at":"2026-08-05T01:35:37Z","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/2608.03366/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Unitary matrix models, among other things, play an important role in representing the irregular conformal block and hence LEEA of some asymptotically free susy gauge theories. Here, we develop a method of how to determine the qualitative structure of phase diagram by the deformation of classical potential, and illustrate this by the examples that contain term up to $\\cos n\\alpha$, $n \\leq 3$. We point out that a set of $\\beta$ functions on critical ``lines\" is nowhere a vanishing vector. This generalizes the $n =1$ GWW case and tells us the third order (rather than second order) phase transiti","authors_text":"Hiroshi Itoyama, Reiji Yoshioka","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"hep-th","submitted_at":"2026-08-04T09:17:08Z","title":"Notes on phase structure and non-vanishing $\\beta$ functions of one-unitary matrix model"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2608.03366","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":"sha256:172e6adcf119641050412ad607b6a031a4f0d2b69eb55884740d61b60619157b","target":"record","created_at":"2026-08-05T01:35:37Z","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":"d5e3bcd7c9b9cb59c9001b293972582e44d0039b5236f9e4a39510eb4000b674","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"hep-th","submitted_at":"2026-08-04T09:17:08Z","title_canon_sha256":"a3987c243812016ec4b5e933b2bf511944b63076087a6e87cf2666a967ff6533"},"schema_version":"1.0","source":{"id":"2608.03366","kind":"arxiv","version":1}},"canonical_sha256":"cc3d2ddafce0f1b340d12a144f94936002662ffb671de663d6d07a2fafa2778b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"cc3d2ddafce0f1b340d12a144f94936002662ffb671de663d6d07a2fafa2778b","first_computed_at":"2026-08-05T01:35:37.523908Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-08-05T01:35:37.523908Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"unbCamndFopxd9kY6eUyo6jRiqtw4u/TwsyoBewwP0wcPI+tLCWLEpRso0QNUFxiUcD2KX40u0GD02c56GlmDA==","signature_status":"signed_v1","signed_at":"2026-08-05T01:35:37.525410Z","signed_message":"canonical_sha256_bytes"},"source_id":"2608.03366","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:172e6adcf119641050412ad607b6a031a4f0d2b69eb55884740d61b60619157b","sha256:41a3aba5549cd95f72cc5ff8087e74b125f614ff6cb0b8974aab5c7ba8989c5d"],"state_sha256":"86274a6ca1bf4d3750401e180a5f4c91d964288aa18537f74b85198060d98282"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"CE3oSDYhG4Zx3WaSuH3SkPc6cqQGfppNQ6MnVv4bVDV5T82/Le30UgPCeoUhPduO4KE7UzNe7ueL/klcxF87Cw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-18T04:42:35.511435Z","bundle_sha256":"ceddb0c9b31666693163d5e99508e8def1fb5033eb9647f6c120a51a94a8bcfe"}}