{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:YOEWPOA5AFPCND2KA3C2WFMM4Q","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":"8bbe4a939d877d7160c21d0a726b4dff2d1e7fda107e3893507b521470ba567d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2019-09-25T15:16:23Z","title_canon_sha256":"2069f69baf95614f0c606768df8f4d10e4cc42562d766664b40f46731bcab9ec"},"schema_version":"1.0","source":{"id":"1909.11548","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1909.11548","created_at":"2026-07-05T01:34:49Z"},{"alias_kind":"arxiv_version","alias_value":"1909.11548v2","created_at":"2026-07-05T01:34:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1909.11548","created_at":"2026-07-05T01:34:49Z"},{"alias_kind":"pith_short_12","alias_value":"YOEWPOA5AFPC","created_at":"2026-07-05T01:34:49Z"},{"alias_kind":"pith_short_16","alias_value":"YOEWPOA5AFPCND2K","created_at":"2026-07-05T01:34:49Z"},{"alias_kind":"pith_short_8","alias_value":"YOEWPOA5","created_at":"2026-07-05T01:34:49Z"}],"graph_snapshots":[{"event_id":"sha256:d8ac0d83d885385379b4a3c1451acd78c8294646c8bc2db69f8bee108605a33e","target":"graph","created_at":"2026-07-05T01:34:49Z","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/1909.11548/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We study singular value potentials of H\\\"older continuous $GL_2(\\mathbb{R})$-cocycles over hyperbolic systems whose canonical holonomies converge and are H\\\"older continuous. Such cocycles include locally constant $GL_2(\\mathbb{R})$-cocycles as well as fiber-bunched $GL_2(\\mathbb{R})$-cocycles. We show that singular value potentials of irreducible such cocycles have unique equilibrium states. Among the reducible cocycles, we provide a characterization for cocycles whose singular value potentials have more than one equilibrium states.","authors_text":"Clark Butler, Kiho Park","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2019-09-25T15:16:23Z","title":"Thermodynamic formalism of $GL_2(\\mathbb{R})$-cocycles with canonical holonomies"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1909.11548","kind":"arxiv","version":2},"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":"sha256:5f83e66c255b93c86b2c658fecd8a57c931d675eb4b68bd9aed5be0fb8a3b6ee","target":"record","created_at":"2026-07-05T01:34:49Z","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":"8bbe4a939d877d7160c21d0a726b4dff2d1e7fda107e3893507b521470ba567d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2019-09-25T15:16:23Z","title_canon_sha256":"2069f69baf95614f0c606768df8f4d10e4cc42562d766664b40f46731bcab9ec"},"schema_version":"1.0","source":{"id":"1909.11548","kind":"arxiv","version":2}},"canonical_sha256":"c38967b81d015e268f4a06c5ab158ce42474d5f84ebb7f3a4aadf45926789dc9","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c38967b81d015e268f4a06c5ab158ce42474d5f84ebb7f3a4aadf45926789dc9","first_computed_at":"2026-07-05T01:34:49.743060Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T01:34:49.743060Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Yhx6uEDu5X1hUu1WCKKDOT7wf7oVWsFdjXYbgX5GUqQ8rsfjozyvSrHROmOYeV/UtFgiVO9tzsOqux7wxKTiAQ==","signature_status":"signed_v1","signed_at":"2026-07-05T01:34:49.743483Z","signed_message":"canonical_sha256_bytes"},"source_id":"1909.11548","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5f83e66c255b93c86b2c658fecd8a57c931d675eb4b68bd9aed5be0fb8a3b6ee","sha256:d8ac0d83d885385379b4a3c1451acd78c8294646c8bc2db69f8bee108605a33e"],"state_sha256":"63895d168dcce62b2d3befc071a4a7a9a4d6246f5a06017dd8d70aaeeef86b3c"}