{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:6GZ2FPS5DKWUPKQFQ6VSBWC6BC","short_pith_number":"pith:6GZ2FPS5","canonical_record":{"source":{"id":"1210.0521","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2012-10-01T19:53:39Z","cross_cats_sorted":[],"title_canon_sha256":"6e0eab8f4aa0210a4ede7a5a053a56e22b05ac4c17cf921356773fc7b51b0e78","abstract_canon_sha256":"c2b816526f9cec520fc1e9dbba3966c22789a6e662b1f7969beef335399de8ca"},"schema_version":"1.0"},"canonical_sha256":"f1b3a2be5d1aad47aa0587ab20d85e08bc6c219de4277996644213aa2ff93ebf","source":{"kind":"arxiv","id":"1210.0521","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1210.0521","created_at":"2026-05-18T02:57:24Z"},{"alias_kind":"arxiv_version","alias_value":"1210.0521v3","created_at":"2026-05-18T02:57:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1210.0521","created_at":"2026-05-18T02:57:24Z"},{"alias_kind":"pith_short_12","alias_value":"6GZ2FPS5DKWU","created_at":"2026-05-18T12:26:56Z"},{"alias_kind":"pith_short_16","alias_value":"6GZ2FPS5DKWUPKQF","created_at":"2026-05-18T12:26:56Z"},{"alias_kind":"pith_short_8","alias_value":"6GZ2FPS5","created_at":"2026-05-18T12:26:56Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:6GZ2FPS5DKWUPKQFQ6VSBWC6BC","target":"record","payload":{"canonical_record":{"source":{"id":"1210.0521","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2012-10-01T19:53:39Z","cross_cats_sorted":[],"title_canon_sha256":"6e0eab8f4aa0210a4ede7a5a053a56e22b05ac4c17cf921356773fc7b51b0e78","abstract_canon_sha256":"c2b816526f9cec520fc1e9dbba3966c22789a6e662b1f7969beef335399de8ca"},"schema_version":"1.0"},"canonical_sha256":"f1b3a2be5d1aad47aa0587ab20d85e08bc6c219de4277996644213aa2ff93ebf","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:57:24.232627Z","signature_b64":"Ik+zCTtkySPiUCLmLFBd3S9Fpo1jqXNwBhoyynwDiqm+rwGHiWGAzAV4+3q+TFAXNwTQhJBNunYmpcF/vwsFBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f1b3a2be5d1aad47aa0587ab20d85e08bc6c219de4277996644213aa2ff93ebf","last_reissued_at":"2026-05-18T02:57:24.232118Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:57:24.232118Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1210.0521","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:57:24Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"sHqPpZJjJJM4jEHFoKOfNIvfNnJR+psHEvkkpwet4zAfNCWpI8YWyy8OpbzjtY89biPm65xv+Dh+z9FJ5AJaBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-22T09:54:45.675473Z"},"content_sha256":"df15140d52251339408d8368a671a8f8be060f3748a5af7fd323bc6ece361fde","schema_version":"1.0","event_id":"sha256:df15140d52251339408d8368a671a8f8be060f3748a5af7fd323bc6ece361fde"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:6GZ2FPS5DKWUPKQFQ6VSBWC6BC","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Equilibrium states of weakly hyperbolic one-dimensional maps for Holder potentials","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Huaibin Li, Juan Rivera-Letelier","submitted_at":"2012-10-01T19:53:39Z","abstract_excerpt":"There is a wealth of results in the literature on the thermodynamic formalism for potentials that are, in some sense, \"hyperbolic\". We show that for a sufficiently regular one-dimensional map satisfying a weak hyperbolicity assumption, every Holder continuous potential is hyperbolic. A sample consequence is the absence of phase transitions: The pressure function is real analytic on the space of Holder continuous functions. Another consequence is that every Holder continuous potential has a unique equilibrium state, and that this measure has exponential decay of correlations."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1210.0521","kind":"arxiv","version":3},"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":"2026-05-18T02:57:24Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"j+hjs0pXGVdazR7ShuWvqvPfkqOS7cCMFU7+hURUNQk+Z+Z2vjqyuH7nIZNVCmIQtR4MYPe43vZq00YGrqgtDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-22T09:54:45.675841Z"},"content_sha256":"ef18de3ab6de43899731c8b7a3c0f0e3bfad2c83171bf824d8b26e91bc2e65d0","schema_version":"1.0","event_id":"sha256:ef18de3ab6de43899731c8b7a3c0f0e3bfad2c83171bf824d8b26e91bc2e65d0"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/6GZ2FPS5DKWUPKQFQ6VSBWC6BC/bundle.json","state_url":"https://pith.science/pith/6GZ2FPS5DKWUPKQFQ6VSBWC6BC/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/6GZ2FPS5DKWUPKQFQ6VSBWC6BC/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":"2026-06-22T09:54:45Z","links":{"resolver":"https://pith.science/pith/6GZ2FPS5DKWUPKQFQ6VSBWC6BC","bundle":"https://pith.science/pith/6GZ2FPS5DKWUPKQFQ6VSBWC6BC/bundle.json","state":"https://pith.science/pith/6GZ2FPS5DKWUPKQFQ6VSBWC6BC/state.json","well_known_bundle":"https://pith.science/.well-known/pith/6GZ2FPS5DKWUPKQFQ6VSBWC6BC/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:6GZ2FPS5DKWUPKQFQ6VSBWC6BC","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":"c2b816526f9cec520fc1e9dbba3966c22789a6e662b1f7969beef335399de8ca","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2012-10-01T19:53:39Z","title_canon_sha256":"6e0eab8f4aa0210a4ede7a5a053a56e22b05ac4c17cf921356773fc7b51b0e78"},"schema_version":"1.0","source":{"id":"1210.0521","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1210.0521","created_at":"2026-05-18T02:57:24Z"},{"alias_kind":"arxiv_version","alias_value":"1210.0521v3","created_at":"2026-05-18T02:57:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1210.0521","created_at":"2026-05-18T02:57:24Z"},{"alias_kind":"pith_short_12","alias_value":"6GZ2FPS5DKWU","created_at":"2026-05-18T12:26:56Z"},{"alias_kind":"pith_short_16","alias_value":"6GZ2FPS5DKWUPKQF","created_at":"2026-05-18T12:26:56Z"},{"alias_kind":"pith_short_8","alias_value":"6GZ2FPS5","created_at":"2026-05-18T12:26:56Z"}],"graph_snapshots":[{"event_id":"sha256:ef18de3ab6de43899731c8b7a3c0f0e3bfad2c83171bf824d8b26e91bc2e65d0","target":"graph","created_at":"2026-05-18T02:57:24Z","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":"There is a wealth of results in the literature on the thermodynamic formalism for potentials that are, in some sense, \"hyperbolic\". We show that for a sufficiently regular one-dimensional map satisfying a weak hyperbolicity assumption, every Holder continuous potential is hyperbolic. A sample consequence is the absence of phase transitions: The pressure function is real analytic on the space of Holder continuous functions. Another consequence is that every Holder continuous potential has a unique equilibrium state, and that this measure has exponential decay of correlations.","authors_text":"Huaibin Li, Juan Rivera-Letelier","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2012-10-01T19:53:39Z","title":"Equilibrium states of weakly hyperbolic one-dimensional maps for Holder potentials"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1210.0521","kind":"arxiv","version":3},"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:df15140d52251339408d8368a671a8f8be060f3748a5af7fd323bc6ece361fde","target":"record","created_at":"2026-05-18T02:57:24Z","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":"c2b816526f9cec520fc1e9dbba3966c22789a6e662b1f7969beef335399de8ca","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2012-10-01T19:53:39Z","title_canon_sha256":"6e0eab8f4aa0210a4ede7a5a053a56e22b05ac4c17cf921356773fc7b51b0e78"},"schema_version":"1.0","source":{"id":"1210.0521","kind":"arxiv","version":3}},"canonical_sha256":"f1b3a2be5d1aad47aa0587ab20d85e08bc6c219de4277996644213aa2ff93ebf","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f1b3a2be5d1aad47aa0587ab20d85e08bc6c219de4277996644213aa2ff93ebf","first_computed_at":"2026-05-18T02:57:24.232118Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:57:24.232118Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Ik+zCTtkySPiUCLmLFBd3S9Fpo1jqXNwBhoyynwDiqm+rwGHiWGAzAV4+3q+TFAXNwTQhJBNunYmpcF/vwsFBA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:57:24.232627Z","signed_message":"canonical_sha256_bytes"},"source_id":"1210.0521","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:df15140d52251339408d8368a671a8f8be060f3748a5af7fd323bc6ece361fde","sha256:ef18de3ab6de43899731c8b7a3c0f0e3bfad2c83171bf824d8b26e91bc2e65d0"],"state_sha256":"5208b3489a54edadd38e9aa46b9822c3e57cc46a23aae6957e33b030bf3124e9"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"adC/w/F7bS/JC5Dbtgsi0R9y0iujZ4mktMvOf1DhMwxniyTp/ZSKP5df+j2eB9eq5s+fwxjCtnGHuEeUydF6AA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-22T09:54:45.677903Z","bundle_sha256":"1ae7dd7b64a19508e9cbabe3dfc5bc28c78fcde6015efd6f60a8545b0e3a8d51"}}