{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:UAT7OGM7NU2CV26FTRQ6UMK6TM","short_pith_number":"pith:UAT7OGM7","canonical_record":{"source":{"id":"1705.07579","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2017-05-22T06:56:49Z","cross_cats_sorted":[],"title_canon_sha256":"d10933b1d9d15948288659a2d248efb15c24f416d335e781196859f33474fbb8","abstract_canon_sha256":"c99afec74b66920a30f7f2a06e8fd0395123eb53803763075737d79fb7360dd2"},"schema_version":"1.0"},"canonical_sha256":"a027f7199f6d342aebc59c61ea315e9b3f80d25be5e5a59682dd8e00cfbd52db","source":{"kind":"arxiv","id":"1705.07579","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1705.07579","created_at":"2026-05-18T00:36:38Z"},{"alias_kind":"arxiv_version","alias_value":"1705.07579v2","created_at":"2026-05-18T00:36:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1705.07579","created_at":"2026-05-18T00:36:38Z"},{"alias_kind":"pith_short_12","alias_value":"UAT7OGM7NU2C","created_at":"2026-05-18T12:31:46Z"},{"alias_kind":"pith_short_16","alias_value":"UAT7OGM7NU2CV26F","created_at":"2026-05-18T12:31:46Z"},{"alias_kind":"pith_short_8","alias_value":"UAT7OGM7","created_at":"2026-05-18T12:31:46Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:UAT7OGM7NU2CV26FTRQ6UMK6TM","target":"record","payload":{"canonical_record":{"source":{"id":"1705.07579","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2017-05-22T06:56:49Z","cross_cats_sorted":[],"title_canon_sha256":"d10933b1d9d15948288659a2d248efb15c24f416d335e781196859f33474fbb8","abstract_canon_sha256":"c99afec74b66920a30f7f2a06e8fd0395123eb53803763075737d79fb7360dd2"},"schema_version":"1.0"},"canonical_sha256":"a027f7199f6d342aebc59c61ea315e9b3f80d25be5e5a59682dd8e00cfbd52db","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:36:38.478215Z","signature_b64":"fijBhfxWb9FbJMMR5SCTAFhGNqvGmnqHnezZsppMHnMDxjIcN1ahEsy9wgYyo7kRke2Itm8UeAHzRR0unELyAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a027f7199f6d342aebc59c61ea315e9b3f80d25be5e5a59682dd8e00cfbd52db","last_reissued_at":"2026-05-18T00:36:38.477689Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:36:38.477689Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1705.07579","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:36:38Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"tjWJYlyKodDYpQSM/cLzsHIqUqnZ1msCjjWNg86MNxujqoGLhhpDuLFNmf8O2GPAiHCkiuOO8aYfCQZy5ehAAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-27T13:15:30.685653Z"},"content_sha256":"32791b85006df0e39bc01eaee661f5efef311c5a8ff28842b738ae1c89eddbfc","schema_version":"1.0","event_id":"sha256:32791b85006df0e39bc01eaee661f5efef311c5a8ff28842b738ae1c89eddbfc"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:UAT7OGM7NU2CV26FTRQ6UMK6TM","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Lyapunov optimization for non-generic one-dimensional expanding Markov maps","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Hiroki Takahasi, Mao Shinoda","submitted_at":"2017-05-22T06:56:49Z","abstract_excerpt":"For a non-generic, yet dense subset of $C^1$ expanding Markov maps of the interval we prove the existence of uncountably many Lyapunov optimizing measures which are ergodic, fully supported and have positive entropy. These measures are equilibrium states for some H\\\"older continuous potentials. We also prove the existence of another non-generic dense subset for which the optimizing measure is unique and supported on a periodic orbit. A key ingredient is a new $C^1$ perturbation lemma which allows us to interpolate between expanding Markov maps and the shift map on a finite number of symbols."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1705.07579","kind":"arxiv","version":2},"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":"2026-05-18T00:36:38Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"TsGI80lPbm5PVrTzawMJ23cW3Yl3O/jKnmL/IBJs0LxF4mI+LOrse+g3JZpFA/kF3Za3dcTIG0/5KPwKEuI/BA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-27T13:15:30.686007Z"},"content_sha256":"44a0bda3807bf23c2e99f4819c08fc66de690bf5ff85fdc23b9e5b723bbb47e4","schema_version":"1.0","event_id":"sha256:44a0bda3807bf23c2e99f4819c08fc66de690bf5ff85fdc23b9e5b723bbb47e4"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/UAT7OGM7NU2CV26FTRQ6UMK6TM/bundle.json","state_url":"https://pith.science/pith/UAT7OGM7NU2CV26FTRQ6UMK6TM/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/UAT7OGM7NU2CV26FTRQ6UMK6TM/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":"2026-06-27T13:15:30Z","links":{"resolver":"https://pith.science/pith/UAT7OGM7NU2CV26FTRQ6UMK6TM","bundle":"https://pith.science/pith/UAT7OGM7NU2CV26FTRQ6UMK6TM/bundle.json","state":"https://pith.science/pith/UAT7OGM7NU2CV26FTRQ6UMK6TM/state.json","well_known_bundle":"https://pith.science/.well-known/pith/UAT7OGM7NU2CV26FTRQ6UMK6TM/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:UAT7OGM7NU2CV26FTRQ6UMK6TM","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":"c99afec74b66920a30f7f2a06e8fd0395123eb53803763075737d79fb7360dd2","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2017-05-22T06:56:49Z","title_canon_sha256":"d10933b1d9d15948288659a2d248efb15c24f416d335e781196859f33474fbb8"},"schema_version":"1.0","source":{"id":"1705.07579","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1705.07579","created_at":"2026-05-18T00:36:38Z"},{"alias_kind":"arxiv_version","alias_value":"1705.07579v2","created_at":"2026-05-18T00:36:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1705.07579","created_at":"2026-05-18T00:36:38Z"},{"alias_kind":"pith_short_12","alias_value":"UAT7OGM7NU2C","created_at":"2026-05-18T12:31:46Z"},{"alias_kind":"pith_short_16","alias_value":"UAT7OGM7NU2CV26F","created_at":"2026-05-18T12:31:46Z"},{"alias_kind":"pith_short_8","alias_value":"UAT7OGM7","created_at":"2026-05-18T12:31:46Z"}],"graph_snapshots":[{"event_id":"sha256:44a0bda3807bf23c2e99f4819c08fc66de690bf5ff85fdc23b9e5b723bbb47e4","target":"graph","created_at":"2026-05-18T00:36:38Z","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":"For a non-generic, yet dense subset of $C^1$ expanding Markov maps of the interval we prove the existence of uncountably many Lyapunov optimizing measures which are ergodic, fully supported and have positive entropy. These measures are equilibrium states for some H\\\"older continuous potentials. We also prove the existence of another non-generic dense subset for which the optimizing measure is unique and supported on a periodic orbit. A key ingredient is a new $C^1$ perturbation lemma which allows us to interpolate between expanding Markov maps and the shift map on a finite number of symbols.","authors_text":"Hiroki Takahasi, Mao Shinoda","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2017-05-22T06:56:49Z","title":"Lyapunov optimization for non-generic one-dimensional expanding Markov maps"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1705.07579","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":"sha256:32791b85006df0e39bc01eaee661f5efef311c5a8ff28842b738ae1c89eddbfc","target":"record","created_at":"2026-05-18T00:36:38Z","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":"c99afec74b66920a30f7f2a06e8fd0395123eb53803763075737d79fb7360dd2","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2017-05-22T06:56:49Z","title_canon_sha256":"d10933b1d9d15948288659a2d248efb15c24f416d335e781196859f33474fbb8"},"schema_version":"1.0","source":{"id":"1705.07579","kind":"arxiv","version":2}},"canonical_sha256":"a027f7199f6d342aebc59c61ea315e9b3f80d25be5e5a59682dd8e00cfbd52db","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a027f7199f6d342aebc59c61ea315e9b3f80d25be5e5a59682dd8e00cfbd52db","first_computed_at":"2026-05-18T00:36:38.477689Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:36:38.477689Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"fijBhfxWb9FbJMMR5SCTAFhGNqvGmnqHnezZsppMHnMDxjIcN1ahEsy9wgYyo7kRke2Itm8UeAHzRR0unELyAA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:36:38.478215Z","signed_message":"canonical_sha256_bytes"},"source_id":"1705.07579","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:32791b85006df0e39bc01eaee661f5efef311c5a8ff28842b738ae1c89eddbfc","sha256:44a0bda3807bf23c2e99f4819c08fc66de690bf5ff85fdc23b9e5b723bbb47e4"],"state_sha256":"395c85afa36315e580f2ffbf93c1836c94abd46d6c9ff60998c8cc8bde34e8ce"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"yXadw47lKrU1V8awO5w1xqxERL7cGkK2u1tCAgdVdVD2YGBlBBduX2eQivzP8pJm6TuDsi5ywiCajZ0V6xvDCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-27T13:15:30.687852Z","bundle_sha256":"63b24f00517e7bcf3e456047ec3f26095b964279924d224a35fa8ee094d49c99"}}