{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:KOSYHO6B3C5H2URVMRUU6GWFP5","short_pith_number":"pith:KOSYHO6B","canonical_record":{"source":{"id":"1508.01297","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2015-08-06T07:30:55Z","cross_cats_sorted":[],"title_canon_sha256":"8039f3d00faa2ec5805fb318c9b8f8ee814d9a4580ae39a28e20118e41cda35b","abstract_canon_sha256":"a2ad0200a4024cbf98b2f11428e619dcf65af0d5c2bf2590477b2f1c30f4b505"},"schema_version":"1.0"},"canonical_sha256":"53a583bbc1d8ba7d523564694f1ac57f5a05dbc2bf08b95d4f862bb4ddebb263","source":{"kind":"arxiv","id":"1508.01297","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1508.01297","created_at":"2026-05-18T01:35:42Z"},{"alias_kind":"arxiv_version","alias_value":"1508.01297v1","created_at":"2026-05-18T01:35:42Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1508.01297","created_at":"2026-05-18T01:35:42Z"},{"alias_kind":"pith_short_12","alias_value":"KOSYHO6B3C5H","created_at":"2026-05-18T12:29:29Z"},{"alias_kind":"pith_short_16","alias_value":"KOSYHO6B3C5H2URV","created_at":"2026-05-18T12:29:29Z"},{"alias_kind":"pith_short_8","alias_value":"KOSYHO6B","created_at":"2026-05-18T12:29:29Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:KOSYHO6B3C5H2URVMRUU6GWFP5","target":"record","payload":{"canonical_record":{"source":{"id":"1508.01297","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2015-08-06T07:30:55Z","cross_cats_sorted":[],"title_canon_sha256":"8039f3d00faa2ec5805fb318c9b8f8ee814d9a4580ae39a28e20118e41cda35b","abstract_canon_sha256":"a2ad0200a4024cbf98b2f11428e619dcf65af0d5c2bf2590477b2f1c30f4b505"},"schema_version":"1.0"},"canonical_sha256":"53a583bbc1d8ba7d523564694f1ac57f5a05dbc2bf08b95d4f862bb4ddebb263","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:35:42.959081Z","signature_b64":"9ZegtXnUd+IB3KZINQjN1d2Io4/FbEFm91Y/Z1XQ6ll+vwFXd6EF2XPqi3ooLyqT+O1PC5B97/HLbpkxU8JoCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"53a583bbc1d8ba7d523564694f1ac57f5a05dbc2bf08b95d4f862bb4ddebb263","last_reissued_at":"2026-05-18T01:35:42.958565Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:35:42.958565Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1508.01297","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":"2026-05-18T01:35:42Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"avkS3VdzKEFB2HyHmGfrbzXw5En/qwSJCrJYCNwXpVCvdSBwYfprDXdGjuC0lllD2J6WTkwj2Sg4VOGR9MzGAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T01:39:24.920019Z"},"content_sha256":"4eda31a3e5c33d9093ea5807e4bbf0cb8c1f75df87b88eb218c2a6e22daadc22","schema_version":"1.0","event_id":"sha256:4eda31a3e5c33d9093ea5807e4bbf0cb8c1f75df87b88eb218c2a6e22daadc22"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:KOSYHO6B3C5H2URVMRUU6GWFP5","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The calculus of thermodynamical formalism","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Artur Lopes, Benoit Kloeckner (LAMA), Diego Marcon, Paolo Giulietti","submitted_at":"2015-08-06T07:30:55Z","abstract_excerpt":"Given a finite-to-one map acting on a compact metric space, one classically constructs for each potential in an appropriate Banach space of functionsa transfer operator acting on functions. Under suitable condition, the Ruelle-Perron-Frobenius enable to define for each potential an invariant measure called the Gibbs measure. The set of potential giving birth to the same Gibbs measure is a linear subspace containing one distinguished potential, said to be normalized.The goal of the present article is to study the geometry of the set of normalized potentials, of the normalization map, and of the"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1508.01297","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":""},"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":"2026-05-18T01:35:42Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"FpGbun4MWG79hDJ9bkymhY606gEptS1AyMfJjahbF3y1reFN+L1pWsQmdZzSxUf4B5S9hPVOKfNGD3Wih5BCDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T01:39:24.920384Z"},"content_sha256":"dd0ead40a897397eea53c4bab85fba255d392e94983da12ad9d52b8c6643d727","schema_version":"1.0","event_id":"sha256:dd0ead40a897397eea53c4bab85fba255d392e94983da12ad9d52b8c6643d727"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/KOSYHO6B3C5H2URVMRUU6GWFP5/bundle.json","state_url":"https://pith.science/pith/KOSYHO6B3C5H2URVMRUU6GWFP5/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/KOSYHO6B3C5H2URVMRUU6GWFP5/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":"2026-06-04T01:39:24Z","links":{"resolver":"https://pith.science/pith/KOSYHO6B3C5H2URVMRUU6GWFP5","bundle":"https://pith.science/pith/KOSYHO6B3C5H2URVMRUU6GWFP5/bundle.json","state":"https://pith.science/pith/KOSYHO6B3C5H2URVMRUU6GWFP5/state.json","well_known_bundle":"https://pith.science/.well-known/pith/KOSYHO6B3C5H2URVMRUU6GWFP5/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:KOSYHO6B3C5H2URVMRUU6GWFP5","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":"a2ad0200a4024cbf98b2f11428e619dcf65af0d5c2bf2590477b2f1c30f4b505","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2015-08-06T07:30:55Z","title_canon_sha256":"8039f3d00faa2ec5805fb318c9b8f8ee814d9a4580ae39a28e20118e41cda35b"},"schema_version":"1.0","source":{"id":"1508.01297","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1508.01297","created_at":"2026-05-18T01:35:42Z"},{"alias_kind":"arxiv_version","alias_value":"1508.01297v1","created_at":"2026-05-18T01:35:42Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1508.01297","created_at":"2026-05-18T01:35:42Z"},{"alias_kind":"pith_short_12","alias_value":"KOSYHO6B3C5H","created_at":"2026-05-18T12:29:29Z"},{"alias_kind":"pith_short_16","alias_value":"KOSYHO6B3C5H2URV","created_at":"2026-05-18T12:29:29Z"},{"alias_kind":"pith_short_8","alias_value":"KOSYHO6B","created_at":"2026-05-18T12:29:29Z"}],"graph_snapshots":[{"event_id":"sha256:dd0ead40a897397eea53c4bab85fba255d392e94983da12ad9d52b8c6643d727","target":"graph","created_at":"2026-05-18T01:35:42Z","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":"Given a finite-to-one map acting on a compact metric space, one classically constructs for each potential in an appropriate Banach space of functionsa transfer operator acting on functions. Under suitable condition, the Ruelle-Perron-Frobenius enable to define for each potential an invariant measure called the Gibbs measure. The set of potential giving birth to the same Gibbs measure is a linear subspace containing one distinguished potential, said to be normalized.The goal of the present article is to study the geometry of the set of normalized potentials, of the normalization map, and of the","authors_text":"Artur Lopes, Benoit Kloeckner (LAMA), Diego Marcon, Paolo Giulietti","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2015-08-06T07:30:55Z","title":"The calculus of thermodynamical formalism"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1508.01297","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":"sha256:4eda31a3e5c33d9093ea5807e4bbf0cb8c1f75df87b88eb218c2a6e22daadc22","target":"record","created_at":"2026-05-18T01:35:42Z","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":"a2ad0200a4024cbf98b2f11428e619dcf65af0d5c2bf2590477b2f1c30f4b505","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2015-08-06T07:30:55Z","title_canon_sha256":"8039f3d00faa2ec5805fb318c9b8f8ee814d9a4580ae39a28e20118e41cda35b"},"schema_version":"1.0","source":{"id":"1508.01297","kind":"arxiv","version":1}},"canonical_sha256":"53a583bbc1d8ba7d523564694f1ac57f5a05dbc2bf08b95d4f862bb4ddebb263","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"53a583bbc1d8ba7d523564694f1ac57f5a05dbc2bf08b95d4f862bb4ddebb263","first_computed_at":"2026-05-18T01:35:42.958565Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:35:42.958565Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"9ZegtXnUd+IB3KZINQjN1d2Io4/FbEFm91Y/Z1XQ6ll+vwFXd6EF2XPqi3ooLyqT+O1PC5B97/HLbpkxU8JoCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:35:42.959081Z","signed_message":"canonical_sha256_bytes"},"source_id":"1508.01297","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4eda31a3e5c33d9093ea5807e4bbf0cb8c1f75df87b88eb218c2a6e22daadc22","sha256:dd0ead40a897397eea53c4bab85fba255d392e94983da12ad9d52b8c6643d727"],"state_sha256":"2216d733c74af7476252359870ff90c2c0e6a3dc4565c535440aa7cbccb77036"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"alGIKIB38RAv8e7Qjx094x/DA99CnfSV6u3FsoZ6GDxUByquwgncreMT0sgxPL2uYoS31anzOrPsPnpqp7UbDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-04T01:39:24.922871Z","bundle_sha256":"c1eb7dcd81f5689ebb18b7ff1c2cbc9d932fe094f0517780b3fe5df37ebc8d4c"}}