{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:GWOQGVFKGRLM2MGOPCBAS7O22C","short_pith_number":"pith:GWOQGVFK","schema_version":"1.0","canonical_sha256":"359d0354aa3456cd30ce7882097ddad086eb6d6a081a91843b7b911803d342a7","source":{"kind":"arxiv","id":"1702.03134","version":3},"attestation_state":"computed","paper":{"title":"A formula for the Entropy of the Convolution of Gibbs probabilities on the circle","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.PR"],"primary_cat":"math.DS","authors_text":"Artur O. Lopes","submitted_at":"2017-02-10T11:20:28Z","abstract_excerpt":"Consider the transformation $T:S^1 \\to S^1$, such that $T(x)=2\\, x$ (mod 1), and where $S^1$ is the unitary circle. Suppose $J:S^1 \\to \\mathbb{R}$ is Holder continuous and positive, and moreover that, for any $y\\in S^1$, we have that $\\sum_{x\\,\\,\\text{such that}\\,\\,\\, T(x)= y} \\, J(x)=1.$\n  We say that $\\rho$ is a Gibbs probability for the Holder continuous potential $\\log J$, if $\\mathcal{L}_{\\log J}^* \\,(\\rho)=\\rho ,$ where $\\mathcal{L}_{\\log J}$ is the Ruelle operator for $\\log J$. We call $J$ the Jacobian of $\\rho$.\n  Suppose $\\nu=\\mu_1*\\mu_2$ is the convolution of two Gibbs probabilities "},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1702.03134","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2017-02-10T11:20:28Z","cross_cats_sorted":["math.PR"],"title_canon_sha256":"08d23b61e97a1ebe50cae74020f14c8cf890130ec9bd9cbbe040437213ab1466","abstract_canon_sha256":"d61844fb31149c1165dd55cfebd7fe8a95b4879e3859f7a8dfd9074cee0522ba"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:11:44.028410Z","signature_b64":"FB10p/qw8VHoYi4qs6+J+tdX+6K9GmVyc2YwlSkkHISNov4AEEGRohdBdBeEbMtJNxvXLV6EzWva9MigxkaLBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"359d0354aa3456cd30ce7882097ddad086eb6d6a081a91843b7b911803d342a7","last_reissued_at":"2026-05-18T00:11:44.027510Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:11:44.027510Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A formula for the Entropy of the Convolution of Gibbs probabilities on the circle","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.PR"],"primary_cat":"math.DS","authors_text":"Artur O. Lopes","submitted_at":"2017-02-10T11:20:28Z","abstract_excerpt":"Consider the transformation $T:S^1 \\to S^1$, such that $T(x)=2\\, x$ (mod 1), and where $S^1$ is the unitary circle. Suppose $J:S^1 \\to \\mathbb{R}$ is Holder continuous and positive, and moreover that, for any $y\\in S^1$, we have that $\\sum_{x\\,\\,\\text{such that}\\,\\,\\, T(x)= y} \\, J(x)=1.$\n  We say that $\\rho$ is a Gibbs probability for the Holder continuous potential $\\log J$, if $\\mathcal{L}_{\\log J}^* \\,(\\rho)=\\rho ,$ where $\\mathcal{L}_{\\log J}$ is the Ruelle operator for $\\log J$. We call $J$ the Jacobian of $\\rho$.\n  Suppose $\\nu=\\mu_1*\\mu_2$ is the convolution of two Gibbs probabilities "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1702.03134","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1702.03134","created_at":"2026-05-18T00:11:44.027663+00:00"},{"alias_kind":"arxiv_version","alias_value":"1702.03134v3","created_at":"2026-05-18T00:11:44.027663+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1702.03134","created_at":"2026-05-18T00:11:44.027663+00:00"},{"alias_kind":"pith_short_12","alias_value":"GWOQGVFKGRLM","created_at":"2026-05-18T12:31:18.294218+00:00"},{"alias_kind":"pith_short_16","alias_value":"GWOQGVFKGRLM2MGO","created_at":"2026-05-18T12:31:18.294218+00:00"},{"alias_kind":"pith_short_8","alias_value":"GWOQGVFK","created_at":"2026-05-18T12:31:18.294218+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/GWOQGVFKGRLM2MGOPCBAS7O22C","json":"https://pith.science/pith/GWOQGVFKGRLM2MGOPCBAS7O22C.json","graph_json":"https://pith.science/api/pith-number/GWOQGVFKGRLM2MGOPCBAS7O22C/graph.json","events_json":"https://pith.science/api/pith-number/GWOQGVFKGRLM2MGOPCBAS7O22C/events.json","paper":"https://pith.science/paper/GWOQGVFK"},"agent_actions":{"view_html":"https://pith.science/pith/GWOQGVFKGRLM2MGOPCBAS7O22C","download_json":"https://pith.science/pith/GWOQGVFKGRLM2MGOPCBAS7O22C.json","view_paper":"https://pith.science/paper/GWOQGVFK","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1702.03134&json=true","fetch_graph":"https://pith.science/api/pith-number/GWOQGVFKGRLM2MGOPCBAS7O22C/graph.json","fetch_events":"https://pith.science/api/pith-number/GWOQGVFKGRLM2MGOPCBAS7O22C/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/GWOQGVFKGRLM2MGOPCBAS7O22C/action/timestamp_anchor","attest_storage":"https://pith.science/pith/GWOQGVFKGRLM2MGOPCBAS7O22C/action/storage_attestation","attest_author":"https://pith.science/pith/GWOQGVFKGRLM2MGOPCBAS7O22C/action/author_attestation","sign_citation":"https://pith.science/pith/GWOQGVFKGRLM2MGOPCBAS7O22C/action/citation_signature","submit_replication":"https://pith.science/pith/GWOQGVFKGRLM2MGOPCBAS7O22C/action/replication_record"}},"created_at":"2026-05-18T00:11:44.027663+00:00","updated_at":"2026-05-18T00:11:44.027663+00:00"}