{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:N7FNOWKW6ELOOP3QN2252GEBOV","short_pith_number":"pith:N7FNOWKW","canonical_record":{"source":{"id":"1707.01762","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2017-07-06T12:58:24Z","cross_cats_sorted":["math.PR"],"title_canon_sha256":"6e6bddca607cd0e72970080af7a70e54bfa837f6aa5f1f033b956a1264893792","abstract_canon_sha256":"50b0dea1ef1a8a3ba1cb8258f697497b6599b6cd7d171e11bd4dd94bcac68825"},"schema_version":"1.0"},"canonical_sha256":"6fcad75956f116e73f706eb5dd1881756bab9861b8ceb03ce491d83b89c05371","source":{"kind":"arxiv","id":"1707.01762","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1707.01762","created_at":"2026-05-18T00:13:55Z"},{"alias_kind":"arxiv_version","alias_value":"1707.01762v3","created_at":"2026-05-18T00:13:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1707.01762","created_at":"2026-05-18T00:13:55Z"},{"alias_kind":"pith_short_12","alias_value":"N7FNOWKW6ELO","created_at":"2026-05-18T12:31:31Z"},{"alias_kind":"pith_short_16","alias_value":"N7FNOWKW6ELOOP3Q","created_at":"2026-05-18T12:31:31Z"},{"alias_kind":"pith_short_8","alias_value":"N7FNOWKW","created_at":"2026-05-18T12:31:31Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:N7FNOWKW6ELOOP3QN2252GEBOV","target":"record","payload":{"canonical_record":{"source":{"id":"1707.01762","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2017-07-06T12:58:24Z","cross_cats_sorted":["math.PR"],"title_canon_sha256":"6e6bddca607cd0e72970080af7a70e54bfa837f6aa5f1f033b956a1264893792","abstract_canon_sha256":"50b0dea1ef1a8a3ba1cb8258f697497b6599b6cd7d171e11bd4dd94bcac68825"},"schema_version":"1.0"},"canonical_sha256":"6fcad75956f116e73f706eb5dd1881756bab9861b8ceb03ce491d83b89c05371","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:13:55.299856Z","signature_b64":"pEgRChdJain4jz1iSvgi8j3b4F5nN4Er0aKSCJQUMYTfKuuN44oaog3uPe/ufbVGxxUYMmsbsdO5m/eSJbr0CQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6fcad75956f116e73f706eb5dd1881756bab9861b8ceb03ce491d83b89c05371","last_reissued_at":"2026-05-18T00:13:55.299150Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:13:55.299150Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1707.01762","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":"2026-05-18T00:13:55Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"lDpXJbv8tiGt4lkXP5H0RbUL9SkCPQrQIVtAQ/Pf2r/8iHAX781MVkAZ8/WEr2KIdy38jGY9L6DTftrgX8x5Bg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-20T19:39:09.283113Z"},"content_sha256":"2fb9599d0bb8e5dcafffe29cecce46b1984e4414e1dc95b1e24fe6a64ce27b5c","schema_version":"1.0","event_id":"sha256:2fb9599d0bb8e5dcafffe29cecce46b1984e4414e1dc95b1e24fe6a64ce27b5c"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:N7FNOWKW6ELOOP3QN2252GEBOV","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A Variational Principle for the Specific Entropy for Symbolic Systems with Uncountable Alphabets","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.PR"],"primary_cat":"math.DS","authors_text":"D. Aguiar, L. Cioletti, R. Ruviaro","submitted_at":"2017-07-06T12:58:24Z","abstract_excerpt":"In this paper we derived a variational principle for the specific entropy on the context of symbolic dynamics of compact metric space alphabets and use this result to obtain the uniqueness of the equilibrium states associated to a Walters potential."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1707.01762","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":"2026-05-18T00:13:55Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"p4qJ7Tu0UH7I6Qy52O1H9As6C4QnZiBETxeyUCYQREvzZa8zwqTF5FeEGQXBaT8NZnIINROxmSex4P6O4GoKCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-20T19:39:09.283467Z"},"content_sha256":"020acbb372bc0e3a34a8da9f1c6f262069a28d65fa8922c734634a2b040e264a","schema_version":"1.0","event_id":"sha256:020acbb372bc0e3a34a8da9f1c6f262069a28d65fa8922c734634a2b040e264a"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/N7FNOWKW6ELOOP3QN2252GEBOV/bundle.json","state_url":"https://pith.science/pith/N7FNOWKW6ELOOP3QN2252GEBOV/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/N7FNOWKW6ELOOP3QN2252GEBOV/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":"2026-06-20T19:39:09Z","links":{"resolver":"https://pith.science/pith/N7FNOWKW6ELOOP3QN2252GEBOV","bundle":"https://pith.science/pith/N7FNOWKW6ELOOP3QN2252GEBOV/bundle.json","state":"https://pith.science/pith/N7FNOWKW6ELOOP3QN2252GEBOV/state.json","well_known_bundle":"https://pith.science/.well-known/pith/N7FNOWKW6ELOOP3QN2252GEBOV/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:N7FNOWKW6ELOOP3QN2252GEBOV","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":"50b0dea1ef1a8a3ba1cb8258f697497b6599b6cd7d171e11bd4dd94bcac68825","cross_cats_sorted":["math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2017-07-06T12:58:24Z","title_canon_sha256":"6e6bddca607cd0e72970080af7a70e54bfa837f6aa5f1f033b956a1264893792"},"schema_version":"1.0","source":{"id":"1707.01762","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1707.01762","created_at":"2026-05-18T00:13:55Z"},{"alias_kind":"arxiv_version","alias_value":"1707.01762v3","created_at":"2026-05-18T00:13:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1707.01762","created_at":"2026-05-18T00:13:55Z"},{"alias_kind":"pith_short_12","alias_value":"N7FNOWKW6ELO","created_at":"2026-05-18T12:31:31Z"},{"alias_kind":"pith_short_16","alias_value":"N7FNOWKW6ELOOP3Q","created_at":"2026-05-18T12:31:31Z"},{"alias_kind":"pith_short_8","alias_value":"N7FNOWKW","created_at":"2026-05-18T12:31:31Z"}],"graph_snapshots":[{"event_id":"sha256:020acbb372bc0e3a34a8da9f1c6f262069a28d65fa8922c734634a2b040e264a","target":"graph","created_at":"2026-05-18T00:13:55Z","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":"In this paper we derived a variational principle for the specific entropy on the context of symbolic dynamics of compact metric space alphabets and use this result to obtain the uniqueness of the equilibrium states associated to a Walters potential.","authors_text":"D. Aguiar, L. Cioletti, R. Ruviaro","cross_cats":["math.PR"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2017-07-06T12:58:24Z","title":"A Variational Principle for the Specific Entropy for Symbolic Systems with Uncountable Alphabets"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1707.01762","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":"sha256:2fb9599d0bb8e5dcafffe29cecce46b1984e4414e1dc95b1e24fe6a64ce27b5c","target":"record","created_at":"2026-05-18T00:13:55Z","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":"50b0dea1ef1a8a3ba1cb8258f697497b6599b6cd7d171e11bd4dd94bcac68825","cross_cats_sorted":["math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2017-07-06T12:58:24Z","title_canon_sha256":"6e6bddca607cd0e72970080af7a70e54bfa837f6aa5f1f033b956a1264893792"},"schema_version":"1.0","source":{"id":"1707.01762","kind":"arxiv","version":3}},"canonical_sha256":"6fcad75956f116e73f706eb5dd1881756bab9861b8ceb03ce491d83b89c05371","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6fcad75956f116e73f706eb5dd1881756bab9861b8ceb03ce491d83b89c05371","first_computed_at":"2026-05-18T00:13:55.299150Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:13:55.299150Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"pEgRChdJain4jz1iSvgi8j3b4F5nN4Er0aKSCJQUMYTfKuuN44oaog3uPe/ufbVGxxUYMmsbsdO5m/eSJbr0CQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:13:55.299856Z","signed_message":"canonical_sha256_bytes"},"source_id":"1707.01762","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2fb9599d0bb8e5dcafffe29cecce46b1984e4414e1dc95b1e24fe6a64ce27b5c","sha256:020acbb372bc0e3a34a8da9f1c6f262069a28d65fa8922c734634a2b040e264a"],"state_sha256":"a12e1f850b7cb1775f48be28af484168149ba2e0d5df7a837d46efa7dc13efac"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ryYTcL3/i+bW6oUAWcGnGD58jMkdBeI9alCMIV2jo+4oo6cf87w7gfwL8aysKfHO9jQNW2iT9FSjtf5m+J6ADQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-20T19:39:09.285260Z","bundle_sha256":"4a43bbdd215cb2ebdd3078606ea116196b94979b5930624205f344a71e8b30bc"}}