{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:YUSY4ZOTNNUXQDLXYTD7T2CTXM","short_pith_number":"pith:YUSY4ZOT","canonical_record":{"source":{"id":"1311.2726","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-11-12T09:51:15Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"3bb52f0cd3362db988c20c3514f3441bcac11a354a4ae99e7c295b2ec0e1634c","abstract_canon_sha256":"7ff5f37e1371f7cdf95a86b74bcae1e6b4cc07667ef04fca2bbada4bb146ba03"},"schema_version":"1.0"},"canonical_sha256":"c5258e65d36b69780d77c4c7f9e853bb3d47fe6efffeac240bc858bf838105b9","source":{"kind":"arxiv","id":"1311.2726","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1311.2726","created_at":"2026-05-18T03:00:49Z"},{"alias_kind":"arxiv_version","alias_value":"1311.2726v3","created_at":"2026-05-18T03:00:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1311.2726","created_at":"2026-05-18T03:00:49Z"},{"alias_kind":"pith_short_12","alias_value":"YUSY4ZOTNNUX","created_at":"2026-05-18T12:28:09Z"},{"alias_kind":"pith_short_16","alias_value":"YUSY4ZOTNNUXQDLX","created_at":"2026-05-18T12:28:09Z"},{"alias_kind":"pith_short_8","alias_value":"YUSY4ZOT","created_at":"2026-05-18T12:28:09Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:YUSY4ZOTNNUXQDLXYTD7T2CTXM","target":"record","payload":{"canonical_record":{"source":{"id":"1311.2726","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-11-12T09:51:15Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"3bb52f0cd3362db988c20c3514f3441bcac11a354a4ae99e7c295b2ec0e1634c","abstract_canon_sha256":"7ff5f37e1371f7cdf95a86b74bcae1e6b4cc07667ef04fca2bbada4bb146ba03"},"schema_version":"1.0"},"canonical_sha256":"c5258e65d36b69780d77c4c7f9e853bb3d47fe6efffeac240bc858bf838105b9","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:00:49.086436Z","signature_b64":"qx+MDiptTgkQtR9oa7MS8CBM/gGWKY0//1wB+WvvW1dN4K6GRpdN55sGYmpYeKLM7pixRHaD0Hiv5YEIEVYVBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c5258e65d36b69780d77c4c7f9e853bb3d47fe6efffeac240bc858bf838105b9","last_reissued_at":"2026-05-18T03:00:49.085751Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:00:49.085751Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1311.2726","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":"2026-05-18T03:00:49Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"tEgaShlGMVvm6U9+6No2Nvaskk+VhbYOoWJdMSQ1HMeMj2MmXT/guo7NKmHfzckwc4CGqS34ZvbYfdpAJlR1Aw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-22T23:06:22.949226Z"},"content_sha256":"160745e6b898425cd2f5bb697a8a0b5c06915466b2fce21ca5eedadfc12a517d","schema_version":"1.0","event_id":"sha256:160745e6b898425cd2f5bb697a8a0b5c06915466b2fce21ca5eedadfc12a517d"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:YUSY4ZOTNNUXQDLXYTD7T2CTXM","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Thermodynamic formalism and large deviations for multiplication-invariant potentials on lattice spin systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.PR","authors_text":"F. Redig, J.-R. Chazottes","submitted_at":"2013-11-12T09:51:15Z","abstract_excerpt":"We introduce the multiplicative Ising model and prove basic properties of its thermodynamic formalism such as existence of pressure and entropies. We generalize to one-dimensional \"layer-unique\" Gibbs measures for which the same results can be obtained. For more general models associated to a $d$-dimensional multiplicative invariant potential, we prove a large deviation theorem in the uniqueness regime for averages of multiplicative shifts of general local functions. This thermodynamic formalism is motivated by the statistical properties of multiple ergodic averages."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1311.2726","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":"2026-05-18T03:00:49Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"SGvaLWjzkXoBH642C9Y9iJZ1FVISDa5a5KMPz6sOf5k2QdV/7nDZxUThepSgD07h3DDYqSXCYfE/40vH1jJbAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-22T23:06:22.949583Z"},"content_sha256":"2e838caf45ade09704b5839f28f645d6daaa98bf4e67af6379bb91c293a3eab1","schema_version":"1.0","event_id":"sha256:2e838caf45ade09704b5839f28f645d6daaa98bf4e67af6379bb91c293a3eab1"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/YUSY4ZOTNNUXQDLXYTD7T2CTXM/bundle.json","state_url":"https://pith.science/pith/YUSY4ZOTNNUXQDLXYTD7T2CTXM/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/YUSY4ZOTNNUXQDLXYTD7T2CTXM/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":"2026-06-22T23:06:22Z","links":{"resolver":"https://pith.science/pith/YUSY4ZOTNNUXQDLXYTD7T2CTXM","bundle":"https://pith.science/pith/YUSY4ZOTNNUXQDLXYTD7T2CTXM/bundle.json","state":"https://pith.science/pith/YUSY4ZOTNNUXQDLXYTD7T2CTXM/state.json","well_known_bundle":"https://pith.science/.well-known/pith/YUSY4ZOTNNUXQDLXYTD7T2CTXM/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:YUSY4ZOTNNUXQDLXYTD7T2CTXM","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":"7ff5f37e1371f7cdf95a86b74bcae1e6b4cc07667ef04fca2bbada4bb146ba03","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-11-12T09:51:15Z","title_canon_sha256":"3bb52f0cd3362db988c20c3514f3441bcac11a354a4ae99e7c295b2ec0e1634c"},"schema_version":"1.0","source":{"id":"1311.2726","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1311.2726","created_at":"2026-05-18T03:00:49Z"},{"alias_kind":"arxiv_version","alias_value":"1311.2726v3","created_at":"2026-05-18T03:00:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1311.2726","created_at":"2026-05-18T03:00:49Z"},{"alias_kind":"pith_short_12","alias_value":"YUSY4ZOTNNUX","created_at":"2026-05-18T12:28:09Z"},{"alias_kind":"pith_short_16","alias_value":"YUSY4ZOTNNUXQDLX","created_at":"2026-05-18T12:28:09Z"},{"alias_kind":"pith_short_8","alias_value":"YUSY4ZOT","created_at":"2026-05-18T12:28:09Z"}],"graph_snapshots":[{"event_id":"sha256:2e838caf45ade09704b5839f28f645d6daaa98bf4e67af6379bb91c293a3eab1","target":"graph","created_at":"2026-05-18T03:00:49Z","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":"We introduce the multiplicative Ising model and prove basic properties of its thermodynamic formalism such as existence of pressure and entropies. We generalize to one-dimensional \"layer-unique\" Gibbs measures for which the same results can be obtained. For more general models associated to a $d$-dimensional multiplicative invariant potential, we prove a large deviation theorem in the uniqueness regime for averages of multiplicative shifts of general local functions. This thermodynamic formalism is motivated by the statistical properties of multiple ergodic averages.","authors_text":"F. Redig, J.-R. Chazottes","cross_cats":["math-ph","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-11-12T09:51:15Z","title":"Thermodynamic formalism and large deviations for multiplication-invariant potentials on lattice spin systems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1311.2726","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":"sha256:160745e6b898425cd2f5bb697a8a0b5c06915466b2fce21ca5eedadfc12a517d","target":"record","created_at":"2026-05-18T03:00:49Z","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":"7ff5f37e1371f7cdf95a86b74bcae1e6b4cc07667ef04fca2bbada4bb146ba03","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-11-12T09:51:15Z","title_canon_sha256":"3bb52f0cd3362db988c20c3514f3441bcac11a354a4ae99e7c295b2ec0e1634c"},"schema_version":"1.0","source":{"id":"1311.2726","kind":"arxiv","version":3}},"canonical_sha256":"c5258e65d36b69780d77c4c7f9e853bb3d47fe6efffeac240bc858bf838105b9","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c5258e65d36b69780d77c4c7f9e853bb3d47fe6efffeac240bc858bf838105b9","first_computed_at":"2026-05-18T03:00:49.085751Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:00:49.085751Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"qx+MDiptTgkQtR9oa7MS8CBM/gGWKY0//1wB+WvvW1dN4K6GRpdN55sGYmpYeKLM7pixRHaD0Hiv5YEIEVYVBw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:00:49.086436Z","signed_message":"canonical_sha256_bytes"},"source_id":"1311.2726","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:160745e6b898425cd2f5bb697a8a0b5c06915466b2fce21ca5eedadfc12a517d","sha256:2e838caf45ade09704b5839f28f645d6daaa98bf4e67af6379bb91c293a3eab1"],"state_sha256":"75edbc734b756fbd7ada2405263c5ebf4cfdc691a44cb0bbb1e2cb47ef4db6da"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"mFyOAMRbNVFNO33nhfIvJk8OCxLVu8ZhHFmH3BaxJyZl3XpG6W5DFcawnkSiUtfOYd+AnViBws+X3ddodDXwBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-22T23:06:22.951522Z","bundle_sha256":"64e16b1e89209aa391d3bc734ec2ef4fe513c02548a55b03ab739e550eb0ceb5"}}