{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:G55VMA32VX4IMWLRNZ6LHR7DZL","short_pith_number":"pith:G55VMA32","canonical_record":{"source":{"id":"1511.02118","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-11-06T15:37:04Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"ab1226b1e928a3680ed92a32a2a89f8d7ccd55d00780e4676946762a202b8dec","abstract_canon_sha256":"82edecebd1482afb8e2046a5c95a842a5f80b12fd73ce159602802812fd4a904"},"schema_version":"1.0"},"canonical_sha256":"377b56037aadf88659716e7cb3c7e3caf161e0f08eb792b26adf49dbf4326c04","source":{"kind":"arxiv","id":"1511.02118","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1511.02118","created_at":"2026-05-18T01:08:12Z"},{"alias_kind":"arxiv_version","alias_value":"1511.02118v2","created_at":"2026-05-18T01:08:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1511.02118","created_at":"2026-05-18T01:08:12Z"},{"alias_kind":"pith_short_12","alias_value":"G55VMA32VX4I","created_at":"2026-05-18T12:29:22Z"},{"alias_kind":"pith_short_16","alias_value":"G55VMA32VX4IMWLR","created_at":"2026-05-18T12:29:22Z"},{"alias_kind":"pith_short_8","alias_value":"G55VMA32","created_at":"2026-05-18T12:29:22Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:G55VMA32VX4IMWLRNZ6LHR7DZL","target":"record","payload":{"canonical_record":{"source":{"id":"1511.02118","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-11-06T15:37:04Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"ab1226b1e928a3680ed92a32a2a89f8d7ccd55d00780e4676946762a202b8dec","abstract_canon_sha256":"82edecebd1482afb8e2046a5c95a842a5f80b12fd73ce159602802812fd4a904"},"schema_version":"1.0"},"canonical_sha256":"377b56037aadf88659716e7cb3c7e3caf161e0f08eb792b26adf49dbf4326c04","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:08:12.814422Z","signature_b64":"FdyquQZcOVXAg/gnIFiUzkjZRkVC+1IHmcTHyS7DfVgrM+t744Lmm50BYj4G9qfnNGAvTR2vukstYXVMNAN0BA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"377b56037aadf88659716e7cb3c7e3caf161e0f08eb792b26adf49dbf4326c04","last_reissued_at":"2026-05-18T01:08:12.813964Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:08:12.813964Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1511.02118","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":"2026-05-18T01:08:12Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Q1/rCRe4FEjrLymUZcdTTUO2SadzKeXgvFS4C8AiOVGDeCC1CdL5pSbdLLFyVaqifdaYtLU1uYmGH1Ck5ZY9Bg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-10T12:00:46.670606Z"},"content_sha256":"ee18baaee384bdcb9a9910afc604e09aae5955c9ba73741f2156ad2b53a28648","schema_version":"1.0","event_id":"sha256:ee18baaee384bdcb9a9910afc604e09aae5955c9ba73741f2156ad2b53a28648"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:G55VMA32VX4IMWLRNZ6LHR7DZL","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Thermodynamics for spatially inhomogeneous magnetization and Young-Gibbs measures","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.PR","authors_text":"A. Montino, D. Tsagkarogiannis, N. Soprano-Loto","submitted_at":"2015-11-06T15:37:04Z","abstract_excerpt":"We derive thermodynamic functionals for spatially inhomogeneous magnetization on a torus in the context of an Ising spin lattice model. We calculate the corresponding free energy and pressure (by applying an appropriate external field using a quadratic Kac potential) and show that they are related via a modified Legendre transform. The local properties of the infinite volume Gibbs measure, related to whether a macroscopic configuration is realized as a homogeneous state or as a mixture of pure states, are also studied by constructing the corresponding Young-Gibbs measures."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1511.02118","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":"2026-05-18T01:08:12Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Zwrrqm+efurWapL3WH2cIRfEZgHFAZT/uVlUvEAbsaSfGkzpjgzERhH9w4OdWWA6uDuI+NYCARrS58SYtBDyBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-10T12:00:46.671250Z"},"content_sha256":"c80dc9b4bade46239572ff9f67ac916263cca313b8c9254fcdde68fb75f1d792","schema_version":"1.0","event_id":"sha256:c80dc9b4bade46239572ff9f67ac916263cca313b8c9254fcdde68fb75f1d792"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/G55VMA32VX4IMWLRNZ6LHR7DZL/bundle.json","state_url":"https://pith.science/pith/G55VMA32VX4IMWLRNZ6LHR7DZL/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/G55VMA32VX4IMWLRNZ6LHR7DZL/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":"2026-06-10T12:00:46Z","links":{"resolver":"https://pith.science/pith/G55VMA32VX4IMWLRNZ6LHR7DZL","bundle":"https://pith.science/pith/G55VMA32VX4IMWLRNZ6LHR7DZL/bundle.json","state":"https://pith.science/pith/G55VMA32VX4IMWLRNZ6LHR7DZL/state.json","well_known_bundle":"https://pith.science/.well-known/pith/G55VMA32VX4IMWLRNZ6LHR7DZL/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:G55VMA32VX4IMWLRNZ6LHR7DZL","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":"82edecebd1482afb8e2046a5c95a842a5f80b12fd73ce159602802812fd4a904","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-11-06T15:37:04Z","title_canon_sha256":"ab1226b1e928a3680ed92a32a2a89f8d7ccd55d00780e4676946762a202b8dec"},"schema_version":"1.0","source":{"id":"1511.02118","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1511.02118","created_at":"2026-05-18T01:08:12Z"},{"alias_kind":"arxiv_version","alias_value":"1511.02118v2","created_at":"2026-05-18T01:08:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1511.02118","created_at":"2026-05-18T01:08:12Z"},{"alias_kind":"pith_short_12","alias_value":"G55VMA32VX4I","created_at":"2026-05-18T12:29:22Z"},{"alias_kind":"pith_short_16","alias_value":"G55VMA32VX4IMWLR","created_at":"2026-05-18T12:29:22Z"},{"alias_kind":"pith_short_8","alias_value":"G55VMA32","created_at":"2026-05-18T12:29:22Z"}],"graph_snapshots":[{"event_id":"sha256:c80dc9b4bade46239572ff9f67ac916263cca313b8c9254fcdde68fb75f1d792","target":"graph","created_at":"2026-05-18T01:08:12Z","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 derive thermodynamic functionals for spatially inhomogeneous magnetization on a torus in the context of an Ising spin lattice model. We calculate the corresponding free energy and pressure (by applying an appropriate external field using a quadratic Kac potential) and show that they are related via a modified Legendre transform. The local properties of the infinite volume Gibbs measure, related to whether a macroscopic configuration is realized as a homogeneous state or as a mixture of pure states, are also studied by constructing the corresponding Young-Gibbs measures.","authors_text":"A. Montino, D. Tsagkarogiannis, N. Soprano-Loto","cross_cats":["math-ph","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-11-06T15:37:04Z","title":"Thermodynamics for spatially inhomogeneous magnetization and Young-Gibbs measures"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1511.02118","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:ee18baaee384bdcb9a9910afc604e09aae5955c9ba73741f2156ad2b53a28648","target":"record","created_at":"2026-05-18T01:08:12Z","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":"82edecebd1482afb8e2046a5c95a842a5f80b12fd73ce159602802812fd4a904","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-11-06T15:37:04Z","title_canon_sha256":"ab1226b1e928a3680ed92a32a2a89f8d7ccd55d00780e4676946762a202b8dec"},"schema_version":"1.0","source":{"id":"1511.02118","kind":"arxiv","version":2}},"canonical_sha256":"377b56037aadf88659716e7cb3c7e3caf161e0f08eb792b26adf49dbf4326c04","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"377b56037aadf88659716e7cb3c7e3caf161e0f08eb792b26adf49dbf4326c04","first_computed_at":"2026-05-18T01:08:12.813964Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:08:12.813964Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"FdyquQZcOVXAg/gnIFiUzkjZRkVC+1IHmcTHyS7DfVgrM+t744Lmm50BYj4G9qfnNGAvTR2vukstYXVMNAN0BA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:08:12.814422Z","signed_message":"canonical_sha256_bytes"},"source_id":"1511.02118","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ee18baaee384bdcb9a9910afc604e09aae5955c9ba73741f2156ad2b53a28648","sha256:c80dc9b4bade46239572ff9f67ac916263cca313b8c9254fcdde68fb75f1d792"],"state_sha256":"6f15b5dd7492e1073de284107d271a59fdc666d4b3af1860451041edbfda3dc5"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"xaa7/7biCJ+iM4nKoN/Y52gB6wtmHyzUArvSu5ewuLJrw0A81KvnDnzTumPb7q/5R4327GtSHOEQnLdesgYgCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-10T12:00:46.675016Z","bundle_sha256":"063cbc158ba729e9edb3ddc88b0d45a6b571bd08bc6776563b0ba04d19a3ac69"}}