{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2003:ZOCWO7FRUM7YWPWRHWRF6MRAR5","short_pith_number":"pith:ZOCWO7FR","canonical_record":{"source":{"id":"cond-mat/0306728","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"cond-mat.stat-mech","submitted_at":"2003-06-30T07:56:29Z","cross_cats_sorted":[],"title_canon_sha256":"b28f6598bc5fd2d0d5830ddd114feacec2093e374d85ee38c557cea77e80460c","abstract_canon_sha256":"cb651317b11b76a037d2541fd5757bbd817e10606bc332c65d91ec3abe82759e"},"schema_version":"1.0"},"canonical_sha256":"cb85677cb1a33f8b3ed13da25f32208f5e71bf4ae077c2f0ab3aa51493d1ac88","source":{"kind":"arxiv","id":"cond-mat/0306728","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"cond-mat/0306728","created_at":"2026-05-18T04:10:24Z"},{"alias_kind":"arxiv_version","alias_value":"cond-mat/0306728v1","created_at":"2026-05-18T04:10:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.cond-mat/0306728","created_at":"2026-05-18T04:10:24Z"},{"alias_kind":"pith_short_12","alias_value":"ZOCWO7FRUM7Y","created_at":"2026-05-18T12:25:52Z"},{"alias_kind":"pith_short_16","alias_value":"ZOCWO7FRUM7YWPWR","created_at":"2026-05-18T12:25:52Z"},{"alias_kind":"pith_short_8","alias_value":"ZOCWO7FR","created_at":"2026-05-18T12:25:52Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2003:ZOCWO7FRUM7YWPWRHWRF6MRAR5","target":"record","payload":{"canonical_record":{"source":{"id":"cond-mat/0306728","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"cond-mat.stat-mech","submitted_at":"2003-06-30T07:56:29Z","cross_cats_sorted":[],"title_canon_sha256":"b28f6598bc5fd2d0d5830ddd114feacec2093e374d85ee38c557cea77e80460c","abstract_canon_sha256":"cb651317b11b76a037d2541fd5757bbd817e10606bc332c65d91ec3abe82759e"},"schema_version":"1.0"},"canonical_sha256":"cb85677cb1a33f8b3ed13da25f32208f5e71bf4ae077c2f0ab3aa51493d1ac88","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:10:24.143107Z","signature_b64":"iEuWddSP0Edv9NHFCVk2l+HvjjF/kXLjjWltpYX5Wr+HQeh73kiTuAWvAZA693BF/lzuurzJmcRk43WfZLy+Bw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"cb85677cb1a33f8b3ed13da25f32208f5e71bf4ae077c2f0ab3aa51493d1ac88","last_reissued_at":"2026-05-18T04:10:24.142604Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:10:24.142604Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"cond-mat/0306728","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":"2026-05-18T04:10:24Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"jhrd5WCj5OYnp9rFSt6pe5JJOAMofJAIuPUaRFVlRTGYc1Wkv/d5bk0Clr4lYBZ4DyUE+W6Dyo4kZzSoq1cpAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T21:50:27.672940Z"},"content_sha256":"8ba2e0ad49aee40a929821011e577840d1d5c383167f74a4cb9e9efe756cb54d","schema_version":"1.0","event_id":"sha256:8ba2e0ad49aee40a929821011e577840d1d5c383167f74a4cb9e9efe756cb54d"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2003:ZOCWO7FRUM7YWPWRHWRF6MRAR5","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The concavity of entropy and extremum principles in thermodynamics","license":"","headline":"","cross_cats":[],"primary_cat":"cond-mat.stat-mech","authors_text":"P. V. Giaquinta, S. Prestipino","submitted_at":"2003-06-30T07:56:29Z","abstract_excerpt":"We revisit the concavity property of the thermodynamic entropy in order to formulate a general proof of the minimum energy principle as well as of other equivalent extremum principles that are valid for thermodynamic potentials and corresponding Massieu functions under different constraints. The current derivation aims at providing a coherent formal framework for such principles which may be also pedagogically useful as it fully exploits and highlights the equivalence between different schemes. We also elucidate the consequences of the extremum principles for the general shape of thermodynamic"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"cond-mat/0306728","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":"2026-05-18T04:10:24Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"uaUzNpAgwgYgPFLuRFXOp3pQvupIzT5kDMUAJqnqEr8u2wSRAUJ+N0XpMca88HwKMPZfQg+HZ8QUxWO1uBRwCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T21:50:27.673620Z"},"content_sha256":"59e2db62e4cea22b0dea42e37d22e30c1defb1f3e49d0c7d6608b1434d392479","schema_version":"1.0","event_id":"sha256:59e2db62e4cea22b0dea42e37d22e30c1defb1f3e49d0c7d6608b1434d392479"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/ZOCWO7FRUM7YWPWRHWRF6MRAR5/bundle.json","state_url":"https://pith.science/pith/ZOCWO7FRUM7YWPWRHWRF6MRAR5/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/ZOCWO7FRUM7YWPWRHWRF6MRAR5/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":"2026-05-25T21:50:27Z","links":{"resolver":"https://pith.science/pith/ZOCWO7FRUM7YWPWRHWRF6MRAR5","bundle":"https://pith.science/pith/ZOCWO7FRUM7YWPWRHWRF6MRAR5/bundle.json","state":"https://pith.science/pith/ZOCWO7FRUM7YWPWRHWRF6MRAR5/state.json","well_known_bundle":"https://pith.science/.well-known/pith/ZOCWO7FRUM7YWPWRHWRF6MRAR5/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2003:ZOCWO7FRUM7YWPWRHWRF6MRAR5","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":"cb651317b11b76a037d2541fd5757bbd817e10606bc332c65d91ec3abe82759e","cross_cats_sorted":[],"license":"","primary_cat":"cond-mat.stat-mech","submitted_at":"2003-06-30T07:56:29Z","title_canon_sha256":"b28f6598bc5fd2d0d5830ddd114feacec2093e374d85ee38c557cea77e80460c"},"schema_version":"1.0","source":{"id":"cond-mat/0306728","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"cond-mat/0306728","created_at":"2026-05-18T04:10:24Z"},{"alias_kind":"arxiv_version","alias_value":"cond-mat/0306728v1","created_at":"2026-05-18T04:10:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.cond-mat/0306728","created_at":"2026-05-18T04:10:24Z"},{"alias_kind":"pith_short_12","alias_value":"ZOCWO7FRUM7Y","created_at":"2026-05-18T12:25:52Z"},{"alias_kind":"pith_short_16","alias_value":"ZOCWO7FRUM7YWPWR","created_at":"2026-05-18T12:25:52Z"},{"alias_kind":"pith_short_8","alias_value":"ZOCWO7FR","created_at":"2026-05-18T12:25:52Z"}],"graph_snapshots":[{"event_id":"sha256:59e2db62e4cea22b0dea42e37d22e30c1defb1f3e49d0c7d6608b1434d392479","target":"graph","created_at":"2026-05-18T04:10:24Z","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 revisit the concavity property of the thermodynamic entropy in order to formulate a general proof of the minimum energy principle as well as of other equivalent extremum principles that are valid for thermodynamic potentials and corresponding Massieu functions under different constraints. The current derivation aims at providing a coherent formal framework for such principles which may be also pedagogically useful as it fully exploits and highlights the equivalence between different schemes. We also elucidate the consequences of the extremum principles for the general shape of thermodynamic","authors_text":"P. V. Giaquinta, S. Prestipino","cross_cats":[],"headline":"","license":"","primary_cat":"cond-mat.stat-mech","submitted_at":"2003-06-30T07:56:29Z","title":"The concavity of entropy and extremum principles in thermodynamics"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"cond-mat/0306728","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":"sha256:8ba2e0ad49aee40a929821011e577840d1d5c383167f74a4cb9e9efe756cb54d","target":"record","created_at":"2026-05-18T04:10:24Z","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":"cb651317b11b76a037d2541fd5757bbd817e10606bc332c65d91ec3abe82759e","cross_cats_sorted":[],"license":"","primary_cat":"cond-mat.stat-mech","submitted_at":"2003-06-30T07:56:29Z","title_canon_sha256":"b28f6598bc5fd2d0d5830ddd114feacec2093e374d85ee38c557cea77e80460c"},"schema_version":"1.0","source":{"id":"cond-mat/0306728","kind":"arxiv","version":1}},"canonical_sha256":"cb85677cb1a33f8b3ed13da25f32208f5e71bf4ae077c2f0ab3aa51493d1ac88","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"cb85677cb1a33f8b3ed13da25f32208f5e71bf4ae077c2f0ab3aa51493d1ac88","first_computed_at":"2026-05-18T04:10:24.142604Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:10:24.142604Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"iEuWddSP0Edv9NHFCVk2l+HvjjF/kXLjjWltpYX5Wr+HQeh73kiTuAWvAZA693BF/lzuurzJmcRk43WfZLy+Bw==","signature_status":"signed_v1","signed_at":"2026-05-18T04:10:24.143107Z","signed_message":"canonical_sha256_bytes"},"source_id":"cond-mat/0306728","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8ba2e0ad49aee40a929821011e577840d1d5c383167f74a4cb9e9efe756cb54d","sha256:59e2db62e4cea22b0dea42e37d22e30c1defb1f3e49d0c7d6608b1434d392479"],"state_sha256":"5cab613d90f7444b08344395bc27d608e26da05157adeea65ae74c3bfc24aca5"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"bhECbktLeDQfAdP8WQstVkxInuqmgu8e4CHppx+olI56hHjHfn+9XE2+EONwYCAdVarT9M+uCjaF9NNpFcYJCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-25T21:50:27.677217Z","bundle_sha256":"d35d86dbfbb142b763bc5aed8f6d6265abe867d9cd6204cabc73c7ad567361b8"}}