{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2007:OL6P4ZZXBMZTRXDYJ7YGL74VHB","short_pith_number":"pith:OL6P4ZZX","canonical_record":{"source":{"id":"0708.1866","kind":"arxiv","version":3},"metadata":{"license":"","primary_cat":"nlin.CD","submitted_at":"2007-08-14T11:39:45Z","cross_cats_sorted":["cond-mat.stat-mech","stat.ME"],"title_canon_sha256":"599825b4a9749a612cb9a11d92ca73e2ebad6db32ad9fa39cfac05c90b3af43d","abstract_canon_sha256":"f60d757b6aaddc130f6102e5be9a837e10cce8821cdb24fef8f29f07178999ba"},"schema_version":"1.0"},"canonical_sha256":"72fcfe67370b3338dc784ff065ff953840dc5c0f65a5abe1b65965ec0f959c09","source":{"kind":"arxiv","id":"0708.1866","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0708.1866","created_at":"2026-05-18T04:09:14Z"},{"alias_kind":"arxiv_version","alias_value":"0708.1866v3","created_at":"2026-05-18T04:09:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0708.1866","created_at":"2026-05-18T04:09:14Z"},{"alias_kind":"pith_short_12","alias_value":"OL6P4ZZXBMZT","created_at":"2026-05-18T12:25:55Z"},{"alias_kind":"pith_short_16","alias_value":"OL6P4ZZXBMZTRXDY","created_at":"2026-05-18T12:25:55Z"},{"alias_kind":"pith_short_8","alias_value":"OL6P4ZZX","created_at":"2026-05-18T12:25:55Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2007:OL6P4ZZXBMZTRXDYJ7YGL74VHB","target":"record","payload":{"canonical_record":{"source":{"id":"0708.1866","kind":"arxiv","version":3},"metadata":{"license":"","primary_cat":"nlin.CD","submitted_at":"2007-08-14T11:39:45Z","cross_cats_sorted":["cond-mat.stat-mech","stat.ME"],"title_canon_sha256":"599825b4a9749a612cb9a11d92ca73e2ebad6db32ad9fa39cfac05c90b3af43d","abstract_canon_sha256":"f60d757b6aaddc130f6102e5be9a837e10cce8821cdb24fef8f29f07178999ba"},"schema_version":"1.0"},"canonical_sha256":"72fcfe67370b3338dc784ff065ff953840dc5c0f65a5abe1b65965ec0f959c09","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:09:14.979184Z","signature_b64":"ahQv2EX2CwyBJcVoRgUaBPTGz549sAxJfq2mYHoiFgFtJ5jK6D6jPYsiBc4U/3cfeOZa3EW84h8OsYwsENOCDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"72fcfe67370b3338dc784ff065ff953840dc5c0f65a5abe1b65965ec0f959c09","last_reissued_at":"2026-05-18T04:09:14.978646Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:09:14.978646Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"0708.1866","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":"2026-05-18T04:09:14Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"igm0ZL9Im4EsEpfgcTw3+1j/ldTup3T7fkXqhs4HO4/fqQu1H976zv7HGYb9IGVFQPNtmAi+fcIAj18WNsXWBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T17:06:29.343855Z"},"content_sha256":"4592159d5a9813cd5cae37b592c56d870435fb128ffb35fabb101984f1a2a076","schema_version":"1.0","event_id":"sha256:4592159d5a9813cd5cae37b592c56d870435fb128ffb35fabb101984f1a2a076"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2007:OL6P4ZZXBMZTRXDYJ7YGL74VHB","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On the equivalence of the microcanonical and the canonical ensembles: a geometrical approach","license":"","headline":"","cross_cats":["cond-mat.stat-mech","stat.ME"],"primary_cat":"nlin.CD","authors_text":"Jaime Sanudo, Ricardo Lopez-Ruiz, Xavier Calbet","submitted_at":"2007-08-14T11:39:45Z","abstract_excerpt":"In this paper, we consider the volume enclosed by the microcanonical ensemble in phase space as a statistical ensemble. This can be interpreted as an intermediate image between the microcanonical and the canonical pictures. By maintaining the ergodic hypothesis over this ensemble, that is, the equiprobability of all its accessible states, the equivalence of this ensemble in the thermodynamic limit with the microcanonical and the canonical ensembles is suggested by means of geometrical arguments. The Maxwellian and the Boltzmann-Gibbs distributions are obtained from this formalism. In the appen"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0708.1866","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":"2026-05-18T04:09:14Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"QFW2dioQjQvYyM1Wp7zgDjEfVGkYRdaZTO+kPp6EDk+XZNFpytSas22JJ7SOiWQg6Xe18g/erY26U12Ovdv3Aw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T17:06:29.344187Z"},"content_sha256":"78b7d03bbfe6195bc681614d76e4bcf42ac13cef046af501289d3cf7dc53f937","schema_version":"1.0","event_id":"sha256:78b7d03bbfe6195bc681614d76e4bcf42ac13cef046af501289d3cf7dc53f937"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/OL6P4ZZXBMZTRXDYJ7YGL74VHB/bundle.json","state_url":"https://pith.science/pith/OL6P4ZZXBMZTRXDYJ7YGL74VHB/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/OL6P4ZZXBMZTRXDYJ7YGL74VHB/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":"2026-06-23T17:06:29Z","links":{"resolver":"https://pith.science/pith/OL6P4ZZXBMZTRXDYJ7YGL74VHB","bundle":"https://pith.science/pith/OL6P4ZZXBMZTRXDYJ7YGL74VHB/bundle.json","state":"https://pith.science/pith/OL6P4ZZXBMZTRXDYJ7YGL74VHB/state.json","well_known_bundle":"https://pith.science/.well-known/pith/OL6P4ZZXBMZTRXDYJ7YGL74VHB/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2007:OL6P4ZZXBMZTRXDYJ7YGL74VHB","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":"f60d757b6aaddc130f6102e5be9a837e10cce8821cdb24fef8f29f07178999ba","cross_cats_sorted":["cond-mat.stat-mech","stat.ME"],"license":"","primary_cat":"nlin.CD","submitted_at":"2007-08-14T11:39:45Z","title_canon_sha256":"599825b4a9749a612cb9a11d92ca73e2ebad6db32ad9fa39cfac05c90b3af43d"},"schema_version":"1.0","source":{"id":"0708.1866","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0708.1866","created_at":"2026-05-18T04:09:14Z"},{"alias_kind":"arxiv_version","alias_value":"0708.1866v3","created_at":"2026-05-18T04:09:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0708.1866","created_at":"2026-05-18T04:09:14Z"},{"alias_kind":"pith_short_12","alias_value":"OL6P4ZZXBMZT","created_at":"2026-05-18T12:25:55Z"},{"alias_kind":"pith_short_16","alias_value":"OL6P4ZZXBMZTRXDY","created_at":"2026-05-18T12:25:55Z"},{"alias_kind":"pith_short_8","alias_value":"OL6P4ZZX","created_at":"2026-05-18T12:25:55Z"}],"graph_snapshots":[{"event_id":"sha256:78b7d03bbfe6195bc681614d76e4bcf42ac13cef046af501289d3cf7dc53f937","target":"graph","created_at":"2026-05-18T04:09:14Z","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 consider the volume enclosed by the microcanonical ensemble in phase space as a statistical ensemble. This can be interpreted as an intermediate image between the microcanonical and the canonical pictures. By maintaining the ergodic hypothesis over this ensemble, that is, the equiprobability of all its accessible states, the equivalence of this ensemble in the thermodynamic limit with the microcanonical and the canonical ensembles is suggested by means of geometrical arguments. The Maxwellian and the Boltzmann-Gibbs distributions are obtained from this formalism. In the appen","authors_text":"Jaime Sanudo, Ricardo Lopez-Ruiz, Xavier Calbet","cross_cats":["cond-mat.stat-mech","stat.ME"],"headline":"","license":"","primary_cat":"nlin.CD","submitted_at":"2007-08-14T11:39:45Z","title":"On the equivalence of the microcanonical and the canonical ensembles: a geometrical approach"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0708.1866","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":"sha256:4592159d5a9813cd5cae37b592c56d870435fb128ffb35fabb101984f1a2a076","target":"record","created_at":"2026-05-18T04:09:14Z","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":"f60d757b6aaddc130f6102e5be9a837e10cce8821cdb24fef8f29f07178999ba","cross_cats_sorted":["cond-mat.stat-mech","stat.ME"],"license":"","primary_cat":"nlin.CD","submitted_at":"2007-08-14T11:39:45Z","title_canon_sha256":"599825b4a9749a612cb9a11d92ca73e2ebad6db32ad9fa39cfac05c90b3af43d"},"schema_version":"1.0","source":{"id":"0708.1866","kind":"arxiv","version":3}},"canonical_sha256":"72fcfe67370b3338dc784ff065ff953840dc5c0f65a5abe1b65965ec0f959c09","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"72fcfe67370b3338dc784ff065ff953840dc5c0f65a5abe1b65965ec0f959c09","first_computed_at":"2026-05-18T04:09:14.978646Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:09:14.978646Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ahQv2EX2CwyBJcVoRgUaBPTGz549sAxJfq2mYHoiFgFtJ5jK6D6jPYsiBc4U/3cfeOZa3EW84h8OsYwsENOCDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T04:09:14.979184Z","signed_message":"canonical_sha256_bytes"},"source_id":"0708.1866","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4592159d5a9813cd5cae37b592c56d870435fb128ffb35fabb101984f1a2a076","sha256:78b7d03bbfe6195bc681614d76e4bcf42ac13cef046af501289d3cf7dc53f937"],"state_sha256":"419bfae2464b4182992d0dd9b0b39afa73b489c1309af328f2d0289d3accc2ee"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"KCnVoY9g+68nUGCuxbopYoz4wI7um18WAYnDZZMtIO2SYfA4mxfBT9VzbvH+kJoBZLz6ogGdsmmbDDgANnHzCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-23T17:06:29.346022Z","bundle_sha256":"9da05d24f23397294af64473853c17a417e5b1c3d69179fda39f7a7244b8a475"}}