{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2010:GSKGBZP5M4X5TSJLINJCLJV2TT","short_pith_number":"pith:GSKGBZP5","canonical_record":{"source":{"id":"1004.5480","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2010-04-30T09:22:59Z","cross_cats_sorted":["math-ph","math.MP","nlin.CD"],"title_canon_sha256":"1480c8c7b7d5aa01881e34c0e9820aba6e73aec93ee8a012a31bc89dddec08ca","abstract_canon_sha256":"bb429196c0d73fa4b7d9fabb6d0e77034251c826e55b829065f2a5f059c164ec"},"schema_version":"1.0"},"canonical_sha256":"349460e5fd672fd9c92b435225a6ba9cf9f7944a10b4985a17a437e760e30417","source":{"kind":"arxiv","id":"1004.5480","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1004.5480","created_at":"2026-05-18T02:07:44Z"},{"alias_kind":"arxiv_version","alias_value":"1004.5480v3","created_at":"2026-05-18T02:07:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1004.5480","created_at":"2026-05-18T02:07:44Z"},{"alias_kind":"pith_short_12","alias_value":"GSKGBZP5M4X5","created_at":"2026-05-18T12:26:07Z"},{"alias_kind":"pith_short_16","alias_value":"GSKGBZP5M4X5TSJL","created_at":"2026-05-18T12:26:07Z"},{"alias_kind":"pith_short_8","alias_value":"GSKGBZP5","created_at":"2026-05-18T12:26:07Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2010:GSKGBZP5M4X5TSJLINJCLJV2TT","target":"record","payload":{"canonical_record":{"source":{"id":"1004.5480","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2010-04-30T09:22:59Z","cross_cats_sorted":["math-ph","math.MP","nlin.CD"],"title_canon_sha256":"1480c8c7b7d5aa01881e34c0e9820aba6e73aec93ee8a012a31bc89dddec08ca","abstract_canon_sha256":"bb429196c0d73fa4b7d9fabb6d0e77034251c826e55b829065f2a5f059c164ec"},"schema_version":"1.0"},"canonical_sha256":"349460e5fd672fd9c92b435225a6ba9cf9f7944a10b4985a17a437e760e30417","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:07:44.589974Z","signature_b64":"oTWhvOlNKxlGGTIY3nKVaPT9tN1STPeuiEcJOBzHEk6MV0qhAy3YrIvXxO1uKeATxppXRw/NeibuqF5FzlJUAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"349460e5fd672fd9c92b435225a6ba9cf9f7944a10b4985a17a437e760e30417","last_reissued_at":"2026-05-18T02:07:44.589183Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:07:44.589183Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1004.5480","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":"2026-05-18T02:07:44Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"E+RxQwfAGNmXZ8EcmDkids6nqFVcSaTl3EvTrUxymaAuL5r/5uWkG1bLRjLAIwgL2YpCtjMEorRrDqF40KXdCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-19T16:25:44.446229Z"},"content_sha256":"47f61ce75e424df7b2138ff29080f894cde7ca56decc217a0a9c97a99a14a26b","schema_version":"1.0","event_id":"sha256:47f61ce75e424df7b2138ff29080f894cde7ca56decc217a0a9c97a99a14a26b"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2010:GSKGBZP5M4X5TSJLINJCLJV2TT","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Microcanonical Entropy and Dynamical Measure of Temperature for Systems with Two First Integrals","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP","nlin.CD"],"primary_cat":"cond-mat.stat-mech","authors_text":"Italy), Roberto Franzosi (C.N.I.S.M., University of Florence","submitted_at":"2010-04-30T09:22:59Z","abstract_excerpt":"We consider a generic classical many particle system described by an autonomous Hamiltonian $H(x^{_1},...,x^{_{N+2}})$ which, in addition, has a conserved quantity $V(x^{_1},...,x^{_{N+2}})=v$, so that the Poisson bracket $\\{H,V \\}$ vanishes. We derive in detail the microcanonical expressions for entropy and temperature. We show that both of these quantities depend on multidimensional integrals over submanifolds given by the intersection of the constant energy hypersurfaces with those defined by $V(x^{_1},...,x^{_{N+2}})=v$. We show that temperature and higher order derivatives of entropy are "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1004.5480","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":"2026-05-18T02:07:44Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"AYtrdEOHW/JzX84gyAj2MMfJtBP/sh4mEUb8y3HFV9fuczYnBGZOfqZJQKh14nvVo+hOg1L9UCDGb45L/M3yCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-19T16:25:44.446808Z"},"content_sha256":"7ff2f16d6c83d6b3b5bd56aa3465322308fad4e08fd2769f560a27eb3c936286","schema_version":"1.0","event_id":"sha256:7ff2f16d6c83d6b3b5bd56aa3465322308fad4e08fd2769f560a27eb3c936286"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/GSKGBZP5M4X5TSJLINJCLJV2TT/bundle.json","state_url":"https://pith.science/pith/GSKGBZP5M4X5TSJLINJCLJV2TT/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/GSKGBZP5M4X5TSJLINJCLJV2TT/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":"2026-05-19T16:25:44Z","links":{"resolver":"https://pith.science/pith/GSKGBZP5M4X5TSJLINJCLJV2TT","bundle":"https://pith.science/pith/GSKGBZP5M4X5TSJLINJCLJV2TT/bundle.json","state":"https://pith.science/pith/GSKGBZP5M4X5TSJLINJCLJV2TT/state.json","well_known_bundle":"https://pith.science/.well-known/pith/GSKGBZP5M4X5TSJLINJCLJV2TT/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:GSKGBZP5M4X5TSJLINJCLJV2TT","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":"bb429196c0d73fa4b7d9fabb6d0e77034251c826e55b829065f2a5f059c164ec","cross_cats_sorted":["math-ph","math.MP","nlin.CD"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2010-04-30T09:22:59Z","title_canon_sha256":"1480c8c7b7d5aa01881e34c0e9820aba6e73aec93ee8a012a31bc89dddec08ca"},"schema_version":"1.0","source":{"id":"1004.5480","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1004.5480","created_at":"2026-05-18T02:07:44Z"},{"alias_kind":"arxiv_version","alias_value":"1004.5480v3","created_at":"2026-05-18T02:07:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1004.5480","created_at":"2026-05-18T02:07:44Z"},{"alias_kind":"pith_short_12","alias_value":"GSKGBZP5M4X5","created_at":"2026-05-18T12:26:07Z"},{"alias_kind":"pith_short_16","alias_value":"GSKGBZP5M4X5TSJL","created_at":"2026-05-18T12:26:07Z"},{"alias_kind":"pith_short_8","alias_value":"GSKGBZP5","created_at":"2026-05-18T12:26:07Z"}],"graph_snapshots":[{"event_id":"sha256:7ff2f16d6c83d6b3b5bd56aa3465322308fad4e08fd2769f560a27eb3c936286","target":"graph","created_at":"2026-05-18T02:07:44Z","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 consider a generic classical many particle system described by an autonomous Hamiltonian $H(x^{_1},...,x^{_{N+2}})$ which, in addition, has a conserved quantity $V(x^{_1},...,x^{_{N+2}})=v$, so that the Poisson bracket $\\{H,V \\}$ vanishes. We derive in detail the microcanonical expressions for entropy and temperature. We show that both of these quantities depend on multidimensional integrals over submanifolds given by the intersection of the constant energy hypersurfaces with those defined by $V(x^{_1},...,x^{_{N+2}})=v$. We show that temperature and higher order derivatives of entropy are ","authors_text":"Italy), Roberto Franzosi (C.N.I.S.M., University of Florence","cross_cats":["math-ph","math.MP","nlin.CD"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2010-04-30T09:22:59Z","title":"Microcanonical Entropy and Dynamical Measure of Temperature for Systems with Two First Integrals"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1004.5480","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":"sha256:47f61ce75e424df7b2138ff29080f894cde7ca56decc217a0a9c97a99a14a26b","target":"record","created_at":"2026-05-18T02:07:44Z","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":"bb429196c0d73fa4b7d9fabb6d0e77034251c826e55b829065f2a5f059c164ec","cross_cats_sorted":["math-ph","math.MP","nlin.CD"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2010-04-30T09:22:59Z","title_canon_sha256":"1480c8c7b7d5aa01881e34c0e9820aba6e73aec93ee8a012a31bc89dddec08ca"},"schema_version":"1.0","source":{"id":"1004.5480","kind":"arxiv","version":3}},"canonical_sha256":"349460e5fd672fd9c92b435225a6ba9cf9f7944a10b4985a17a437e760e30417","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"349460e5fd672fd9c92b435225a6ba9cf9f7944a10b4985a17a437e760e30417","first_computed_at":"2026-05-18T02:07:44.589183Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:07:44.589183Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"oTWhvOlNKxlGGTIY3nKVaPT9tN1STPeuiEcJOBzHEk6MV0qhAy3YrIvXxO1uKeATxppXRw/NeibuqF5FzlJUAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:07:44.589974Z","signed_message":"canonical_sha256_bytes"},"source_id":"1004.5480","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:47f61ce75e424df7b2138ff29080f894cde7ca56decc217a0a9c97a99a14a26b","sha256:7ff2f16d6c83d6b3b5bd56aa3465322308fad4e08fd2769f560a27eb3c936286"],"state_sha256":"9015c1c35d7eb4057989e729bf1c05b5f24751788a9af4c341932afc7c928093"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"t+O7DP0LG6f8j3lLGtdeLtZUTnuM3IAUE4p7Fz1SYg56sWu5V3pr53Ez5T85CaSZak0wzSFnI0qLfG/BxKtUCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-19T16:25:44.449164Z","bundle_sha256":"bf607890ee8cacd7660cfde125257d4ef5097ef3ae1249b3b0df9b36cd4f5481"}}