{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2025:RHTOD5CTXTEXNE3K43KLBDWF2Q","short_pith_number":"pith:RHTOD5CT","canonical_record":{"source":{"id":"2501.05192","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-ph","submitted_at":"2025-01-09T12:33:15Z","cross_cats_sorted":["nucl-th","physics.comp-ph"],"title_canon_sha256":"607f412294fb37d32f963569265420978a031bd49a1d38d63502a1ca6279b16c","abstract_canon_sha256":"8ac5929bfed3d11386eef11d17edd77a9926c8fc48853bde9d7e0bc4d1479951"},"schema_version":"1.0"},"canonical_sha256":"89e6e1f453bcc976936ae6d4b08ec5d42f3deab1aeccdcb4763d962e4083de2b","source":{"kind":"arxiv","id":"2501.05192","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2501.05192","created_at":"2026-07-05T09:59:05Z"},{"alias_kind":"arxiv_version","alias_value":"2501.05192v1","created_at":"2026-07-05T09:59:05Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2501.05192","created_at":"2026-07-05T09:59:05Z"},{"alias_kind":"pith_short_12","alias_value":"RHTOD5CTXTEX","created_at":"2026-07-05T09:59:05Z"},{"alias_kind":"pith_short_16","alias_value":"RHTOD5CTXTEXNE3K","created_at":"2026-07-05T09:59:05Z"},{"alias_kind":"pith_short_8","alias_value":"RHTOD5CT","created_at":"2026-07-05T09:59:05Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2025:RHTOD5CTXTEXNE3K43KLBDWF2Q","target":"record","payload":{"canonical_record":{"source":{"id":"2501.05192","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-ph","submitted_at":"2025-01-09T12:33:15Z","cross_cats_sorted":["nucl-th","physics.comp-ph"],"title_canon_sha256":"607f412294fb37d32f963569265420978a031bd49a1d38d63502a1ca6279b16c","abstract_canon_sha256":"8ac5929bfed3d11386eef11d17edd77a9926c8fc48853bde9d7e0bc4d1479951"},"schema_version":"1.0"},"canonical_sha256":"89e6e1f453bcc976936ae6d4b08ec5d42f3deab1aeccdcb4763d962e4083de2b","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T09:59:05.900371Z","signature_b64":"IgQyFNt54Pieg5J4Xhp+us/9y8rtu218efow1gTU5SC4c5l45UtT5kZVDc1vuBahuoGb7vpJmFPmYQVT+ttIDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"89e6e1f453bcc976936ae6d4b08ec5d42f3deab1aeccdcb4763d962e4083de2b","last_reissued_at":"2026-07-05T09:59:05.899915Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T09:59:05.899915Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2501.05192","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":"2026-07-05T09:59:05Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"EqeS5zMdhvmfQ/bIT3ieqnOvDX7N1X+hUkpuewFMl6FV7zkMhn9/CCZahc6efNd3tmh/RALEfsWLJ4kTKP19DA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-08T09:30:48.213058Z"},"content_sha256":"5d5f78e5e90db197a115e58b6b0f192f1d19513fa9f50cb333d2f2c604efaa38","schema_version":"1.0","event_id":"sha256:5d5f78e5e90db197a115e58b6b0f192f1d19513fa9f50cb333d2f2c604efaa38"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2025:RHTOD5CTXTEXNE3K43KLBDWF2Q","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On the Calculation of Pressure Derivatives in Mean-Field Thermal Field Theories","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["nucl-th","physics.comp-ph"],"primary_cat":"hep-ph","authors_text":"Hosein Gholami","submitted_at":"2025-01-09T12:33:15Z","abstract_excerpt":"Accurate determination of higher-order pressure derivatives with respect to temperature $T$ and chemical potential $\\mu$ is essential for analyzing critical phenomena, transport properties, and phase transitions in strongly interacting matter. However, standard numerical differentiation methods often suffer from large numerical instabilities, especially in more complex mean-field thermal field theories. In this work, we present an approach that systematically derives symbolic expressions for these higher-order derivatives, bypassing the numerical instabilities commonly encountered in conventio"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2501.05192","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2501.05192/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-05T09:59:05Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"qmqVrjIrZ6QQNCI3MsbRmOux5SKebRTYOiZ0het1viaFCP4BiRVkxg7fi8I/tYOQBu4QMTqn7WJyl/9/LypWCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-08T09:30:48.213980Z"},"content_sha256":"9bd722619699a804ee2ff1d6bda04f3b56baaa70f1bdae7a72e79f07a933d751","schema_version":"1.0","event_id":"sha256:9bd722619699a804ee2ff1d6bda04f3b56baaa70f1bdae7a72e79f07a933d751"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/RHTOD5CTXTEXNE3K43KLBDWF2Q/bundle.json","state_url":"https://pith.science/pith/RHTOD5CTXTEXNE3K43KLBDWF2Q/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/RHTOD5CTXTEXNE3K43KLBDWF2Q/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":"2026-08-08T09:30:48Z","links":{"resolver":"https://pith.science/pith/RHTOD5CTXTEXNE3K43KLBDWF2Q","bundle":"https://pith.science/pith/RHTOD5CTXTEXNE3K43KLBDWF2Q/bundle.json","state":"https://pith.science/pith/RHTOD5CTXTEXNE3K43KLBDWF2Q/state.json","well_known_bundle":"https://pith.science/.well-known/pith/RHTOD5CTXTEXNE3K43KLBDWF2Q/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:RHTOD5CTXTEXNE3K43KLBDWF2Q","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":"8ac5929bfed3d11386eef11d17edd77a9926c8fc48853bde9d7e0bc4d1479951","cross_cats_sorted":["nucl-th","physics.comp-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-ph","submitted_at":"2025-01-09T12:33:15Z","title_canon_sha256":"607f412294fb37d32f963569265420978a031bd49a1d38d63502a1ca6279b16c"},"schema_version":"1.0","source":{"id":"2501.05192","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2501.05192","created_at":"2026-07-05T09:59:05Z"},{"alias_kind":"arxiv_version","alias_value":"2501.05192v1","created_at":"2026-07-05T09:59:05Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2501.05192","created_at":"2026-07-05T09:59:05Z"},{"alias_kind":"pith_short_12","alias_value":"RHTOD5CTXTEX","created_at":"2026-07-05T09:59:05Z"},{"alias_kind":"pith_short_16","alias_value":"RHTOD5CTXTEXNE3K","created_at":"2026-07-05T09:59:05Z"},{"alias_kind":"pith_short_8","alias_value":"RHTOD5CT","created_at":"2026-07-05T09:59:05Z"}],"graph_snapshots":[{"event_id":"sha256:9bd722619699a804ee2ff1d6bda04f3b56baaa70f1bdae7a72e79f07a933d751","target":"graph","created_at":"2026-07-05T09:59:05Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2501.05192/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Accurate determination of higher-order pressure derivatives with respect to temperature $T$ and chemical potential $\\mu$ is essential for analyzing critical phenomena, transport properties, and phase transitions in strongly interacting matter. However, standard numerical differentiation methods often suffer from large numerical instabilities, especially in more complex mean-field thermal field theories. In this work, we present an approach that systematically derives symbolic expressions for these higher-order derivatives, bypassing the numerical instabilities commonly encountered in conventio","authors_text":"Hosein Gholami","cross_cats":["nucl-th","physics.comp-ph"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-ph","submitted_at":"2025-01-09T12:33:15Z","title":"On the Calculation of Pressure Derivatives in Mean-Field Thermal Field Theories"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2501.05192","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":"sha256:5d5f78e5e90db197a115e58b6b0f192f1d19513fa9f50cb333d2f2c604efaa38","target":"record","created_at":"2026-07-05T09:59:05Z","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":"8ac5929bfed3d11386eef11d17edd77a9926c8fc48853bde9d7e0bc4d1479951","cross_cats_sorted":["nucl-th","physics.comp-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-ph","submitted_at":"2025-01-09T12:33:15Z","title_canon_sha256":"607f412294fb37d32f963569265420978a031bd49a1d38d63502a1ca6279b16c"},"schema_version":"1.0","source":{"id":"2501.05192","kind":"arxiv","version":1}},"canonical_sha256":"89e6e1f453bcc976936ae6d4b08ec5d42f3deab1aeccdcb4763d962e4083de2b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"89e6e1f453bcc976936ae6d4b08ec5d42f3deab1aeccdcb4763d962e4083de2b","first_computed_at":"2026-07-05T09:59:05.899915Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T09:59:05.899915Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"IgQyFNt54Pieg5J4Xhp+us/9y8rtu218efow1gTU5SC4c5l45UtT5kZVDc1vuBahuoGb7vpJmFPmYQVT+ttIDw==","signature_status":"signed_v1","signed_at":"2026-07-05T09:59:05.900371Z","signed_message":"canonical_sha256_bytes"},"source_id":"2501.05192","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5d5f78e5e90db197a115e58b6b0f192f1d19513fa9f50cb333d2f2c604efaa38","sha256:9bd722619699a804ee2ff1d6bda04f3b56baaa70f1bdae7a72e79f07a933d751"],"state_sha256":"93a21399e73217da75391381b84177fedc377b11b8615186fdc441a8dd776099"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"KUVYj8/rNPQsdLg3knrot31SYqtFUXZIfyN0Rsik4nMwui0jAP6dLF5turH2nVJB0vHm6MIhpX50BV7P58miAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-08T09:30:48.288734Z","bundle_sha256":"950dfaf241542093d4c1404710d66f559ed98c111d7ada35efc37c1cd272eeaf"}}