{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2004:QZ3KR7Q46WTONOWQPY2R6G672L","short_pith_number":"pith:QZ3KR7Q4","schema_version":"1.0","canonical_sha256":"8676a8fe1cf5a6e6bad07e351f1bdfd2c751b5cb445b76d928e9ca5f51dac2c5","source":{"kind":"arxiv","id":"hep-ph/0406163","version":2},"attestation_state":"computed","paper":{"title":"Three-loop Phi-derivable Approximation in QED","license":"","headline":"","cross_cats":[],"primary_cat":"hep-ph","authors_text":"Jens O. Andersen, Michael Strickland","submitted_at":"2004-06-15T14:13:35Z","abstract_excerpt":"In this paper we examine Phi-derivable approximations in QED. General theorems tell us that the gauge dependence of the n-loop Phi-derivable approximation shows up at order g^(2n) where g is the coupling constant. We consider the gauge dependence of the two-loop Phi-derivable approximation to the Debye mass and show that it is of order e^4 as expected. We solve the three-loop Phi-derivable approximation in QED by expanding sum-integrals in powers of e^2 and m/T, where m is the Debye mass which satisfies a variational gap equation. The results for the pressure and the Debye mass are accurate to"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"hep-ph/0406163","kind":"arxiv","version":2},"metadata":{"license":"","primary_cat":"hep-ph","submitted_at":"2004-06-15T14:13:35Z","cross_cats_sorted":[],"title_canon_sha256":"88d87d0d75bd1d77bdb075d6de1ee99af106aff4a09093286d40c32f1a5dc9b0","abstract_canon_sha256":"45b42b58bc120549559b0cf0a0050ef49c171409ddebf26f2f94f573f6f876e6"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-04T16:48:16.353631Z","signature_b64":"70YeJfggq5yPvSXcK1qOXPwbO9oDhSdL9EGBWZ4VjQ7zz8+l32Dnr6jfV5fykGcI5nChgGwFUpKUfvGk6A9SCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8676a8fe1cf5a6e6bad07e351f1bdfd2c751b5cb445b76d928e9ca5f51dac2c5","last_reissued_at":"2026-07-04T16:48:16.353246Z","signature_status":"signed_v1","first_computed_at":"2026-07-04T16:48:16.353246Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Three-loop Phi-derivable Approximation in QED","license":"","headline":"","cross_cats":[],"primary_cat":"hep-ph","authors_text":"Jens O. Andersen, Michael Strickland","submitted_at":"2004-06-15T14:13:35Z","abstract_excerpt":"In this paper we examine Phi-derivable approximations in QED. General theorems tell us that the gauge dependence of the n-loop Phi-derivable approximation shows up at order g^(2n) where g is the coupling constant. We consider the gauge dependence of the two-loop Phi-derivable approximation to the Debye mass and show that it is of order e^4 as expected. We solve the three-loop Phi-derivable approximation in QED by expanding sum-integrals in powers of e^2 and m/T, where m is the Debye mass which satisfies a variational gap equation. The results for the pressure and the Debye mass are accurate to"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"hep-ph/0406163","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/hep-ph/0406163/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"},"aliases":[{"alias_kind":"arxiv","alias_value":"hep-ph/0406163","created_at":"2026-07-04T16:48:16.353307+00:00"},{"alias_kind":"arxiv_version","alias_value":"hep-ph/0406163v2","created_at":"2026-07-04T16:48:16.353307+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.hep-ph/0406163","created_at":"2026-07-04T16:48:16.353307+00:00"},{"alias_kind":"pith_short_12","alias_value":"QZ3KR7Q46WTO","created_at":"2026-07-04T16:48:16.353307+00:00"},{"alias_kind":"pith_short_16","alias_value":"QZ3KR7Q46WTONOWQ","created_at":"2026-07-04T16:48:16.353307+00:00"},{"alias_kind":"pith_short_8","alias_value":"QZ3KR7Q4","created_at":"2026-07-04T16:48:16.353307+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2608.04102","citing_title":"Consistent Thermal Resummation and Phase Transitions with 2PI Methods","ref_index":71,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/QZ3KR7Q46WTONOWQPY2R6G672L","json":"https://pith.science/pith/QZ3KR7Q46WTONOWQPY2R6G672L.json","graph_json":"https://pith.science/api/pith-number/QZ3KR7Q46WTONOWQPY2R6G672L/graph.json","events_json":"https://pith.science/api/pith-number/QZ3KR7Q46WTONOWQPY2R6G672L/events.json","paper":"https://pith.science/paper/QZ3KR7Q4"},"agent_actions":{"view_html":"https://pith.science/pith/QZ3KR7Q46WTONOWQPY2R6G672L","download_json":"https://pith.science/pith/QZ3KR7Q46WTONOWQPY2R6G672L.json","view_paper":"https://pith.science/paper/QZ3KR7Q4","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=hep-ph/0406163&json=true","fetch_graph":"https://pith.science/api/pith-number/QZ3KR7Q46WTONOWQPY2R6G672L/graph.json","fetch_events":"https://pith.science/api/pith-number/QZ3KR7Q46WTONOWQPY2R6G672L/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/QZ3KR7Q46WTONOWQPY2R6G672L/action/timestamp_anchor","attest_storage":"https://pith.science/pith/QZ3KR7Q46WTONOWQPY2R6G672L/action/storage_attestation","attest_author":"https://pith.science/pith/QZ3KR7Q46WTONOWQPY2R6G672L/action/author_attestation","sign_citation":"https://pith.science/pith/QZ3KR7Q46WTONOWQPY2R6G672L/action/citation_signature","submit_replication":"https://pith.science/pith/QZ3KR7Q46WTONOWQPY2R6G672L/action/replication_record"}},"created_at":"2026-07-04T16:48:16.353307+00:00","updated_at":"2026-07-04T16:48:16.353307+00:00"}