{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:JLDXNUIKZRWOY4DTXT474SOUIT","short_pith_number":"pith:JLDXNUIK","canonical_record":{"source":{"id":"2604.13636","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2026-04-15T09:03:22Z","cross_cats_sorted":[],"title_canon_sha256":"21cef0afb7491d69c7b0c8224dde6fd6d7d9e9eb90d92db0098aa7136c0b27c5","abstract_canon_sha256":"228974143529b452d8e3936670178217395d39fcf934659b16b5d3cf982f0fb5"},"schema_version":"1.0"},"canonical_sha256":"4ac776d10acc6cec7073bcf9fe49d444cf3273b57e9d6ce12ef4fa06a2209ce8","source":{"kind":"arxiv","id":"2604.13636","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2604.13636","created_at":"2026-06-09T02:08:42Z"},{"alias_kind":"arxiv_version","alias_value":"2604.13636v2","created_at":"2026-06-09T02:08:42Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2604.13636","created_at":"2026-06-09T02:08:42Z"},{"alias_kind":"pith_short_12","alias_value":"JLDXNUIKZRWO","created_at":"2026-06-09T02:08:42Z"},{"alias_kind":"pith_short_16","alias_value":"JLDXNUIKZRWOY4DT","created_at":"2026-06-09T02:08:42Z"},{"alias_kind":"pith_short_8","alias_value":"JLDXNUIK","created_at":"2026-06-09T02:08:42Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:JLDXNUIKZRWOY4DTXT474SOUIT","target":"record","payload":{"canonical_record":{"source":{"id":"2604.13636","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2026-04-15T09:03:22Z","cross_cats_sorted":[],"title_canon_sha256":"21cef0afb7491d69c7b0c8224dde6fd6d7d9e9eb90d92db0098aa7136c0b27c5","abstract_canon_sha256":"228974143529b452d8e3936670178217395d39fcf934659b16b5d3cf982f0fb5"},"schema_version":"1.0"},"canonical_sha256":"4ac776d10acc6cec7073bcf9fe49d444cf3273b57e9d6ce12ef4fa06a2209ce8","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-09T02:08:42.244439Z","signature_b64":"GR+zGL6cMHZlyirO3kaAMyRxIWmPazxEvvDk8H+roWfSWvFiNNp//Pw3ahE8p4kEE3x4tJGmrYgNQ8VZK9WpDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4ac776d10acc6cec7073bcf9fe49d444cf3273b57e9d6ce12ef4fa06a2209ce8","last_reissued_at":"2026-06-09T02:08:42.243526Z","signature_status":"signed_v1","first_computed_at":"2026-06-09T02:08:42.243526Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2604.13636","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-06-09T02:08:42Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"c2nVbKxuebrDGOVI4XnD7pnbKXAuY6ch/qO4PDb/5Jle9tT+V2xYfSq4ugtglmdWKMfqdoSGHN/EKGx2DlzcDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-07T15:46:48.912056Z"},"content_sha256":"96027152d15c9670fefd1dbdc8cf9e387d5dd98b60ea4fccb55a8ceefb478376","schema_version":"1.0","event_id":"sha256:96027152d15c9670fefd1dbdc8cf9e387d5dd98b60ea4fccb55a8ceefb478376"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:JLDXNUIKZRWOY4DTXT474SOUIT","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Euler-Heisenberg actions in higher dimensions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"Schwinger's proper-time method extends to higher dimensions, yielding a closed-form Euler-Heisenberg action in six-dimensional QED.","cross_cats":[],"primary_cat":"hep-th","authors_text":"Sergei M. Kuzenko, Terry Hatzis","submitted_at":"2026-04-15T09:03:22Z","abstract_excerpt":"We extend Schwinger's proper-time formalism to provide a method for computing the one-loop effective action for both spinor and scalar quantum electrodynamics in $d=2n>4$ dimensions. We give the closed form expression for the higher-dimensional Euler-Heisenberg Lagrangian, and extract its weak-field approximation in 6, 8 and 10 dimensions. A subsequent analysis of pair production in $d$ dimensions is also given. In the $d=6$ case, we present a composite conformal primary field of dimension $+6$ which determines the contribution of the electromagnetic field to the Weyl anomaly in curved space."},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"The closed form expression for the six-dimensional Euler-Heisenberg action is given, along with a subsequent analysis of pair production in d dimensions. In the d=6 case, we present a composite conformal primary field of dimension +6 which determines the contribution of the electromagnetic field to the Weyl anomaly in curved space.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"The extension of Schwinger's proper-time formalism to d=2n>4 dimensions remains valid and free of new divergences or regularization artifacts that would invalidate the closed-form result.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"Closed-form expression for the six-dimensional Euler-Heisenberg action in QED is derived via extended proper-time methods, with pair production analysis in d dimensions and a dimension-6 conformal primary determining the electromagnetic contribution to the Weyl anomaly.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"Schwinger's proper-time method extends to higher dimensions, yielding a closed-form Euler-Heisenberg action in six-dimensional QED.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"a2571a0a1a17c7bd181ecc1bb29770997c79140f875006f8f6769dee5618601d"},"source":{"id":"2604.13636","kind":"arxiv","version":2},"verdict":{"id":"242479d3-db58-4267-8ee3-df8e052f680b","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-10T13:16:29.817072Z","strongest_claim":"The closed form expression for the six-dimensional Euler-Heisenberg action is given, along with a subsequent analysis of pair production in d dimensions. In the d=6 case, we present a composite conformal primary field of dimension +6 which determines the contribution of the electromagnetic field to the Weyl anomaly in curved space.","one_line_summary":"Closed-form expression for the six-dimensional Euler-Heisenberg action in QED is derived via extended proper-time methods, with pair production analysis in d dimensions and a dimension-6 conformal primary determining the electromagnetic contribution to the Weyl anomaly.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"The extension of Schwinger's proper-time formalism to d=2n>4 dimensions remains valid and free of new divergences or regularization artifacts that would invalidate the closed-form result.","pith_extraction_headline":"Schwinger's proper-time method extends to higher dimensions, yielding a closed-form Euler-Heisenberg action in six-dimensional QED."},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2604.13636/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":"242479d3-db58-4267-8ee3-df8e052f680b"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-06-09T02:08:42Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Uf2AL7wJU7OBg19Exilv5JgVrK6oV8oSlPPpIeyrfejy3RcOhMZvVZ84/x9LtVdsQ5jxuehkwVJsIfG13hO1CQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-07T15:46:48.912531Z"},"content_sha256":"0e255ea29b1c9243b257c7fc7847c05090c1f595a7e165115ce0036d35680591","schema_version":"1.0","event_id":"sha256:0e255ea29b1c9243b257c7fc7847c05090c1f595a7e165115ce0036d35680591"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/JLDXNUIKZRWOY4DTXT474SOUIT/bundle.json","state_url":"https://pith.science/pith/JLDXNUIKZRWOY4DTXT474SOUIT/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/JLDXNUIKZRWOY4DTXT474SOUIT/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":"2026-07-07T15:46:48Z","links":{"resolver":"https://pith.science/pith/JLDXNUIKZRWOY4DTXT474SOUIT","bundle":"https://pith.science/pith/JLDXNUIKZRWOY4DTXT474SOUIT/bundle.json","state":"https://pith.science/pith/JLDXNUIKZRWOY4DTXT474SOUIT/state.json","well_known_bundle":"https://pith.science/.well-known/pith/JLDXNUIKZRWOY4DTXT474SOUIT/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:JLDXNUIKZRWOY4DTXT474SOUIT","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":"228974143529b452d8e3936670178217395d39fcf934659b16b5d3cf982f0fb5","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2026-04-15T09:03:22Z","title_canon_sha256":"21cef0afb7491d69c7b0c8224dde6fd6d7d9e9eb90d92db0098aa7136c0b27c5"},"schema_version":"1.0","source":{"id":"2604.13636","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2604.13636","created_at":"2026-06-09T02:08:42Z"},{"alias_kind":"arxiv_version","alias_value":"2604.13636v2","created_at":"2026-06-09T02:08:42Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2604.13636","created_at":"2026-06-09T02:08:42Z"},{"alias_kind":"pith_short_12","alias_value":"JLDXNUIKZRWO","created_at":"2026-06-09T02:08:42Z"},{"alias_kind":"pith_short_16","alias_value":"JLDXNUIKZRWOY4DT","created_at":"2026-06-09T02:08:42Z"},{"alias_kind":"pith_short_8","alias_value":"JLDXNUIK","created_at":"2026-06-09T02:08:42Z"}],"graph_snapshots":[{"event_id":"sha256:0e255ea29b1c9243b257c7fc7847c05090c1f595a7e165115ce0036d35680591","target":"graph","created_at":"2026-06-09T02:08:42Z","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":4,"items":[{"attestation":"unclaimed","claim_id":"C1","kind":"strongest_claim","source":"verdict.strongest_claim","status":"machine_extracted","text":"The closed form expression for the six-dimensional Euler-Heisenberg action is given, along with a subsequent analysis of pair production in d dimensions. In the d=6 case, we present a composite conformal primary field of dimension +6 which determines the contribution of the electromagnetic field to the Weyl anomaly in curved space."},{"attestation":"unclaimed","claim_id":"C2","kind":"weakest_assumption","source":"verdict.weakest_assumption","status":"machine_extracted","text":"The extension of Schwinger's proper-time formalism to d=2n>4 dimensions remains valid and free of new divergences or regularization artifacts that would invalidate the closed-form result."},{"attestation":"unclaimed","claim_id":"C3","kind":"one_line_summary","source":"verdict.one_line_summary","status":"machine_extracted","text":"Closed-form expression for the six-dimensional Euler-Heisenberg action in QED is derived via extended proper-time methods, with pair production analysis in d dimensions and a dimension-6 conformal primary determining the electromagnetic contribution to the Weyl anomaly."},{"attestation":"unclaimed","claim_id":"C4","kind":"headline","source":"verdict.pith_extraction.headline","status":"machine_extracted","text":"Schwinger's proper-time method extends to higher dimensions, yielding a closed-form Euler-Heisenberg action in six-dimensional QED."}],"snapshot_sha256":"a2571a0a1a17c7bd181ecc1bb29770997c79140f875006f8f6769dee5618601d"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2604.13636/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We extend Schwinger's proper-time formalism to provide a method for computing the one-loop effective action for both spinor and scalar quantum electrodynamics in $d=2n>4$ dimensions. We give the closed form expression for the higher-dimensional Euler-Heisenberg Lagrangian, and extract its weak-field approximation in 6, 8 and 10 dimensions. A subsequent analysis of pair production in $d$ dimensions is also given. In the $d=6$ case, we present a composite conformal primary field of dimension $+6$ which determines the contribution of the electromagnetic field to the Weyl anomaly in curved space.","authors_text":"Sergei M. Kuzenko, Terry Hatzis","cross_cats":[],"headline":"Schwinger's proper-time method extends to higher dimensions, yielding a closed-form Euler-Heisenberg action in six-dimensional QED.","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2026-04-15T09:03:22Z","title":"Euler-Heisenberg actions in higher dimensions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2604.13636","kind":"arxiv","version":2},"verdict":{"created_at":"2026-05-10T13:16:29.817072Z","id":"242479d3-db58-4267-8ee3-df8e052f680b","model_set":{"reader":"grok-4.3"},"one_line_summary":"Closed-form expression for the six-dimensional Euler-Heisenberg action in QED is derived via extended proper-time methods, with pair production analysis in d dimensions and a dimension-6 conformal primary determining the electromagnetic contribution to the Weyl anomaly.","pipeline_version":"pith-pipeline@v0.9.0","pith_extraction_headline":"Schwinger's proper-time method extends to higher dimensions, yielding a closed-form Euler-Heisenberg action in six-dimensional QED.","strongest_claim":"The closed form expression for the six-dimensional Euler-Heisenberg action is given, along with a subsequent analysis of pair production in d dimensions. In the d=6 case, we present a composite conformal primary field of dimension +6 which determines the contribution of the electromagnetic field to the Weyl anomaly in curved space.","weakest_assumption":"The extension of Schwinger's proper-time formalism to d=2n>4 dimensions remains valid and free of new divergences or regularization artifacts that would invalidate the closed-form result."}},"verdict_id":"242479d3-db58-4267-8ee3-df8e052f680b"}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:96027152d15c9670fefd1dbdc8cf9e387d5dd98b60ea4fccb55a8ceefb478376","target":"record","created_at":"2026-06-09T02:08:42Z","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":"228974143529b452d8e3936670178217395d39fcf934659b16b5d3cf982f0fb5","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2026-04-15T09:03:22Z","title_canon_sha256":"21cef0afb7491d69c7b0c8224dde6fd6d7d9e9eb90d92db0098aa7136c0b27c5"},"schema_version":"1.0","source":{"id":"2604.13636","kind":"arxiv","version":2}},"canonical_sha256":"4ac776d10acc6cec7073bcf9fe49d444cf3273b57e9d6ce12ef4fa06a2209ce8","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4ac776d10acc6cec7073bcf9fe49d444cf3273b57e9d6ce12ef4fa06a2209ce8","first_computed_at":"2026-06-09T02:08:42.243526Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-09T02:08:42.243526Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"GR+zGL6cMHZlyirO3kaAMyRxIWmPazxEvvDk8H+roWfSWvFiNNp//Pw3ahE8p4kEE3x4tJGmrYgNQ8VZK9WpDA==","signature_status":"signed_v1","signed_at":"2026-06-09T02:08:42.244439Z","signed_message":"canonical_sha256_bytes"},"source_id":"2604.13636","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:96027152d15c9670fefd1dbdc8cf9e387d5dd98b60ea4fccb55a8ceefb478376","sha256:0e255ea29b1c9243b257c7fc7847c05090c1f595a7e165115ce0036d35680591"],"state_sha256":"e434e130e30596f5788ba788237d9a7467b1a4b368dd757a57c31b8c675e35eb"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"jQIV4Q8JQ9vQP26tE1xS16Gjcz7+H7AG22NLtjj7Pa3Bz/C843hq2WWkdQ5BOXKJwJZgbiFbp4zqQ1/aWwi2BA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-07T15:46:48.914671Z","bundle_sha256":"3c8ccd114c6205f67c8c26cc400cab46689f4adc830e532981743902920e536d"}}