{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2009:XR3KD64OMWDJ7QF5SU5VBITF4T","short_pith_number":"pith:XR3KD64O","canonical_record":{"source":{"id":"0906.3837","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2009-06-20T23:48:32Z","cross_cats_sorted":[],"title_canon_sha256":"9e79a38d7812cf0e77dc795b2375ca2da6e93981535124264e12704c93a24512","abstract_canon_sha256":"8a026c7bf33fb68f2fd84663b39ecf0d49ea0a4758b440303aa5827d71fcdc84"},"schema_version":"1.0"},"canonical_sha256":"bc76a1fb8e65869fc0bd953b50a265e4de621da52c27b113b349a33aa0c0ed05","source":{"kind":"arxiv","id":"0906.3837","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0906.3837","created_at":"2026-05-18T03:23:59Z"},{"alias_kind":"arxiv_version","alias_value":"0906.3837v3","created_at":"2026-05-18T03:23:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0906.3837","created_at":"2026-05-18T03:23:59Z"},{"alias_kind":"pith_short_12","alias_value":"XR3KD64OMWDJ","created_at":"2026-05-18T12:26:02Z"},{"alias_kind":"pith_short_16","alias_value":"XR3KD64OMWDJ7QF5","created_at":"2026-05-18T12:26:02Z"},{"alias_kind":"pith_short_8","alias_value":"XR3KD64O","created_at":"2026-05-18T12:26:02Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2009:XR3KD64OMWDJ7QF5SU5VBITF4T","target":"record","payload":{"canonical_record":{"source":{"id":"0906.3837","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2009-06-20T23:48:32Z","cross_cats_sorted":[],"title_canon_sha256":"9e79a38d7812cf0e77dc795b2375ca2da6e93981535124264e12704c93a24512","abstract_canon_sha256":"8a026c7bf33fb68f2fd84663b39ecf0d49ea0a4758b440303aa5827d71fcdc84"},"schema_version":"1.0"},"canonical_sha256":"bc76a1fb8e65869fc0bd953b50a265e4de621da52c27b113b349a33aa0c0ed05","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:23:59.293460Z","signature_b64":"jxuMyT9OYnJbM0gr6g4lovyFBfl1OcKQ8E7D6OJsmRHXJ/4rC51BhyP01v8V452czM5w/bHvGOcQhMJ5wSvHBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"bc76a1fb8e65869fc0bd953b50a265e4de621da52c27b113b349a33aa0c0ed05","last_reissued_at":"2026-05-18T03:23:59.292716Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:23:59.292716Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"0906.3837","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":"2026-05-18T03:23:59Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"89XT4pawv8hGw5NMC0U2h8eUxH9SHxwZt9UJEpR6jaND1oHlqa2n98C1tXsGl+gYbOW2c3vVLykCxCmKAcV8BA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-23T23:56:13.869187Z"},"content_sha256":"f951f315bd6d0d8abc6f906f90810ab4c92724423ed876d65958c44985495644","schema_version":"1.0","event_id":"sha256:f951f315bd6d0d8abc6f906f90810ab4c92724423ed876d65958c44985495644"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2009:XR3KD64OMWDJ7QF5SU5VBITF4T","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"One-loop corrections to the photon propagator in the curved-space QED","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"hep-th","authors_text":"Bruno Gon\\c{c}alves, Guilherme de Berredo-Peixoto, Ilya L. Shapiro","submitted_at":"2009-06-20T23:48:32Z","abstract_excerpt":"We calculate and discuss the one-loop corrections to the photon sector of QED interacting to a background gravitational field. At high energies the fermion field can be taken as massless and the quantum terms can be obtained by integrating conformal anomaly. We present a covariant local expression for the corresponding effective action, similar to the one obtained earlier for the gravitational sector. At the moderate energies the quantum terms can be obtained through the heat kernel method. In this way we derive the exact one-loop beta-function for the electric charge in the momentum subtracti"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0906.3837","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":"2026-05-18T03:23:59Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"i2wLsVtY3p4OVZwmrXjDDD7ZTnT7a39JONAcO+cnncm0dtkspsZIZ4WgYxERxulBPYDf5l7Pz3ypfeV8UCWPAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-23T23:56:13.869582Z"},"content_sha256":"63a998b2ed94b1c734107c72559aa66c1d3d2943b408ccc74bacf81aeae609ac","schema_version":"1.0","event_id":"sha256:63a998b2ed94b1c734107c72559aa66c1d3d2943b408ccc74bacf81aeae609ac"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/XR3KD64OMWDJ7QF5SU5VBITF4T/bundle.json","state_url":"https://pith.science/pith/XR3KD64OMWDJ7QF5SU5VBITF4T/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/XR3KD64OMWDJ7QF5SU5VBITF4T/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":"2026-05-23T23:56:13Z","links":{"resolver":"https://pith.science/pith/XR3KD64OMWDJ7QF5SU5VBITF4T","bundle":"https://pith.science/pith/XR3KD64OMWDJ7QF5SU5VBITF4T/bundle.json","state":"https://pith.science/pith/XR3KD64OMWDJ7QF5SU5VBITF4T/state.json","well_known_bundle":"https://pith.science/.well-known/pith/XR3KD64OMWDJ7QF5SU5VBITF4T/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2009:XR3KD64OMWDJ7QF5SU5VBITF4T","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":"8a026c7bf33fb68f2fd84663b39ecf0d49ea0a4758b440303aa5827d71fcdc84","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2009-06-20T23:48:32Z","title_canon_sha256":"9e79a38d7812cf0e77dc795b2375ca2da6e93981535124264e12704c93a24512"},"schema_version":"1.0","source":{"id":"0906.3837","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0906.3837","created_at":"2026-05-18T03:23:59Z"},{"alias_kind":"arxiv_version","alias_value":"0906.3837v3","created_at":"2026-05-18T03:23:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0906.3837","created_at":"2026-05-18T03:23:59Z"},{"alias_kind":"pith_short_12","alias_value":"XR3KD64OMWDJ","created_at":"2026-05-18T12:26:02Z"},{"alias_kind":"pith_short_16","alias_value":"XR3KD64OMWDJ7QF5","created_at":"2026-05-18T12:26:02Z"},{"alias_kind":"pith_short_8","alias_value":"XR3KD64O","created_at":"2026-05-18T12:26:02Z"}],"graph_snapshots":[{"event_id":"sha256:63a998b2ed94b1c734107c72559aa66c1d3d2943b408ccc74bacf81aeae609ac","target":"graph","created_at":"2026-05-18T03:23:59Z","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 calculate and discuss the one-loop corrections to the photon sector of QED interacting to a background gravitational field. At high energies the fermion field can be taken as massless and the quantum terms can be obtained by integrating conformal anomaly. We present a covariant local expression for the corresponding effective action, similar to the one obtained earlier for the gravitational sector. At the moderate energies the quantum terms can be obtained through the heat kernel method. In this way we derive the exact one-loop beta-function for the electric charge in the momentum subtracti","authors_text":"Bruno Gon\\c{c}alves, Guilherme de Berredo-Peixoto, Ilya L. Shapiro","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2009-06-20T23:48:32Z","title":"One-loop corrections to the photon propagator in the curved-space QED"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0906.3837","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:f951f315bd6d0d8abc6f906f90810ab4c92724423ed876d65958c44985495644","target":"record","created_at":"2026-05-18T03:23:59Z","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":"8a026c7bf33fb68f2fd84663b39ecf0d49ea0a4758b440303aa5827d71fcdc84","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2009-06-20T23:48:32Z","title_canon_sha256":"9e79a38d7812cf0e77dc795b2375ca2da6e93981535124264e12704c93a24512"},"schema_version":"1.0","source":{"id":"0906.3837","kind":"arxiv","version":3}},"canonical_sha256":"bc76a1fb8e65869fc0bd953b50a265e4de621da52c27b113b349a33aa0c0ed05","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"bc76a1fb8e65869fc0bd953b50a265e4de621da52c27b113b349a33aa0c0ed05","first_computed_at":"2026-05-18T03:23:59.292716Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:23:59.292716Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"jxuMyT9OYnJbM0gr6g4lovyFBfl1OcKQ8E7D6OJsmRHXJ/4rC51BhyP01v8V452czM5w/bHvGOcQhMJ5wSvHBw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:23:59.293460Z","signed_message":"canonical_sha256_bytes"},"source_id":"0906.3837","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f951f315bd6d0d8abc6f906f90810ab4c92724423ed876d65958c44985495644","sha256:63a998b2ed94b1c734107c72559aa66c1d3d2943b408ccc74bacf81aeae609ac"],"state_sha256":"1568fe63a4a7988259bc04ba495ba229b7a3b6a2a95b1b427504c99ce70dbf19"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"9IcPosnGmMu2T/k7WI59oetAvmjSJcsQ39CxMygP0S71tkdRy3rc8lVsVwkmQXAnR0uxiMKJX0HQRggpJPwZDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-23T23:56:13.872126Z","bundle_sha256":"8d634b7631a22df3cce62bb08da76e9bc32f4d3e3f007d247a91994ea0a9e9e5"}}