{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2001:6EBSCUKUGCWVHBX4RQ32ITQY62","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":"066426d712c4618a5f2e7d43460c2c7e890ede2696220f4ea4dcdcb2389ffdd4","cross_cats_sorted":["gr-qc","hep-th","math.AP","math.MP","math.SP"],"license":"","primary_cat":"math-ph","submitted_at":"2001-07-19T19:25:32Z","title_canon_sha256":"9f1c74bed953ea3b50b25e26ad52a74f70ff602b81cdda02a1d9e95db58c057a"},"schema_version":"1.0","source":{"id":"math-ph/0107018","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math-ph/0107018","created_at":"2026-07-04T16:28:14Z"},{"alias_kind":"arxiv_version","alias_value":"math-ph/0107018v1","created_at":"2026-07-04T16:28:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math-ph/0107018","created_at":"2026-07-04T16:28:14Z"},{"alias_kind":"pith_short_12","alias_value":"6EBSCUKUGCWV","created_at":"2026-07-04T16:28:14Z"},{"alias_kind":"pith_short_16","alias_value":"6EBSCUKUGCWVHBX4","created_at":"2026-07-04T16:28:14Z"},{"alias_kind":"pith_short_8","alias_value":"6EBSCUKU","created_at":"2026-07-04T16:28:14Z"}],"graph_snapshots":[{"event_id":"sha256:183750cb6685ee95d252986d1c461f301b7f0f0aa07c3e7e828058c4bee64d0e","target":"graph","created_at":"2026-07-04T16:28:14Z","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/math-ph/0107018/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We give a short overview of the effective action approach in quantum field theory and quantum gravity and describe various methods for calculation of the asymptotic expansion of the heat kernel for second-order elliptic partial differential operators acting on sections of vector bundles over a compact Riemannian manifold. We consider both Laplace type operators and non-Laplace type operators on manifolds without boundary as well as Laplace type operators on manifolds with boundary with oblique and non-smooth boundary conditions.","authors_text":"Ivan Avramidi","cross_cats":["gr-qc","hep-th","math.AP","math.MP","math.SP"],"headline":"","license":"","primary_cat":"math-ph","submitted_at":"2001-07-19T19:25:32Z","title":"Heat Kernel Approach in Quantum Field Theory"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math-ph/0107018","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":"sha256:0b10d713e28490d161c801c4d3d6e4a885d6317e285648392014d83d09e9dce0","target":"record","created_at":"2026-07-04T16:28:14Z","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":"066426d712c4618a5f2e7d43460c2c7e890ede2696220f4ea4dcdcb2389ffdd4","cross_cats_sorted":["gr-qc","hep-th","math.AP","math.MP","math.SP"],"license":"","primary_cat":"math-ph","submitted_at":"2001-07-19T19:25:32Z","title_canon_sha256":"9f1c74bed953ea3b50b25e26ad52a74f70ff602b81cdda02a1d9e95db58c057a"},"schema_version":"1.0","source":{"id":"math-ph/0107018","kind":"arxiv","version":1}},"canonical_sha256":"f10321515430ad5386fc8c37a44e18f686f9f6d8a5d25e13b05c7a43122fcbc6","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f10321515430ad5386fc8c37a44e18f686f9f6d8a5d25e13b05c7a43122fcbc6","first_computed_at":"2026-07-04T16:28:14.520177Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-04T16:28:14.520177Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"W1fFSLwZUIv/9uSMI2GHzuSyiKm7MW9ELo1IekAWpTjFpgT0LIqXSB7/1POeA87dL6CwzisH/fCpbzCDHse6BA==","signature_status":"signed_v1","signed_at":"2026-07-04T16:28:14.520533Z","signed_message":"canonical_sha256_bytes"},"source_id":"math-ph/0107018","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0b10d713e28490d161c801c4d3d6e4a885d6317e285648392014d83d09e9dce0","sha256:183750cb6685ee95d252986d1c461f301b7f0f0aa07c3e7e828058c4bee64d0e"],"state_sha256":"971b63305dbb025de92c49a82daf6ef109dffdc18d3cb4bdef67d0f5cd690116"}