{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2009:6Z77ONQSNPWZW6ZRPXYVL6SKTR","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":"190bb433fb75e9df6f71e19dfc89040d84d73f426a4fbc622d3b8a53954f91d2","cross_cats_sorted":["hep-th","math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2009-05-29T20:04:43Z","title_canon_sha256":"a45ab6297b3c05c5adb2e96021bb9e796539e0b27448a22f5d1da9ff6e7a4302"},"schema_version":"1.0","source":{"id":"0906.0005","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0906.0005","created_at":"2026-07-05T00:32:35Z"},{"alias_kind":"arxiv_version","alias_value":"0906.0005v4","created_at":"2026-07-05T00:32:35Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0906.0005","created_at":"2026-07-05T00:32:35Z"},{"alias_kind":"pith_short_12","alias_value":"6Z77ONQSNPWZ","created_at":"2026-07-05T00:32:35Z"},{"alias_kind":"pith_short_16","alias_value":"6Z77ONQSNPWZW6ZR","created_at":"2026-07-05T00:32:35Z"},{"alias_kind":"pith_short_8","alias_value":"6Z77ONQS","created_at":"2026-07-05T00:32:35Z"}],"graph_snapshots":[{"event_id":"sha256:340b53d04621fe4ba01c261537074a46bb7537bbb5d9fe23c3b37af8079c13b9","target":"graph","created_at":"2026-07-05T00:32:35Z","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/0906.0005/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Building on an insight due to Avramidi, we provide a system of transport equations for determining key fundamental bi-tensors, including derivatives of the world-function, \\sigma(x,x'), the square root of the Van Vleck determinant, \\Delta^{1/2}(x,x'), and the tail-term, V(x,x'), appearing in the Hadamard form of the Green function. These bi-tensors are central to a broad range of problems from radiation reaction to quantum field theory in curved spacetime and quantum gravity. Their transport equations may be used either in a semi-recursive approach to determining their covariant Taylor series ","authors_text":"Adrian C. Ottewill, Barry Wardell","cross_cats":["hep-th","math-ph","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2009-05-29T20:04:43Z","title":"Transport Equation Approach to Calculations of Hadamard Green functions and non-coincident DeWitt coefficients"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0906.0005","kind":"arxiv","version":4},"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":"sha256:1ed74b0490ebece793564304597925dd5e8610f5cfcb60dc84b1168abaa0a15a","target":"record","created_at":"2026-07-05T00:32:35Z","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":"190bb433fb75e9df6f71e19dfc89040d84d73f426a4fbc622d3b8a53954f91d2","cross_cats_sorted":["hep-th","math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2009-05-29T20:04:43Z","title_canon_sha256":"a45ab6297b3c05c5adb2e96021bb9e796539e0b27448a22f5d1da9ff6e7a4302"},"schema_version":"1.0","source":{"id":"0906.0005","kind":"arxiv","version":4}},"canonical_sha256":"f67ff736126bed9b7b317df155fa4a9c506aa4455d1aaf3a2d1cf4a4276737c6","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f67ff736126bed9b7b317df155fa4a9c506aa4455d1aaf3a2d1cf4a4276737c6","first_computed_at":"2026-07-05T00:32:35.018963Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T00:32:35.018963Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"kkr4zU+PxXXitKO2UMP00A5FWeuzuQ1zfwtkgtHoul7GP9W5ZFc8x9//C8zea/c5Iqg7KR/xl044iERzHyItBQ==","signature_status":"signed_v1","signed_at":"2026-07-05T00:32:35.019390Z","signed_message":"canonical_sha256_bytes"},"source_id":"0906.0005","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1ed74b0490ebece793564304597925dd5e8610f5cfcb60dc84b1168abaa0a15a","sha256:340b53d04621fe4ba01c261537074a46bb7537bbb5d9fe23c3b37af8079c13b9"],"state_sha256":"ed8673aa9a43a1d8140cfb335bb41b506a75fd2020ea9867e6caa65ca7f7d344"}