{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:QVZKR3A5WGVSWPIEX3FLFXSSXB","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":"577167aff27b40b1a65c27fe99728115af454c73c87cba210e608593cbbea8e4","cross_cats_sorted":["hep-th","math.DG","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2015-05-18T20:22:14Z","title_canon_sha256":"910eabb7c247a48c5ac0e835a774ec1c663e49240651960f5f5390a4542d4c40"},"schema_version":"1.0","source":{"id":"1505.04809","kind":"arxiv","version":5}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1505.04809","created_at":"2026-05-18T01:02:45Z"},{"alias_kind":"arxiv_version","alias_value":"1505.04809v5","created_at":"2026-05-18T01:02:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1505.04809","created_at":"2026-05-18T01:02:45Z"},{"alias_kind":"pith_short_12","alias_value":"QVZKR3A5WGVS","created_at":"2026-05-18T12:29:39Z"},{"alias_kind":"pith_short_16","alias_value":"QVZKR3A5WGVSWPIE","created_at":"2026-05-18T12:29:39Z"},{"alias_kind":"pith_short_8","alias_value":"QVZKR3A5","created_at":"2026-05-18T12:29:39Z"}],"graph_snapshots":[{"event_id":"sha256:1a19e061097a507c66b01dfd96de58d9a8a48b67e4a41626fa26fa7a32a8316e","target":"graph","created_at":"2026-05-18T01:02:45Z","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 study finite-dimensional integrals in a way that elucidates the mathematical meaning behind the formal manipulations of path integrals occurring in quantum field theory. This involves a proper understanding of how Wick's theorem allows one to evaluate integrals perturbatively, i.e., as a series expansion in a formal parameter irrespective of convergence properties. We establish invariance properties of such a Wick expansion under coordinate changes and the action of a Lie group of symmetries, and we use this to study essential features of path integral manipulations, including coordinate ch","authors_text":"Timothy Nguyen","cross_cats":["hep-th","math.DG","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2015-05-18T20:22:14Z","title":"The Perturbative Approach to Path Integrals: A Succinct Mathematical Treatment"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1505.04809","kind":"arxiv","version":5},"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:adc34f1e5c1faeda3dd03fbe8a18c67be938c29dca6e51fef319ab1ca898c57c","target":"record","created_at":"2026-05-18T01:02:45Z","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":"577167aff27b40b1a65c27fe99728115af454c73c87cba210e608593cbbea8e4","cross_cats_sorted":["hep-th","math.DG","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2015-05-18T20:22:14Z","title_canon_sha256":"910eabb7c247a48c5ac0e835a774ec1c663e49240651960f5f5390a4542d4c40"},"schema_version":"1.0","source":{"id":"1505.04809","kind":"arxiv","version":5}},"canonical_sha256":"8572a8ec1db1ab2b3d04becab2de52b8733c43a9a3ede2b5d1f228a7c347ae23","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8572a8ec1db1ab2b3d04becab2de52b8733c43a9a3ede2b5d1f228a7c347ae23","first_computed_at":"2026-05-18T01:02:45.897790Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:02:45.897790Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"GD3hZ2jGDNk8RdrULWFqVU7jrDsk3xS4RHNhrKrt9cR1feNWw6X93a0pQ1cHC+F11V3qWAq0dhd9DK61h2Z2Ag==","signature_status":"signed_v1","signed_at":"2026-05-18T01:02:45.898260Z","signed_message":"canonical_sha256_bytes"},"source_id":"1505.04809","source_kind":"arxiv","source_version":5}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:adc34f1e5c1faeda3dd03fbe8a18c67be938c29dca6e51fef319ab1ca898c57c","sha256:1a19e061097a507c66b01dfd96de58d9a8a48b67e4a41626fa26fa7a32a8316e"],"state_sha256":"ca4531c6a43a3595d4104761bec1a6e7da66df68e0d549b098650adccb33b8df"}