{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:SJO57Z6ECURQIA3GW5EVWFPIEN","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":"81472d56911d04e9d19aa41bdf21475c45f8fb0f3b95c9c4bedbb7663c5ddd2b","cross_cats_sorted":["gr-qc","hep-th","math.CA","math.MP"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math-ph","submitted_at":"2026-06-26T17:12:39Z","title_canon_sha256":"783afbc87f3c9636b530d4786b413a314268a515ece571b60f972d7deeed98aa"},"schema_version":"1.0","source":{"id":"2606.28271","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2606.28271","created_at":"2026-06-29T01:15:11Z"},{"alias_kind":"arxiv_version","alias_value":"2606.28271v1","created_at":"2026-06-29T01:15:11Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.28271","created_at":"2026-06-29T01:15:11Z"},{"alias_kind":"pith_short_12","alias_value":"SJO57Z6ECURQ","created_at":"2026-06-29T01:15:11Z"},{"alias_kind":"pith_short_16","alias_value":"SJO57Z6ECURQIA3G","created_at":"2026-06-29T01:15:11Z"},{"alias_kind":"pith_short_8","alias_value":"SJO57Z6E","created_at":"2026-06-29T01:15:11Z"}],"graph_snapshots":[{"event_id":"sha256:c13bd43cb8500747cb992343c98b4ede466ee52572223bc40866e854ef6cdbf2","target":"graph","created_at":"2026-06-29T01:15:11Z","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/2606.28271/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In this paper, we introduce and demonstrate a simple geometric algorithm to determine which critical points, both complex as well as real, contribute to the asymptotic evaluation of multiple integrals with exponential integrands of the form $e^{ikf(\\boldsymbol{x})}$ over $\\mathbb R^d$, for finite $d\\ge 1$ and $f$ is analytic. In so doing, the algorithm removes the need to compute the flows of $-\\text{Re} (i\\nabla f)$ in $\\mathbb C^d$ that is required to identify such relevant critical points in Picard-Lefschetz approaches to the derivation of such asymptotic expansions. By contrast, our algori","authors_text":"Christopher J. Howls, In\\^es Aniceto, Job Feldbrugge","cross_cats":["gr-qc","hep-th","math.CA","math.MP"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math-ph","submitted_at":"2026-06-26T17:12:39Z","title":"Which Saddles Contribute? The South-East Rule for Multidimensional Integrals"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.28271","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:e4f86501443604dc8aee1252bae9b7d03755b0d917c1f629ecd34cdbea2a5600","target":"record","created_at":"2026-06-29T01:15:11Z","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":"81472d56911d04e9d19aa41bdf21475c45f8fb0f3b95c9c4bedbb7663c5ddd2b","cross_cats_sorted":["gr-qc","hep-th","math.CA","math.MP"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math-ph","submitted_at":"2026-06-26T17:12:39Z","title_canon_sha256":"783afbc87f3c9636b530d4786b413a314268a515ece571b60f972d7deeed98aa"},"schema_version":"1.0","source":{"id":"2606.28271","kind":"arxiv","version":1}},"canonical_sha256":"925ddfe7c41523040366b7495b15e8234f4008853f5c5c36bacae1a007edb02c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"925ddfe7c41523040366b7495b15e8234f4008853f5c5c36bacae1a007edb02c","first_computed_at":"2026-06-29T01:15:11.390123Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-29T01:15:11.390123Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"nkUjPj3iUDFn8dxujKpnTg8XwP36A+SodCkkqTC3fhffH0whsVMvwBni+HEWVjf9SzplHz1pfkm32VUYa3vyDg==","signature_status":"signed_v1","signed_at":"2026-06-29T01:15:11.390614Z","signed_message":"canonical_sha256_bytes"},"source_id":"2606.28271","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e4f86501443604dc8aee1252bae9b7d03755b0d917c1f629ecd34cdbea2a5600","sha256:c13bd43cb8500747cb992343c98b4ede466ee52572223bc40866e854ef6cdbf2"],"state_sha256":"86c389e4ba36a3c7468c2c1ab162272900bc6b2a8e5077b725cd9b652e4ebc57"}