{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2021:AMHHYGAABC7Q3TZF42F7UNHTT3","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":"9677663754d8c774924d7233511fca88be60d60bd1995aeb35c5b5403bc56e1d","cross_cats_sorted":["hep-th"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"hep-ph","submitted_at":"2021-02-09T19:00:06Z","title_canon_sha256":"aefcb15afa08afda0159075940061f51835094bd87140cbff95652e5c5d0a89e"},"schema_version":"1.0","source":{"id":"2102.05062","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2102.05062","created_at":"2026-07-05T03:11:59Z"},{"alias_kind":"arxiv_version","alias_value":"2102.05062v2","created_at":"2026-07-05T03:11:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2102.05062","created_at":"2026-07-05T03:11:59Z"},{"alias_kind":"pith_short_12","alias_value":"AMHHYGAABC7Q","created_at":"2026-07-05T03:11:59Z"},{"alias_kind":"pith_short_16","alias_value":"AMHHYGAABC7Q3TZF","created_at":"2026-07-05T03:11:59Z"},{"alias_kind":"pith_short_8","alias_value":"AMHHYGAA","created_at":"2026-07-05T03:11:59Z"}],"graph_snapshots":[{"event_id":"sha256:10e9f842467ba8feb91e0b4fcddd1552f0e24390c9c0680d17dadd282986488d","target":"graph","created_at":"2026-07-05T03:11:59Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2102.05062/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"An impressive effort is being placed in order to develop new strategies that allow an efficient computation of multi-loop multi-leg Feynman integrals and scattering amplitudes, with a particular emphasis on removing spurious singularities and numerical instabilities. In this article, we describe an innovative geometric approach based on graph theory to unveil the causal structure of any multi-loop multi-leg amplitude in Quantum Field Theory. Our purely geometric construction reproduces faithfully the manifestly causal integrand-level behaviour of the Loop-Tree Duality representation. We found ","authors_text":"German F. R. Sborlini","cross_cats":["hep-th"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"hep-ph","submitted_at":"2021-02-09T19:00:06Z","title":"Geometrical approach to causality in multi-loop amplitudes"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2102.05062","kind":"arxiv","version":2},"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:ab978195ad5efbde727586addfc1c7747bf63ca7a5158171107dbeadf2108f44","target":"record","created_at":"2026-07-05T03:11:59Z","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":"9677663754d8c774924d7233511fca88be60d60bd1995aeb35c5b5403bc56e1d","cross_cats_sorted":["hep-th"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"hep-ph","submitted_at":"2021-02-09T19:00:06Z","title_canon_sha256":"aefcb15afa08afda0159075940061f51835094bd87140cbff95652e5c5d0a89e"},"schema_version":"1.0","source":{"id":"2102.05062","kind":"arxiv","version":2}},"canonical_sha256":"030e7c180008bf0dcf25e68bfa34f39ec548b24e521512d134bbba1b2b1afc51","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"030e7c180008bf0dcf25e68bfa34f39ec548b24e521512d134bbba1b2b1afc51","first_computed_at":"2026-07-05T03:11:59.019680Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T03:11:59.019680Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"uIPugiozwj4M3kUixVT7RDL77rtZeR0AgdY3QdCYPDBLe5KjDojznWMdiU3GNdqwwhknNr3uMgxXqlPLhmCiCA==","signature_status":"signed_v1","signed_at":"2026-07-05T03:11:59.020128Z","signed_message":"canonical_sha256_bytes"},"source_id":"2102.05062","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ab978195ad5efbde727586addfc1c7747bf63ca7a5158171107dbeadf2108f44","sha256:10e9f842467ba8feb91e0b4fcddd1552f0e24390c9c0680d17dadd282986488d"],"state_sha256":"998d7dd65d5060767829aeeab0117be2940a00fde8aa5648b86568c4a3ffc6fa"}