{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:WDDTDKVXF26NZEN5SOQLB4N4PV","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":"10477e179719c80c77bec5ae4c83e5ed67ae45429c79c4eae789608981046679","cross_cats_sorted":["hep-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2024-03-07T19:00:00Z","title_canon_sha256":"70e0c36b695cb44664b0a652a04693f5440a4b2ef7eaeaf0488e2b088a148e08"},"schema_version":"1.0","source":{"id":"2403.04826","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2403.04826","created_at":"2026-07-05T07:53:34Z"},{"alias_kind":"arxiv_version","alias_value":"2403.04826v1","created_at":"2026-07-05T07:53:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2403.04826","created_at":"2026-07-05T07:53:34Z"},{"alias_kind":"pith_short_12","alias_value":"WDDTDKVXF26N","created_at":"2026-07-05T07:53:34Z"},{"alias_kind":"pith_short_16","alias_value":"WDDTDKVXF26NZEN5","created_at":"2026-07-05T07:53:34Z"},{"alias_kind":"pith_short_8","alias_value":"WDDTDKVX","created_at":"2026-07-05T07:53:34Z"}],"graph_snapshots":[{"event_id":"sha256:2147a1b0edbd1c527ea088ad24356e73746f93fe408283f350aa2bad855ff575","target":"graph","created_at":"2026-07-05T07:53:34Z","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/2403.04826/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"A surprising connection has recently been made between the amplitudes for Tr($\\Phi^3$) theory and the non-linear sigma model (NLSM). A simple shift of kinematic variables naturally suggested by the associahedron/stringy representation of Tr$(\\Phi^3$) theory yields pion amplitudes at all loops. In this note we provide an elementary motivation and proof for this link going in the opposite direction, starting from the non-linear sigma model and discovering its formulation as a sum over triangulations of surfaces with simple numerator factors. This uses an ancient connection between \"circles\" and ","authors_text":"Carolina Figueiredo, Nima Arkani-Hamed","cross_cats":["hep-ph"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2024-03-07T19:00:00Z","title":"Circles and Triangles, the NLSM and Tr($\\Phi^3$)"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2403.04826","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:ebf9a25866f203ce93f36667d66edc592c1b8635630a332cc45e538df7e5936e","target":"record","created_at":"2026-07-05T07:53:34Z","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":"10477e179719c80c77bec5ae4c83e5ed67ae45429c79c4eae789608981046679","cross_cats_sorted":["hep-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2024-03-07T19:00:00Z","title_canon_sha256":"70e0c36b695cb44664b0a652a04693f5440a4b2ef7eaeaf0488e2b088a148e08"},"schema_version":"1.0","source":{"id":"2403.04826","kind":"arxiv","version":1}},"canonical_sha256":"b0c731aab72ebcdc91bd93a0b0f1bc7d69acbb7a540cd60ca424b4109600916b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b0c731aab72ebcdc91bd93a0b0f1bc7d69acbb7a540cd60ca424b4109600916b","first_computed_at":"2026-07-05T07:53:34.924740Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T07:53:34.924740Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"LO531056RVx8rfvG0bbIEqqksyt3jLd6Vkl5utgJ6hsT2tOt7Vu+OzId1DVruT1FHKqFawBc+oDCeAJMCSk+Aw==","signature_status":"signed_v1","signed_at":"2026-07-05T07:53:34.925247Z","signed_message":"canonical_sha256_bytes"},"source_id":"2403.04826","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ebf9a25866f203ce93f36667d66edc592c1b8635630a332cc45e538df7e5936e","sha256:2147a1b0edbd1c527ea088ad24356e73746f93fe408283f350aa2bad855ff575"],"state_sha256":"e69860ee58983041d4166c66b7844232b36d96565dab49e0fcbc8b682a2f5f2f"}