{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2024:U3XII7LJU76STIL65MFMBJRLN6","short_pith_number":"pith:U3XII7LJ","canonical_record":{"source":{"id":"2403.17051","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"hep-th","submitted_at":"2024-03-25T18:00:01Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"b72b5a783285035cc980b9dd935203e5a06f320ceb29259c8a89e926b17b8b1b","abstract_canon_sha256":"49e64967e6683f5409241efa7f8b22571287d4d6c8cc83a3b1a891d7b99a5811"},"schema_version":"1.0"},"canonical_sha256":"a6ee847d69a7fd29a17eeb0ac0a62b6fb468234864de41b164a0c1f887af4907","source":{"kind":"arxiv","id":"2403.17051","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2403.17051","created_at":"2026-07-05T08:00:44Z"},{"alias_kind":"arxiv_version","alias_value":"2403.17051v1","created_at":"2026-07-05T08:00:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2403.17051","created_at":"2026-07-05T08:00:44Z"},{"alias_kind":"pith_short_12","alias_value":"U3XII7LJU76S","created_at":"2026-07-05T08:00:44Z"},{"alias_kind":"pith_short_16","alias_value":"U3XII7LJU76STIL6","created_at":"2026-07-05T08:00:44Z"},{"alias_kind":"pith_short_8","alias_value":"U3XII7LJ","created_at":"2026-07-05T08:00:44Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2024:U3XII7LJU76STIL65MFMBJRLN6","target":"record","payload":{"canonical_record":{"source":{"id":"2403.17051","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"hep-th","submitted_at":"2024-03-25T18:00:01Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"b72b5a783285035cc980b9dd935203e5a06f320ceb29259c8a89e926b17b8b1b","abstract_canon_sha256":"49e64967e6683f5409241efa7f8b22571287d4d6c8cc83a3b1a891d7b99a5811"},"schema_version":"1.0"},"canonical_sha256":"a6ee847d69a7fd29a17eeb0ac0a62b6fb468234864de41b164a0c1f887af4907","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T08:00:44.354225Z","signature_b64":"I+AIyUQk5evaS3Lesu7yPdb1YYTuBBhAp4MbzuzZ+Aqkitj7RzIWHyH/Xt00m2kLSO6OfuKIdkZXy9E40WMMAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a6ee847d69a7fd29a17eeb0ac0a62b6fb468234864de41b164a0c1f887af4907","last_reissued_at":"2026-07-05T08:00:44.353736Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T08:00:44.353736Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2403.17051","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T08:00:44Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"C/iP3HNA+4N/TZGMefO5c7bxBdcR2K5PxBDENp94/8SaW4knEaScg0ctdEuYYWPrT0qpsxaYUNIgFoLV8xDVBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-04T22:02:46.167803Z"},"content_sha256":"f18c0599526fc357787d442d0c41aff3f81a9a0697673121ef65a9a79f412f1f","schema_version":"1.0","event_id":"sha256:f18c0599526fc357787d442d0c41aff3f81a9a0697673121ef65a9a79f412f1f"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2024:U3XII7LJU76STIL65MFMBJRLN6","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"$\\Phi^p$ Amplitudes from the Positive Tropical Grassmannian: Triangulations of Extended Diagrams","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"hep-th","authors_text":"Bruno Gim\\'enez Umbert, Karen Yeats","submitted_at":"2024-03-25T18:00:01Z","abstract_excerpt":"The global Schwinger formula, introduced by Cachazo and Early as a single integral over the positive tropical Grassmannian, provides a way to uncover properties of scattering amplitudes which are hard to see in their standard Feynman diagram formulation. In a recent work, Cachazo and one of the authors extended the global Schwinger formula to general $\\phi^p$ theories. When $p=4$, it was conjectured that the integral decomposes as a sum over cones which are in bijection with non-crossing chord diagrams, and further that these can be obtained by finding the zeroes of a piece-wise linear functio"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2403.17051","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2403.17051/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T08:00:44Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"mLsbCN1plN3VxN/JUErdfenteVVkmHpjruG5D0EjzRF0Xh2pOIfjBP9NkN5t0OXQY/OAutQ/+2QV1h8PMkDXAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-04T22:02:46.168309Z"},"content_sha256":"24cc4230e1baa563c46b47b9169d8220860e74a7b691c9c08d2ac4265f2da4f8","schema_version":"1.0","event_id":"sha256:24cc4230e1baa563c46b47b9169d8220860e74a7b691c9c08d2ac4265f2da4f8"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/U3XII7LJU76STIL65MFMBJRLN6/bundle.json","state_url":"https://pith.science/pith/U3XII7LJU76STIL65MFMBJRLN6/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/U3XII7LJU76STIL65MFMBJRLN6/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-08-04T22:02:46Z","links":{"resolver":"https://pith.science/pith/U3XII7LJU76STIL65MFMBJRLN6","bundle":"https://pith.science/pith/U3XII7LJU76STIL65MFMBJRLN6/bundle.json","state":"https://pith.science/pith/U3XII7LJU76STIL65MFMBJRLN6/state.json","well_known_bundle":"https://pith.science/.well-known/pith/U3XII7LJU76STIL65MFMBJRLN6/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:U3XII7LJU76STIL65MFMBJRLN6","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":"49e64967e6683f5409241efa7f8b22571287d4d6c8cc83a3b1a891d7b99a5811","cross_cats_sorted":["math.CO"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"hep-th","submitted_at":"2024-03-25T18:00:01Z","title_canon_sha256":"b72b5a783285035cc980b9dd935203e5a06f320ceb29259c8a89e926b17b8b1b"},"schema_version":"1.0","source":{"id":"2403.17051","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2403.17051","created_at":"2026-07-05T08:00:44Z"},{"alias_kind":"arxiv_version","alias_value":"2403.17051v1","created_at":"2026-07-05T08:00:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2403.17051","created_at":"2026-07-05T08:00:44Z"},{"alias_kind":"pith_short_12","alias_value":"U3XII7LJU76S","created_at":"2026-07-05T08:00:44Z"},{"alias_kind":"pith_short_16","alias_value":"U3XII7LJU76STIL6","created_at":"2026-07-05T08:00:44Z"},{"alias_kind":"pith_short_8","alias_value":"U3XII7LJ","created_at":"2026-07-05T08:00:44Z"}],"graph_snapshots":[{"event_id":"sha256:24cc4230e1baa563c46b47b9169d8220860e74a7b691c9c08d2ac4265f2da4f8","target":"graph","created_at":"2026-07-05T08:00:44Z","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/2403.17051/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"The global Schwinger formula, introduced by Cachazo and Early as a single integral over the positive tropical Grassmannian, provides a way to uncover properties of scattering amplitudes which are hard to see in their standard Feynman diagram formulation. In a recent work, Cachazo and one of the authors extended the global Schwinger formula to general $\\phi^p$ theories. When $p=4$, it was conjectured that the integral decomposes as a sum over cones which are in bijection with non-crossing chord diagrams, and further that these can be obtained by finding the zeroes of a piece-wise linear functio","authors_text":"Bruno Gim\\'enez Umbert, Karen Yeats","cross_cats":["math.CO"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"hep-th","submitted_at":"2024-03-25T18:00:01Z","title":"$\\Phi^p$ Amplitudes from the Positive Tropical Grassmannian: Triangulations of Extended Diagrams"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2403.17051","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:f18c0599526fc357787d442d0c41aff3f81a9a0697673121ef65a9a79f412f1f","target":"record","created_at":"2026-07-05T08:00:44Z","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":"49e64967e6683f5409241efa7f8b22571287d4d6c8cc83a3b1a891d7b99a5811","cross_cats_sorted":["math.CO"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"hep-th","submitted_at":"2024-03-25T18:00:01Z","title_canon_sha256":"b72b5a783285035cc980b9dd935203e5a06f320ceb29259c8a89e926b17b8b1b"},"schema_version":"1.0","source":{"id":"2403.17051","kind":"arxiv","version":1}},"canonical_sha256":"a6ee847d69a7fd29a17eeb0ac0a62b6fb468234864de41b164a0c1f887af4907","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a6ee847d69a7fd29a17eeb0ac0a62b6fb468234864de41b164a0c1f887af4907","first_computed_at":"2026-07-05T08:00:44.353736Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T08:00:44.353736Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"I+AIyUQk5evaS3Lesu7yPdb1YYTuBBhAp4MbzuzZ+Aqkitj7RzIWHyH/Xt00m2kLSO6OfuKIdkZXy9E40WMMAQ==","signature_status":"signed_v1","signed_at":"2026-07-05T08:00:44.354225Z","signed_message":"canonical_sha256_bytes"},"source_id":"2403.17051","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f18c0599526fc357787d442d0c41aff3f81a9a0697673121ef65a9a79f412f1f","sha256:24cc4230e1baa563c46b47b9169d8220860e74a7b691c9c08d2ac4265f2da4f8"],"state_sha256":"aa5236391241676398de4f5e321229898bd0dbbf62c3f3d5466891c21d213be1"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"PiJIvthbomkRjlAcgrrpooEXqsnDs0Ac5APR0qxCy8u88cIM13V/d+KYntDhr2v/uisq54G6Na6f5tZ8/FsuBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-04T22:02:46.173217Z","bundle_sha256":"05816944bb07bd7fb18d81a83e9b69ea15f8aac9b150c6efa40f72b079964af0"}}