{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2022:AA65CUYI5SLYBRHXME6DT7BLC7","short_pith_number":"pith:AA65CUYI","canonical_record":{"source":{"id":"2205.02722","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"hep-th","submitted_at":"2022-05-05T15:53:17Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"5add11cbcbe59932e9951b60283763e795f33798685231f374e6cfc5afdf1720","abstract_canon_sha256":"35ac1bac1089ea8fe9ac4c3bcc7813443aeb75d1263cedbe3126fb90edfaf268"},"schema_version":"1.0"},"canonical_sha256":"003dd15308ec9780c4f7613c39fc2b17c34bfe673e074a690bdbef096cdbd572","source":{"kind":"arxiv","id":"2205.02722","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2205.02722","created_at":"2026-07-05T04:20:40Z"},{"alias_kind":"arxiv_version","alias_value":"2205.02722v1","created_at":"2026-07-05T04:20:40Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2205.02722","created_at":"2026-07-05T04:20:40Z"},{"alias_kind":"pith_short_12","alias_value":"AA65CUYI5SLY","created_at":"2026-07-05T04:20:40Z"},{"alias_kind":"pith_short_16","alias_value":"AA65CUYI5SLYBRHX","created_at":"2026-07-05T04:20:40Z"},{"alias_kind":"pith_short_8","alias_value":"AA65CUYI","created_at":"2026-07-05T04:20:40Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2022:AA65CUYI5SLYBRHXME6DT7BLC7","target":"record","payload":{"canonical_record":{"source":{"id":"2205.02722","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"hep-th","submitted_at":"2022-05-05T15:53:17Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"5add11cbcbe59932e9951b60283763e795f33798685231f374e6cfc5afdf1720","abstract_canon_sha256":"35ac1bac1089ea8fe9ac4c3bcc7813443aeb75d1263cedbe3126fb90edfaf268"},"schema_version":"1.0"},"canonical_sha256":"003dd15308ec9780c4f7613c39fc2b17c34bfe673e074a690bdbef096cdbd572","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T04:20:40.433401Z","signature_b64":"vu5pwahdALyp0pEiZvVMdXoA4eB0iKEf+kr6CyAxA8Ys178eGfx3cnRjgO4Je40Fqn57wvVQttrk3cbWNL0zCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"003dd15308ec9780c4f7613c39fc2b17c34bfe673e074a690bdbef096cdbd572","last_reissued_at":"2026-07-05T04:20:40.432990Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T04:20:40.432990Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2205.02722","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":"2026-07-05T04:20:40Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"4sRr0zdFiyq2MVHuj4fPJELHwH9QMLktZnkhTca+2oDj5kdWy/UfJKENtXU/0fNJlQyTzNIFht4Y+5BFA0vGAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-04T20:19:18.364383Z"},"content_sha256":"99196581371f841b6f80ba0592b9f327325d452778716e6326940f460c32766e","schema_version":"1.0","event_id":"sha256:99196581371f841b6f80ba0592b9f327325d452778716e6326940f460c32766e"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2022:AA65CUYI5SLYBRHXME6DT7BLC7","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Connecting Scalar Amplitudes using The Positive Tropical Grassmannian","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"hep-th","authors_text":"Bruno Gim\\'enez Umbert, Freddy Cachazo","submitted_at":"2022-05-05T15:53:17Z","abstract_excerpt":"The biadjoint scalar partial amplitude, $m_n(\\mathbb{I},\\mathbb{I})$, can be expressed as a single integral over the positive tropical Grassmannian thus producing a Global Schwinger Parameterization. The first result in this work is an extension to all partial amplitudes $m_n(\\alpha,\\beta)$ using a limiting procedure on kinematic invariants that produces indicator functions in the integrand. The same limiting procedure leads to an integral representation of $\\phi^4$ amplitudes where indicator functions turn into Dirac delta functions. Their support decomposes into $\\textrm{C}_{n/2-1}$ regions,"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2205.02722","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/2205.02722/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":"2026-07-05T04:20:40Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"6FQW7SC8NJ+yTGnDps6UtjVFpH/Ssbyz7JaJnSZKriCBxKk2CON9HObavQsvEpP90c4uKXCSd8SrKQS2u7goAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-04T20:19:18.364888Z"},"content_sha256":"50a3dd87ab48c6b5d373637e9eba064a83f98e56f4279058863b8c8354d12835","schema_version":"1.0","event_id":"sha256:50a3dd87ab48c6b5d373637e9eba064a83f98e56f4279058863b8c8354d12835"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/AA65CUYI5SLYBRHXME6DT7BLC7/bundle.json","state_url":"https://pith.science/pith/AA65CUYI5SLYBRHXME6DT7BLC7/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/AA65CUYI5SLYBRHXME6DT7BLC7/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":"2026-08-04T20:19:18Z","links":{"resolver":"https://pith.science/pith/AA65CUYI5SLYBRHXME6DT7BLC7","bundle":"https://pith.science/pith/AA65CUYI5SLYBRHXME6DT7BLC7/bundle.json","state":"https://pith.science/pith/AA65CUYI5SLYBRHXME6DT7BLC7/state.json","well_known_bundle":"https://pith.science/.well-known/pith/AA65CUYI5SLYBRHXME6DT7BLC7/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2022:AA65CUYI5SLYBRHXME6DT7BLC7","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":"35ac1bac1089ea8fe9ac4c3bcc7813443aeb75d1263cedbe3126fb90edfaf268","cross_cats_sorted":["math.CO"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"hep-th","submitted_at":"2022-05-05T15:53:17Z","title_canon_sha256":"5add11cbcbe59932e9951b60283763e795f33798685231f374e6cfc5afdf1720"},"schema_version":"1.0","source":{"id":"2205.02722","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2205.02722","created_at":"2026-07-05T04:20:40Z"},{"alias_kind":"arxiv_version","alias_value":"2205.02722v1","created_at":"2026-07-05T04:20:40Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2205.02722","created_at":"2026-07-05T04:20:40Z"},{"alias_kind":"pith_short_12","alias_value":"AA65CUYI5SLY","created_at":"2026-07-05T04:20:40Z"},{"alias_kind":"pith_short_16","alias_value":"AA65CUYI5SLYBRHX","created_at":"2026-07-05T04:20:40Z"},{"alias_kind":"pith_short_8","alias_value":"AA65CUYI","created_at":"2026-07-05T04:20:40Z"}],"graph_snapshots":[{"event_id":"sha256:50a3dd87ab48c6b5d373637e9eba064a83f98e56f4279058863b8c8354d12835","target":"graph","created_at":"2026-07-05T04:20:40Z","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/2205.02722/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"The biadjoint scalar partial amplitude, $m_n(\\mathbb{I},\\mathbb{I})$, can be expressed as a single integral over the positive tropical Grassmannian thus producing a Global Schwinger Parameterization. The first result in this work is an extension to all partial amplitudes $m_n(\\alpha,\\beta)$ using a limiting procedure on kinematic invariants that produces indicator functions in the integrand. The same limiting procedure leads to an integral representation of $\\phi^4$ amplitudes where indicator functions turn into Dirac delta functions. Their support decomposes into $\\textrm{C}_{n/2-1}$ regions,","authors_text":"Bruno Gim\\'enez Umbert, Freddy Cachazo","cross_cats":["math.CO"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"hep-th","submitted_at":"2022-05-05T15:53:17Z","title":"Connecting Scalar Amplitudes using The Positive Tropical Grassmannian"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2205.02722","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":"sha256:99196581371f841b6f80ba0592b9f327325d452778716e6326940f460c32766e","target":"record","created_at":"2026-07-05T04:20:40Z","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":"35ac1bac1089ea8fe9ac4c3bcc7813443aeb75d1263cedbe3126fb90edfaf268","cross_cats_sorted":["math.CO"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"hep-th","submitted_at":"2022-05-05T15:53:17Z","title_canon_sha256":"5add11cbcbe59932e9951b60283763e795f33798685231f374e6cfc5afdf1720"},"schema_version":"1.0","source":{"id":"2205.02722","kind":"arxiv","version":1}},"canonical_sha256":"003dd15308ec9780c4f7613c39fc2b17c34bfe673e074a690bdbef096cdbd572","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"003dd15308ec9780c4f7613c39fc2b17c34bfe673e074a690bdbef096cdbd572","first_computed_at":"2026-07-05T04:20:40.432990Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T04:20:40.432990Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"vu5pwahdALyp0pEiZvVMdXoA4eB0iKEf+kr6CyAxA8Ys178eGfx3cnRjgO4Je40Fqn57wvVQttrk3cbWNL0zCg==","signature_status":"signed_v1","signed_at":"2026-07-05T04:20:40.433401Z","signed_message":"canonical_sha256_bytes"},"source_id":"2205.02722","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:99196581371f841b6f80ba0592b9f327325d452778716e6326940f460c32766e","sha256:50a3dd87ab48c6b5d373637e9eba064a83f98e56f4279058863b8c8354d12835"],"state_sha256":"3ea10f258898cd17d4a548d6fd4d0c20ab257e373dfe7cb4c2e12f9387e63ebb"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"KScI4BcnvVZNbDEr1BoBNX92QA6iQhYR+idGHMaVNCIsVW0cJviN4lafI6CIoxORwJrjYAdezYJDGVCuD07SAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-04T20:19:18.369742Z","bundle_sha256":"471312dbe6e09d34181cc638959bcf1a0bb9a8e19b33153300f97708c4dcf08a"}}