{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2020:JLWPPD23WDDAFNZN2VUWN46D47","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":"8e9ea6393a70f7bfe42cfc2d88b26367c7141fc1bf426e666a6816a8dbe4fbd9","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2020-09-11T18:48:51Z","title_canon_sha256":"d06829da54c47a2e3d521d06c45fe680be17f11f1e934e30d47d76f4f4b418c1"},"schema_version":"1.0","source":{"id":"2009.05607","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2009.05607","created_at":"2026-07-05T02:12:03Z"},{"alias_kind":"arxiv_version","alias_value":"2009.05607v1","created_at":"2026-07-05T02:12:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2009.05607","created_at":"2026-07-05T02:12:03Z"},{"alias_kind":"pith_short_12","alias_value":"JLWPPD23WDDA","created_at":"2026-07-05T02:12:03Z"},{"alias_kind":"pith_short_16","alias_value":"JLWPPD23WDDAFNZN","created_at":"2026-07-05T02:12:03Z"},{"alias_kind":"pith_short_8","alias_value":"JLWPPD23","created_at":"2026-07-05T02:12:03Z"}],"graph_snapshots":[{"event_id":"sha256:3a233e6ef3c57d23f591e901816e5146548139afc0965460ba9700d877d4cf53","target":"graph","created_at":"2026-07-05T02:12:03Z","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/2009.05607/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We initiate the systematic study of \\emph{local positive spaces} which arise in the context of the Amplituhedron construction for scattering amplitudes in planar maximally supersymmetric Yang-Mills theory. We show that all local positive spaces relevant for one-loop MHV amplitudes are characterized by certain sign-flip conditions and are associated with surprisingly simple logarithmic forms. In the maximal sign-flip case they are finite one-loop octagons. Particular combinations of sign-flip spaces can be glued into new local positive geometries. These correspond to local pentagon integrands t","authors_text":"Cameron Langer, Enrico Herrmann, Jaroslav Trnka, Minshan Zheng","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2020-09-11T18:48:51Z","title":"Positive geometry, local triangulations, and the dual of the Amplituhedron"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2009.05607","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":"sha256:8f899ed4fbe405e469a652403b97ecf5219f3105729239263482f69f48f374fa","target":"record","created_at":"2026-07-05T02:12:03Z","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":"8e9ea6393a70f7bfe42cfc2d88b26367c7141fc1bf426e666a6816a8dbe4fbd9","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2020-09-11T18:48:51Z","title_canon_sha256":"d06829da54c47a2e3d521d06c45fe680be17f11f1e934e30d47d76f4f4b418c1"},"schema_version":"1.0","source":{"id":"2009.05607","kind":"arxiv","version":1}},"canonical_sha256":"4aecf78f5bb0c602b72dd56966f3c3e7c62ef7045d0660d1d5b71767c347394e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4aecf78f5bb0c602b72dd56966f3c3e7c62ef7045d0660d1d5b71767c347394e","first_computed_at":"2026-07-05T02:12:03.621200Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T02:12:03.621200Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"0nKRn9rAbVbU9iT3P7d3VrYFb4ExmTn10rfGliCsZNyieJH1bCImviv0TGHjwAZ28Bgf7KAiQURxOClYU2dtDA==","signature_status":"signed_v1","signed_at":"2026-07-05T02:12:03.621730Z","signed_message":"canonical_sha256_bytes"},"source_id":"2009.05607","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8f899ed4fbe405e469a652403b97ecf5219f3105729239263482f69f48f374fa","sha256:3a233e6ef3c57d23f591e901816e5146548139afc0965460ba9700d877d4cf53"],"state_sha256":"17564d051722dbee83932b20b332ca9ffd0ad12915c71562e681ba00d195670c"}