{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2020:74I6NNDUPBO3FI3KPJZKIAZPWA","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":"a673278a377aa0dc4786a941b6a9a5592f75f82d79e83f2184585fca5f6d7c14","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2020-01-27T06:45:41Z","title_canon_sha256":"4d8ff6b21e7da994a5a8631365b50059b96ab9d35d708a26b56485c81418e0bf"},"schema_version":"1.0","source":{"id":"2001.09603","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2001.09603","created_at":"2026-07-05T03:03:24Z"},{"alias_kind":"arxiv_version","alias_value":"2001.09603v3","created_at":"2026-07-05T03:03:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2001.09603","created_at":"2026-07-05T03:03:24Z"},{"alias_kind":"pith_short_12","alias_value":"74I6NNDUPBO3","created_at":"2026-07-05T03:03:24Z"},{"alias_kind":"pith_short_16","alias_value":"74I6NNDUPBO3FI3K","created_at":"2026-07-05T03:03:24Z"},{"alias_kind":"pith_short_8","alias_value":"74I6NNDU","created_at":"2026-07-05T03:03:24Z"}],"graph_snapshots":[{"event_id":"sha256:3d47bdf362f34fa0bddc88c8d69c45bb5ec85bcf6b76eea2bf157d6c5142e295","target":"graph","created_at":"2026-07-05T03:03:24Z","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/2001.09603/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We continue the study of positive geometries underlying the {\\it Grassmannian string integrals}, which are a class of \"stringy canonical forms\", or stringy integrals, over the positive Grassmannian mod torus action, $G_+(k,n)/T$. The leading order of any such stringy integral is given by the canonical function of a polytope, which can be obtained using the Minkowski sum of the Newton polytopes for the regulators of the integral, or equivalently given by the so-called scattering-equation map. The canonical function of the polytopes for Grassmannian string integrals, or the volume of their dual ","authors_text":"Lecheng Ren, Song He, Yong Zhang","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2020-01-27T06:45:41Z","title":"Notes on polytopes, amplitudes and boundary configurations for Grassmannian string integrals"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2001.09603","kind":"arxiv","version":3},"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:fe066197b11035c4dde9658512d23ebcac0d369b734a02cdd1da7bca9c7d93a2","target":"record","created_at":"2026-07-05T03:03:24Z","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":"a673278a377aa0dc4786a941b6a9a5592f75f82d79e83f2184585fca5f6d7c14","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2020-01-27T06:45:41Z","title_canon_sha256":"4d8ff6b21e7da994a5a8631365b50059b96ab9d35d708a26b56485c81418e0bf"},"schema_version":"1.0","source":{"id":"2001.09603","kind":"arxiv","version":3}},"canonical_sha256":"ff11e6b474785db2a36a7a72a4032fb007963b213d236e86557a9460dc02d3f4","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ff11e6b474785db2a36a7a72a4032fb007963b213d236e86557a9460dc02d3f4","first_computed_at":"2026-07-05T03:03:24.428114Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T03:03:24.428114Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"SjNaC8P8PFwkIlDuJri38EskELTh+jo8hOUZn2T+JnOQD3rP/Mtpx9FCXw5qrCC+FZVfXPu5hTy8yruHJPkHDg==","signature_status":"signed_v1","signed_at":"2026-07-05T03:03:24.428555Z","signed_message":"canonical_sha256_bytes"},"source_id":"2001.09603","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:fe066197b11035c4dde9658512d23ebcac0d369b734a02cdd1da7bca9c7d93a2","sha256:3d47bdf362f34fa0bddc88c8d69c45bb5ec85bcf6b76eea2bf157d6c5142e295"],"state_sha256":"521e8969da8123d020bdff5f4aa65c4303f127d31d92c15d098b175de708f23d"}