{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:RPQKBDNTKXIG2WQCGHHCJMTBCV","short_pith_number":"pith:RPQKBDNT","canonical_record":{"source":{"id":"1704.05069","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2017-04-17T18:00:02Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"4e42dc8f72abfab379a22b84324cd776c0962f505d2d590b4caf82a6ae938fd3","abstract_canon_sha256":"aca2e8f31b7de97c914e404305385c6fc632a636e8583842e8b7f571f9b33705"},"schema_version":"1.0"},"canonical_sha256":"8be0a08db355d06d5a0231ce24b261154197f56a5a3d38e4cbb5813f8c9e7041","source":{"kind":"arxiv","id":"1704.05069","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1704.05069","created_at":"2026-05-18T00:23:39Z"},{"alias_kind":"arxiv_version","alias_value":"1704.05069v1","created_at":"2026-05-18T00:23:39Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1704.05069","created_at":"2026-05-18T00:23:39Z"},{"alias_kind":"pith_short_12","alias_value":"RPQKBDNTKXIG","created_at":"2026-05-18T12:31:39Z"},{"alias_kind":"pith_short_16","alias_value":"RPQKBDNTKXIG2WQC","created_at":"2026-05-18T12:31:39Z"},{"alias_kind":"pith_short_8","alias_value":"RPQKBDNT","created_at":"2026-05-18T12:31:39Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:RPQKBDNTKXIG2WQCGHHCJMTBCV","target":"record","payload":{"canonical_record":{"source":{"id":"1704.05069","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2017-04-17T18:00:02Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"4e42dc8f72abfab379a22b84324cd776c0962f505d2d590b4caf82a6ae938fd3","abstract_canon_sha256":"aca2e8f31b7de97c914e404305385c6fc632a636e8583842e8b7f571f9b33705"},"schema_version":"1.0"},"canonical_sha256":"8be0a08db355d06d5a0231ce24b261154197f56a5a3d38e4cbb5813f8c9e7041","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:23:39.455587Z","signature_b64":"a/BlG3UrImU5Cax3LkqjkOtJZTz3zlXRXVPPcrhsOqZ209+BYnZJ+6xPMq+2sCHlA0MxWFwcWd9VfVBJmC8HCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8be0a08db355d06d5a0231ce24b261154197f56a5a3d38e4cbb5813f8c9e7041","last_reissued_at":"2026-05-18T00:23:39.454894Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:23:39.454894Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1704.05069","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":"2026-05-18T00:23:39Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"TuiFgo28rFzloy+53y8CdlP4RSUGCJn9m2iLXbQibSs/o9F0QnulvxlmbOsJeoyXD3/m7qCpYZgPb/UCDTcZCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T01:17:02.734769Z"},"content_sha256":"923c2e3ede4641d54fba3974dc35ed9aaa80ecde4fa00463fba3c348e7dc15ad","schema_version":"1.0","event_id":"sha256:923c2e3ede4641d54fba3974dc35ed9aaa80ecde4fa00463fba3c348e7dc15ad"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:RPQKBDNTKXIG2WQCGHHCJMTBCV","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Unwinding the Amplituhedron in Binary","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"hep-th","authors_text":"Hugh Thomas, Jaroslav Trnka, Nima Arkani-Hamed","submitted_at":"2017-04-17T18:00:02Z","abstract_excerpt":"We present new, fundamentally combinatorial and topological characterizations of the amplituhedron. Upon projecting external data through the amplituhedron, the resulting configuration of points has a specified (and maximal) generalized 'winding number'. Equivalently, the amplituhedron can be fully described in binary: canonical projections of the geometry down to one dimension have a specified (and maximal) number of 'sign flips' of the projected data. The locality and unitarity of scattering amplitudes are easily derived as elementary consequences of this binary code. Minimal winding defines"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1704.05069","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":""},"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":"2026-05-18T00:23:39Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"RaZYyuiTolMe/Onk3pVudHwOj+vKtzb/CCaCVexDBwwrYAPtkW9f/sglEVRQBgPO0Qj+0iLxYZGQ1BmwgK21Dg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T01:17:02.735151Z"},"content_sha256":"41b858ca7e8b196648a05f447a5f0ce5be4d011d7847f719134e962850aa34a4","schema_version":"1.0","event_id":"sha256:41b858ca7e8b196648a05f447a5f0ce5be4d011d7847f719134e962850aa34a4"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/RPQKBDNTKXIG2WQCGHHCJMTBCV/bundle.json","state_url":"https://pith.science/pith/RPQKBDNTKXIG2WQCGHHCJMTBCV/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/RPQKBDNTKXIG2WQCGHHCJMTBCV/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":"2026-05-31T01:17:02Z","links":{"resolver":"https://pith.science/pith/RPQKBDNTKXIG2WQCGHHCJMTBCV","bundle":"https://pith.science/pith/RPQKBDNTKXIG2WQCGHHCJMTBCV/bundle.json","state":"https://pith.science/pith/RPQKBDNTKXIG2WQCGHHCJMTBCV/state.json","well_known_bundle":"https://pith.science/.well-known/pith/RPQKBDNTKXIG2WQCGHHCJMTBCV/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:RPQKBDNTKXIG2WQCGHHCJMTBCV","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":"aca2e8f31b7de97c914e404305385c6fc632a636e8583842e8b7f571f9b33705","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2017-04-17T18:00:02Z","title_canon_sha256":"4e42dc8f72abfab379a22b84324cd776c0962f505d2d590b4caf82a6ae938fd3"},"schema_version":"1.0","source":{"id":"1704.05069","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1704.05069","created_at":"2026-05-18T00:23:39Z"},{"alias_kind":"arxiv_version","alias_value":"1704.05069v1","created_at":"2026-05-18T00:23:39Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1704.05069","created_at":"2026-05-18T00:23:39Z"},{"alias_kind":"pith_short_12","alias_value":"RPQKBDNTKXIG","created_at":"2026-05-18T12:31:39Z"},{"alias_kind":"pith_short_16","alias_value":"RPQKBDNTKXIG2WQC","created_at":"2026-05-18T12:31:39Z"},{"alias_kind":"pith_short_8","alias_value":"RPQKBDNT","created_at":"2026-05-18T12:31:39Z"}],"graph_snapshots":[{"event_id":"sha256:41b858ca7e8b196648a05f447a5f0ce5be4d011d7847f719134e962850aa34a4","target":"graph","created_at":"2026-05-18T00:23:39Z","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"},"paper":{"abstract_excerpt":"We present new, fundamentally combinatorial and topological characterizations of the amplituhedron. Upon projecting external data through the amplituhedron, the resulting configuration of points has a specified (and maximal) generalized 'winding number'. Equivalently, the amplituhedron can be fully described in binary: canonical projections of the geometry down to one dimension have a specified (and maximal) number of 'sign flips' of the projected data. The locality and unitarity of scattering amplitudes are easily derived as elementary consequences of this binary code. Minimal winding defines","authors_text":"Hugh Thomas, Jaroslav Trnka, Nima Arkani-Hamed","cross_cats":["math.CO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2017-04-17T18:00:02Z","title":"Unwinding the Amplituhedron in Binary"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1704.05069","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":"sha256:923c2e3ede4641d54fba3974dc35ed9aaa80ecde4fa00463fba3c348e7dc15ad","target":"record","created_at":"2026-05-18T00:23:39Z","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":"aca2e8f31b7de97c914e404305385c6fc632a636e8583842e8b7f571f9b33705","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2017-04-17T18:00:02Z","title_canon_sha256":"4e42dc8f72abfab379a22b84324cd776c0962f505d2d590b4caf82a6ae938fd3"},"schema_version":"1.0","source":{"id":"1704.05069","kind":"arxiv","version":1}},"canonical_sha256":"8be0a08db355d06d5a0231ce24b261154197f56a5a3d38e4cbb5813f8c9e7041","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8be0a08db355d06d5a0231ce24b261154197f56a5a3d38e4cbb5813f8c9e7041","first_computed_at":"2026-05-18T00:23:39.454894Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:23:39.454894Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"a/BlG3UrImU5Cax3LkqjkOtJZTz3zlXRXVPPcrhsOqZ209+BYnZJ+6xPMq+2sCHlA0MxWFwcWd9VfVBJmC8HCw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:23:39.455587Z","signed_message":"canonical_sha256_bytes"},"source_id":"1704.05069","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:923c2e3ede4641d54fba3974dc35ed9aaa80ecde4fa00463fba3c348e7dc15ad","sha256:41b858ca7e8b196648a05f447a5f0ce5be4d011d7847f719134e962850aa34a4"],"state_sha256":"81966f9218f02120ab9752ab8eea9a04888f6e71b37d4d3668eba6521e26560b"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"dmxPdz/2MUkExWICu57vpLAT3wgINrSbG2kbdzC5/UBhOmpQsNox8spIrtreaYHhjMpm3m69Ued1HMi3RDceDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-31T01:17:02.738686Z","bundle_sha256":"db351b747b6f9a7343d72221a48eeb6528a071291de6648c0b3e32fdfbd0fb96"}}