{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2019:QBRBDQZ3HKC5FBZPO63DESMH5B","short_pith_number":"pith:QBRBDQZ3","canonical_record":{"source":{"id":"1905.04216","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2019-05-10T15:25:31Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"950a367cc6e504f65b97128598be6a18fc18fdee2a885ffb90c7f74f003119ec","abstract_canon_sha256":"d265bb40b76c89742233c7959fe22985165e58cb21ab1f099d46833832f8ffa5"},"schema_version":"1.0"},"canonical_sha256":"806211c33b3a85d2872f77b6324987e848aa9bfbab8937587e623d79a7eda862","source":{"kind":"arxiv","id":"1905.04216","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1905.04216","created_at":"2026-07-05T00:01:51Z"},{"alias_kind":"arxiv_version","alias_value":"1905.04216v1","created_at":"2026-07-05T00:01:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1905.04216","created_at":"2026-07-05T00:01:51Z"},{"alias_kind":"pith_short_12","alias_value":"QBRBDQZ3HKC5","created_at":"2026-07-05T00:01:51Z"},{"alias_kind":"pith_short_16","alias_value":"QBRBDQZ3HKC5FBZP","created_at":"2026-07-05T00:01:51Z"},{"alias_kind":"pith_short_8","alias_value":"QBRBDQZ3","created_at":"2026-07-05T00:01:51Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2019:QBRBDQZ3HKC5FBZPO63DESMH5B","target":"record","payload":{"canonical_record":{"source":{"id":"1905.04216","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2019-05-10T15:25:31Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"950a367cc6e504f65b97128598be6a18fc18fdee2a885ffb90c7f74f003119ec","abstract_canon_sha256":"d265bb40b76c89742233c7959fe22985165e58cb21ab1f099d46833832f8ffa5"},"schema_version":"1.0"},"canonical_sha256":"806211c33b3a85d2872f77b6324987e848aa9bfbab8937587e623d79a7eda862","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T00:01:51.723881Z","signature_b64":"+bqjlCetve/bBZ9dAMcgTLAP4Sz80XEEohNwhc/Wn/ALaL+geo4NJwPL8/y9fTLX8TzVhQeAZUEJT5ypyLQFBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"806211c33b3a85d2872f77b6324987e848aa9bfbab8937587e623d79a7eda862","last_reissued_at":"2026-07-05T00:01:51.723420Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T00:01:51.723420Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1905.04216","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":"2026-07-05T00:01:51Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"H0XDRrPtNPX6expmF0N7FxgHh29+gtAXfFOu6cJkcxX4tJJtGfvptruWuvP61pyUT7emu/a2wWkz+Emm8Tq+Bg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-13T03:25:36.112737Z"},"content_sha256":"ca84b9af89db35b9bc6c6e0c09ab1a38bdbac211e3a05503ccb1a5128446a0ae","schema_version":"1.0","event_id":"sha256:ca84b9af89db35b9bc6c6e0c09ab1a38bdbac211e3a05503ccb1a5128446a0ae"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2019:QBRBDQZ3HKC5FBZPO63DESMH5B","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The Momentum Amplituhedron","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"hep-th","authors_text":"David Damgaard, Livia Ferro, Matteo Parisi, Tomasz Lukowski","submitted_at":"2019-05-10T15:25:31Z","abstract_excerpt":"In this paper we define a new object, the momentum amplituhedron, which is the long sought-after positive geometry for tree-level scattering amplitudes in $\\mathcal{N}=4$ super Yang-Mills theory in spinor helicity space. Inspired by the construction of the ordinary amplituhedron, we introduce bosonized spinor helicity variables to represent our external kinematical data, and restrict them to a particular positive region. The momentum amplituhedron $\\mathcal{M}_{n,k}$ is then the image of the positive Grassmannian via a map determined by such kinematics. The scattering amplitudes are extracted "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1905.04216","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/1905.04216/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":"2026-07-05T00:01:51Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"8e6robH+gOvoCUiFZlRLgZohP9Xsp7HwHkcDdtxW79B58jaFhyb3Nluh97DH84q/i+PoC1Qs7fdPF1PIyOhKBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-13T03:25:36.113295Z"},"content_sha256":"501630f5277e90f7adad093647e0a34cfa8be6f15841060c449fbc58878c6630","schema_version":"1.0","event_id":"sha256:501630f5277e90f7adad093647e0a34cfa8be6f15841060c449fbc58878c6630"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/QBRBDQZ3HKC5FBZPO63DESMH5B/bundle.json","state_url":"https://pith.science/pith/QBRBDQZ3HKC5FBZPO63DESMH5B/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/QBRBDQZ3HKC5FBZPO63DESMH5B/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":"2026-08-13T03:25:36Z","links":{"resolver":"https://pith.science/pith/QBRBDQZ3HKC5FBZPO63DESMH5B","bundle":"https://pith.science/pith/QBRBDQZ3HKC5FBZPO63DESMH5B/bundle.json","state":"https://pith.science/pith/QBRBDQZ3HKC5FBZPO63DESMH5B/state.json","well_known_bundle":"https://pith.science/.well-known/pith/QBRBDQZ3HKC5FBZPO63DESMH5B/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:QBRBDQZ3HKC5FBZPO63DESMH5B","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":"d265bb40b76c89742233c7959fe22985165e58cb21ab1f099d46833832f8ffa5","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2019-05-10T15:25:31Z","title_canon_sha256":"950a367cc6e504f65b97128598be6a18fc18fdee2a885ffb90c7f74f003119ec"},"schema_version":"1.0","source":{"id":"1905.04216","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1905.04216","created_at":"2026-07-05T00:01:51Z"},{"alias_kind":"arxiv_version","alias_value":"1905.04216v1","created_at":"2026-07-05T00:01:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1905.04216","created_at":"2026-07-05T00:01:51Z"},{"alias_kind":"pith_short_12","alias_value":"QBRBDQZ3HKC5","created_at":"2026-07-05T00:01:51Z"},{"alias_kind":"pith_short_16","alias_value":"QBRBDQZ3HKC5FBZP","created_at":"2026-07-05T00:01:51Z"},{"alias_kind":"pith_short_8","alias_value":"QBRBDQZ3","created_at":"2026-07-05T00:01:51Z"}],"graph_snapshots":[{"event_id":"sha256:501630f5277e90f7adad093647e0a34cfa8be6f15841060c449fbc58878c6630","target":"graph","created_at":"2026-07-05T00:01:51Z","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/1905.04216/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In this paper we define a new object, the momentum amplituhedron, which is the long sought-after positive geometry for tree-level scattering amplitudes in $\\mathcal{N}=4$ super Yang-Mills theory in spinor helicity space. Inspired by the construction of the ordinary amplituhedron, we introduce bosonized spinor helicity variables to represent our external kinematical data, and restrict them to a particular positive region. The momentum amplituhedron $\\mathcal{M}_{n,k}$ is then the image of the positive Grassmannian via a map determined by such kinematics. The scattering amplitudes are extracted ","authors_text":"David Damgaard, Livia Ferro, Matteo Parisi, Tomasz Lukowski","cross_cats":["math-ph","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2019-05-10T15:25:31Z","title":"The Momentum Amplituhedron"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1905.04216","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:ca84b9af89db35b9bc6c6e0c09ab1a38bdbac211e3a05503ccb1a5128446a0ae","target":"record","created_at":"2026-07-05T00:01:51Z","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":"d265bb40b76c89742233c7959fe22985165e58cb21ab1f099d46833832f8ffa5","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2019-05-10T15:25:31Z","title_canon_sha256":"950a367cc6e504f65b97128598be6a18fc18fdee2a885ffb90c7f74f003119ec"},"schema_version":"1.0","source":{"id":"1905.04216","kind":"arxiv","version":1}},"canonical_sha256":"806211c33b3a85d2872f77b6324987e848aa9bfbab8937587e623d79a7eda862","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"806211c33b3a85d2872f77b6324987e848aa9bfbab8937587e623d79a7eda862","first_computed_at":"2026-07-05T00:01:51.723420Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T00:01:51.723420Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"+bqjlCetve/bBZ9dAMcgTLAP4Sz80XEEohNwhc/Wn/ALaL+geo4NJwPL8/y9fTLX8TzVhQeAZUEJT5ypyLQFBQ==","signature_status":"signed_v1","signed_at":"2026-07-05T00:01:51.723881Z","signed_message":"canonical_sha256_bytes"},"source_id":"1905.04216","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ca84b9af89db35b9bc6c6e0c09ab1a38bdbac211e3a05503ccb1a5128446a0ae","sha256:501630f5277e90f7adad093647e0a34cfa8be6f15841060c449fbc58878c6630"],"state_sha256":"f34bc275357086ea11f5846749f394e5b8e614963c1ff265ec13a23c8b57b4f6"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"8nWeRnNd8zZpVE2F4FCx9HoCfvrj1iaSOCtglIAcRHaR96Fb01D7UgD65f60t+gtJNg44n1HReRaGk/tNwqeCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-13T03:25:36.118250Z","bundle_sha256":"3e3e500cbc100eba019313744d43b577bfbdfc3cb9e518da888ba10b76b7e613"}}