{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2024:BSP7KSTRPWJAZQGSNOHGJLWELX","short_pith_number":"pith:BSP7KSTR","canonical_record":{"source":{"id":"2403.06948","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2024-03-11T17:33:30Z","cross_cats_sorted":["hep-th","math-ph","math.AG","math.MP"],"title_canon_sha256":"a353cbb7452e284581b0b4c3a8a27f62a7f62a0cc1567f0c8287ee2081c83d6b","abstract_canon_sha256":"583fb133e39e54f127d1566f977147072e38dde366b3b545c605d89d721b16b5"},"schema_version":"1.0"},"canonical_sha256":"0c9ff54a717d920cc0d26b8e64aec45dee12ca38c679e71a0353519f84682bb3","source":{"kind":"arxiv","id":"2403.06948","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2403.06948","created_at":"2026-07-05T10:58:15Z"},{"alias_kind":"arxiv_version","alias_value":"2403.06948v3","created_at":"2026-07-05T10:58:15Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2403.06948","created_at":"2026-07-05T10:58:15Z"},{"alias_kind":"pith_short_12","alias_value":"BSP7KSTRPWJA","created_at":"2026-07-05T10:58:15Z"},{"alias_kind":"pith_short_16","alias_value":"BSP7KSTRPWJAZQGS","created_at":"2026-07-05T10:58:15Z"},{"alias_kind":"pith_short_8","alias_value":"BSP7KSTR","created_at":"2026-07-05T10:58:15Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2024:BSP7KSTRPWJAZQGSNOHGJLWELX","target":"record","payload":{"canonical_record":{"source":{"id":"2403.06948","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2024-03-11T17:33:30Z","cross_cats_sorted":["hep-th","math-ph","math.AG","math.MP"],"title_canon_sha256":"a353cbb7452e284581b0b4c3a8a27f62a7f62a0cc1567f0c8287ee2081c83d6b","abstract_canon_sha256":"583fb133e39e54f127d1566f977147072e38dde366b3b545c605d89d721b16b5"},"schema_version":"1.0"},"canonical_sha256":"0c9ff54a717d920cc0d26b8e64aec45dee12ca38c679e71a0353519f84682bb3","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T10:58:15.304291Z","signature_b64":"SkTKh/cvAt2loMXvDumJFPNlwC9yRh6rleL/y8bfrf9y0kHID/SDQ96y2OHXfoVU49cR4PAtTgGG0RmKCM+tDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0c9ff54a717d920cc0d26b8e64aec45dee12ca38c679e71a0353519f84682bb3","last_reissued_at":"2026-07-05T10:58:15.303808Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T10:58:15.303808Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2403.06948","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T10:58:15Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"7dNkolCRiFM9JMrlf+/c/3Lv2hGgBr6XgEwj8p8KSSDb2opsDmimeSEWeZBzLrB29mZMEwStgquN1dmCwPe8Aw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-11T01:06:48.556166Z"},"content_sha256":"609782d33caf6540563b89bcf1ddd4e8a8d7e5c6abf50682a619f9651df50178","schema_version":"1.0","event_id":"sha256:609782d33caf6540563b89bcf1ddd4e8a8d7e5c6abf50682a619f9651df50178"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2024:BSP7KSTRPWJAZQGSNOHGJLWELX","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On the face stratification of the $m=2$ amplituhedron","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["hep-th","math-ph","math.AG","math.MP"],"primary_cat":"math.CO","authors_text":"Thomas Lam","submitted_at":"2024-03-11T17:33:30Z","abstract_excerpt":"We define and study the face stratification of the m=2 amplituhedron. We show that the face poset is an upper order ideal in the face poset of the totally nonnegative Grassmannian. Our construction is consistent with earlier work of Lukowski, and we confirm various predictions of Lukowski."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2403.06948","kind":"arxiv","version":3},"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/2403.06948/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":"2026-07-05T10:58:15Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"nIrn+raTKRS5Uo81yIGYVqqo+lm2QQHwjuWSbXVSpr/1VLln1HacQVDKt63wfuHbaoKNBbqiIRcLOdvY8ofQBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-11T01:06:48.557041Z"},"content_sha256":"d46df16e4666c8f28dab05c14ae613e9223225966bc32c0def408242c7ddbd09","schema_version":"1.0","event_id":"sha256:d46df16e4666c8f28dab05c14ae613e9223225966bc32c0def408242c7ddbd09"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/BSP7KSTRPWJAZQGSNOHGJLWELX/bundle.json","state_url":"https://pith.science/pith/BSP7KSTRPWJAZQGSNOHGJLWELX/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/BSP7KSTRPWJAZQGSNOHGJLWELX/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":"2026-08-11T01:06:48Z","links":{"resolver":"https://pith.science/pith/BSP7KSTRPWJAZQGSNOHGJLWELX","bundle":"https://pith.science/pith/BSP7KSTRPWJAZQGSNOHGJLWELX/bundle.json","state":"https://pith.science/pith/BSP7KSTRPWJAZQGSNOHGJLWELX/state.json","well_known_bundle":"https://pith.science/.well-known/pith/BSP7KSTRPWJAZQGSNOHGJLWELX/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:BSP7KSTRPWJAZQGSNOHGJLWELX","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":"583fb133e39e54f127d1566f977147072e38dde366b3b545c605d89d721b16b5","cross_cats_sorted":["hep-th","math-ph","math.AG","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2024-03-11T17:33:30Z","title_canon_sha256":"a353cbb7452e284581b0b4c3a8a27f62a7f62a0cc1567f0c8287ee2081c83d6b"},"schema_version":"1.0","source":{"id":"2403.06948","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2403.06948","created_at":"2026-07-05T10:58:15Z"},{"alias_kind":"arxiv_version","alias_value":"2403.06948v3","created_at":"2026-07-05T10:58:15Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2403.06948","created_at":"2026-07-05T10:58:15Z"},{"alias_kind":"pith_short_12","alias_value":"BSP7KSTRPWJA","created_at":"2026-07-05T10:58:15Z"},{"alias_kind":"pith_short_16","alias_value":"BSP7KSTRPWJAZQGS","created_at":"2026-07-05T10:58:15Z"},{"alias_kind":"pith_short_8","alias_value":"BSP7KSTR","created_at":"2026-07-05T10:58:15Z"}],"graph_snapshots":[{"event_id":"sha256:d46df16e4666c8f28dab05c14ae613e9223225966bc32c0def408242c7ddbd09","target":"graph","created_at":"2026-07-05T10:58:15Z","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/2403.06948/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We define and study the face stratification of the m=2 amplituhedron. We show that the face poset is an upper order ideal in the face poset of the totally nonnegative Grassmannian. Our construction is consistent with earlier work of Lukowski, and we confirm various predictions of Lukowski.","authors_text":"Thomas Lam","cross_cats":["hep-th","math-ph","math.AG","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2024-03-11T17:33:30Z","title":"On the face stratification of the $m=2$ amplituhedron"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2403.06948","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":"sha256:609782d33caf6540563b89bcf1ddd4e8a8d7e5c6abf50682a619f9651df50178","target":"record","created_at":"2026-07-05T10:58:15Z","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":"583fb133e39e54f127d1566f977147072e38dde366b3b545c605d89d721b16b5","cross_cats_sorted":["hep-th","math-ph","math.AG","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2024-03-11T17:33:30Z","title_canon_sha256":"a353cbb7452e284581b0b4c3a8a27f62a7f62a0cc1567f0c8287ee2081c83d6b"},"schema_version":"1.0","source":{"id":"2403.06948","kind":"arxiv","version":3}},"canonical_sha256":"0c9ff54a717d920cc0d26b8e64aec45dee12ca38c679e71a0353519f84682bb3","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0c9ff54a717d920cc0d26b8e64aec45dee12ca38c679e71a0353519f84682bb3","first_computed_at":"2026-07-05T10:58:15.303808Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T10:58:15.303808Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"SkTKh/cvAt2loMXvDumJFPNlwC9yRh6rleL/y8bfrf9y0kHID/SDQ96y2OHXfoVU49cR4PAtTgGG0RmKCM+tDA==","signature_status":"signed_v1","signed_at":"2026-07-05T10:58:15.304291Z","signed_message":"canonical_sha256_bytes"},"source_id":"2403.06948","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:609782d33caf6540563b89bcf1ddd4e8a8d7e5c6abf50682a619f9651df50178","sha256:d46df16e4666c8f28dab05c14ae613e9223225966bc32c0def408242c7ddbd09"],"state_sha256":"414a89e6f8d762ac25e7b6dbfcaf48e21e5318d64b3fbe8b7d2de46addbc122b"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ObA6Rt5SqtOeglfEQhpiyjFiaShrWdGnZMJf5DAVI74x5wtO0meGIXPlmQzpHuF1XWlI09SxxfdbZS9YgLVsCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-11T01:06:48.563474Z","bundle_sha256":"41f60b4d5df8952680bb4f1de4dfe46b079e77bcaf55c925cf71c2282e675229"}}