{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2019:IUUBOX77HO5VHBZTDAE45Q4Q4X","short_pith_number":"pith:IUUBOX77","canonical_record":{"source":{"id":"1912.08222","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2019-12-17T19:00:17Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"16ad304a058edbde043dc1564899b2ab1594bfecd46048704fc663f9ad4f66f6","abstract_canon_sha256":"7fefae968b28902f88419c5e65d728e670e32d6ff218b48927e02804229ec171"},"schema_version":"1.0"},"canonical_sha256":"4528175fff3bbb5387331809cec390e5ef090263f7637f5354df84f250ef893e","source":{"kind":"arxiv","id":"1912.08222","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1912.08222","created_at":"2026-07-05T00:27:20Z"},{"alias_kind":"arxiv_version","alias_value":"1912.08222v1","created_at":"2026-07-05T00:27:20Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1912.08222","created_at":"2026-07-05T00:27:20Z"},{"alias_kind":"pith_short_12","alias_value":"IUUBOX77HO5V","created_at":"2026-07-05T00:27:20Z"},{"alias_kind":"pith_short_16","alias_value":"IUUBOX77HO5VHBZT","created_at":"2026-07-05T00:27:20Z"},{"alias_kind":"pith_short_8","alias_value":"IUUBOX77","created_at":"2026-07-05T00:27:20Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2019:IUUBOX77HO5VHBZTDAE45Q4Q4X","target":"record","payload":{"canonical_record":{"source":{"id":"1912.08222","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2019-12-17T19:00:17Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"16ad304a058edbde043dc1564899b2ab1594bfecd46048704fc663f9ad4f66f6","abstract_canon_sha256":"7fefae968b28902f88419c5e65d728e670e32d6ff218b48927e02804229ec171"},"schema_version":"1.0"},"canonical_sha256":"4528175fff3bbb5387331809cec390e5ef090263f7637f5354df84f250ef893e","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T00:27:20.518768Z","signature_b64":"8wnslruwH7bA5uziZMBbijxdbWIVZOn6DMjrqqJW/BGHidGNqOidvx6on8KW5lvvquvQ8rMc4DOnB/4JFcjcDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4528175fff3bbb5387331809cec390e5ef090263f7637f5354df84f250ef893e","last_reissued_at":"2026-07-05T00:27:20.518305Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T00:27:20.518305Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1912.08222","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":"2026-07-05T00:27:20Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Ju8mo7vIgt4j96/aQqmPhJ+9LekaGr5NSeLmzmSz3yGZsWcGdIyfKJ0msr/5Pr9EjWA9rFaFOqKUjqGLqNFuBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-03T16:00:13.464619Z"},"content_sha256":"f66cb9547339618c7ee2d9b479242a8b9a4abc1b2ba0d2bf0d14fc71ca7615f1","schema_version":"1.0","event_id":"sha256:f66cb9547339618c7ee2d9b479242a8b9a4abc1b2ba0d2bf0d14fc71ca7615f1"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2019:IUUBOX77HO5VHBZTDAE45Q4Q4X","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Non-perturbative geometries for planar $\\mathcal{N}=4$ SYM amplitudes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"hep-th","authors_text":"Marcus Spradlin, Nima Arkani-Hamed, Thomas Lam","submitted_at":"2019-12-17T19:00:17Z","abstract_excerpt":"There is a remarkable well-known connection between the G$(4,n)$ cluster algebra and $n$-particle amplitudes in $\\mathcal{N}=4$ SYM theory. For $n \\ge 8$ two long-standing open questions have been to find a mathematically natural way to identify a finite list of amplitude symbol letters from among the infinitely many cluster variables, and to find an explanation for certain algebraic functions, such as the square roots of four-mass-box type, that are expected to appear in symbols but are not cluster variables. In this letter we use the notion of \"stringy canonical forms\" to construct polytopal"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1912.08222","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/1912.08222/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":"2026-07-05T00:27:20Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"DjHIFEbJ4LBaONvHH2azx+h5uvDDGxx6/08gMwJI4b+ZwBBgHwVG9iUDvQDW4S0Mh0MLcvc7nwIupjKA10GCBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-03T16:00:13.465548Z"},"content_sha256":"a293d6d3a113513cf7df42a6910e56db3df6c6f3e71c5bf044b12f3a2b1bc656","schema_version":"1.0","event_id":"sha256:a293d6d3a113513cf7df42a6910e56db3df6c6f3e71c5bf044b12f3a2b1bc656"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/IUUBOX77HO5VHBZTDAE45Q4Q4X/bundle.json","state_url":"https://pith.science/pith/IUUBOX77HO5VHBZTDAE45Q4Q4X/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/IUUBOX77HO5VHBZTDAE45Q4Q4X/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":"2026-08-03T16:00:13Z","links":{"resolver":"https://pith.science/pith/IUUBOX77HO5VHBZTDAE45Q4Q4X","bundle":"https://pith.science/pith/IUUBOX77HO5VHBZTDAE45Q4Q4X/bundle.json","state":"https://pith.science/pith/IUUBOX77HO5VHBZTDAE45Q4Q4X/state.json","well_known_bundle":"https://pith.science/.well-known/pith/IUUBOX77HO5VHBZTDAE45Q4Q4X/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:IUUBOX77HO5VHBZTDAE45Q4Q4X","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":"7fefae968b28902f88419c5e65d728e670e32d6ff218b48927e02804229ec171","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2019-12-17T19:00:17Z","title_canon_sha256":"16ad304a058edbde043dc1564899b2ab1594bfecd46048704fc663f9ad4f66f6"},"schema_version":"1.0","source":{"id":"1912.08222","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1912.08222","created_at":"2026-07-05T00:27:20Z"},{"alias_kind":"arxiv_version","alias_value":"1912.08222v1","created_at":"2026-07-05T00:27:20Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1912.08222","created_at":"2026-07-05T00:27:20Z"},{"alias_kind":"pith_short_12","alias_value":"IUUBOX77HO5V","created_at":"2026-07-05T00:27:20Z"},{"alias_kind":"pith_short_16","alias_value":"IUUBOX77HO5VHBZT","created_at":"2026-07-05T00:27:20Z"},{"alias_kind":"pith_short_8","alias_value":"IUUBOX77","created_at":"2026-07-05T00:27:20Z"}],"graph_snapshots":[{"event_id":"sha256:a293d6d3a113513cf7df42a6910e56db3df6c6f3e71c5bf044b12f3a2b1bc656","target":"graph","created_at":"2026-07-05T00:27:20Z","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/1912.08222/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"There is a remarkable well-known connection between the G$(4,n)$ cluster algebra and $n$-particle amplitudes in $\\mathcal{N}=4$ SYM theory. For $n \\ge 8$ two long-standing open questions have been to find a mathematically natural way to identify a finite list of amplitude symbol letters from among the infinitely many cluster variables, and to find an explanation for certain algebraic functions, such as the square roots of four-mass-box type, that are expected to appear in symbols but are not cluster variables. In this letter we use the notion of \"stringy canonical forms\" to construct polytopal","authors_text":"Marcus Spradlin, Nima Arkani-Hamed, Thomas Lam","cross_cats":["math.CO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2019-12-17T19:00:17Z","title":"Non-perturbative geometries for planar $\\mathcal{N}=4$ SYM amplitudes"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1912.08222","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:f66cb9547339618c7ee2d9b479242a8b9a4abc1b2ba0d2bf0d14fc71ca7615f1","target":"record","created_at":"2026-07-05T00:27:20Z","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":"7fefae968b28902f88419c5e65d728e670e32d6ff218b48927e02804229ec171","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2019-12-17T19:00:17Z","title_canon_sha256":"16ad304a058edbde043dc1564899b2ab1594bfecd46048704fc663f9ad4f66f6"},"schema_version":"1.0","source":{"id":"1912.08222","kind":"arxiv","version":1}},"canonical_sha256":"4528175fff3bbb5387331809cec390e5ef090263f7637f5354df84f250ef893e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4528175fff3bbb5387331809cec390e5ef090263f7637f5354df84f250ef893e","first_computed_at":"2026-07-05T00:27:20.518305Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T00:27:20.518305Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"8wnslruwH7bA5uziZMBbijxdbWIVZOn6DMjrqqJW/BGHidGNqOidvx6on8KW5lvvquvQ8rMc4DOnB/4JFcjcDA==","signature_status":"signed_v1","signed_at":"2026-07-05T00:27:20.518768Z","signed_message":"canonical_sha256_bytes"},"source_id":"1912.08222","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f66cb9547339618c7ee2d9b479242a8b9a4abc1b2ba0d2bf0d14fc71ca7615f1","sha256:a293d6d3a113513cf7df42a6910e56db3df6c6f3e71c5bf044b12f3a2b1bc656"],"state_sha256":"8b97e8ae7242af184e58d3a5c56393b4f39921a561d0f49e0bf0f6ef461436d8"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"T2SMq5NTeHW9D8hTI0Ipehsb9AYaHKYTHUIZoYisC5UtHVGGpvj78/etzNMSGAwWOlSyWptNzy3gQKEa05TdBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-03T16:00:13.470700Z","bundle_sha256":"146e77bf6b8e1c037d328ff29cc96727c6267afce0994d41ee439b91bab2ea30"}}