{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2021:ZBDGFGV2MWSWW5U7G2MFACYCCU","short_pith_number":"pith:ZBDGFGV2","canonical_record":{"source":{"id":"2106.01392","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2021-06-02T18:00:29Z","cross_cats_sorted":[],"title_canon_sha256":"2ef3f5e440803c145f1fdc0025e0952b0af114727e004cb31ab4969ff6ed15da","abstract_canon_sha256":"409f66dc038e136ad93927d9eac89e30a66f72025de7533912783e562a9e7d67"},"schema_version":"1.0"},"canonical_sha256":"c846629aba65a56b769f3698500b0215150e01a43a496efe784bfa3fa4198213","source":{"kind":"arxiv","id":"2106.01392","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2106.01392","created_at":"2026-07-05T03:21:50Z"},{"alias_kind":"arxiv_version","alias_value":"2106.01392v2","created_at":"2026-07-05T03:21:50Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2106.01392","created_at":"2026-07-05T03:21:50Z"},{"alias_kind":"pith_short_12","alias_value":"ZBDGFGV2MWSW","created_at":"2026-07-05T03:21:50Z"},{"alias_kind":"pith_short_16","alias_value":"ZBDGFGV2MWSWW5U7","created_at":"2026-07-05T03:21:50Z"},{"alias_kind":"pith_short_8","alias_value":"ZBDGFGV2","created_at":"2026-07-05T03:21:50Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2021:ZBDGFGV2MWSWW5U7G2MFACYCCU","target":"record","payload":{"canonical_record":{"source":{"id":"2106.01392","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2021-06-02T18:00:29Z","cross_cats_sorted":[],"title_canon_sha256":"2ef3f5e440803c145f1fdc0025e0952b0af114727e004cb31ab4969ff6ed15da","abstract_canon_sha256":"409f66dc038e136ad93927d9eac89e30a66f72025de7533912783e562a9e7d67"},"schema_version":"1.0"},"canonical_sha256":"c846629aba65a56b769f3698500b0215150e01a43a496efe784bfa3fa4198213","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T03:21:50.330064Z","signature_b64":"nAqSAZYlLCj3Xi0CCW0ujTsiN0UCGfCOW3PaAxkilD+ejjKh1FrtEBhZEiKOaI9J3jjZCUAocvo0vfy9Hg+iDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c846629aba65a56b769f3698500b0215150e01a43a496efe784bfa3fa4198213","last_reissued_at":"2026-07-05T03:21:50.329477Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T03:21:50.329477Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2106.01392","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T03:21:50Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"af5MsGHQlNdkwHwcbFvyRb7pE6Rn21J+StV5Q1jD+ccqdppZlxXxK1iUPUyKQ8p2XyQUWcbQ9TpGC2e/l8aYDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-03T08:03:23.227210Z"},"content_sha256":"d4df4583647bb695c0a1ffa77c151bb92540a03aa4a1f3d2f60c339ba5e1431f","schema_version":"1.0","event_id":"sha256:d4df4583647bb695c0a1ffa77c151bb92540a03aa4a1f3d2f60c339ba5e1431f"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2021:ZBDGFGV2MWSWW5U7G2MFACYCCU","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Singularities of eight- and nine-particle amplitudes from cluster algebras and tropical geometry","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"hep-th","authors_text":"Georgios Papathanasiou, Niklas Henke","submitted_at":"2021-06-02T18:00:29Z","abstract_excerpt":"We further exploit the relation between tropical Grassmannians and $\\operatorname{Gr}(4,n)$ cluster algebras in order to make and refine predictions for the singularities of scattering amplitudes in $\\mathcal{N}=4$ planar super Yang-Mills theory at higher multiplicity $n\\ge 8$. As a mathematical foundation that provides access to square-root symbol letters in principle for any $n$, we analyse infinite mutation sequences in cluster algebras with general coefficients. First specialising our analysis to the eight-particle amplitude, and comparing it with a recent, closely related approach based o"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2106.01392","kind":"arxiv","version":2},"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/2106.01392/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":"2026-07-05T03:21:50Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"r29Aiug9si2Z+ZRClWSx11RkEMk9IgxyshASyqoAweVme+Hujt/BiGDqsU2XVvbUtWLiE8dk8m/dYnXknTlLBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-03T08:03:23.227772Z"},"content_sha256":"09b02597e8bcd42bf1c7ab3ab5b28756ab359a9fcca1aeb233a0255c78fcfdc8","schema_version":"1.0","event_id":"sha256:09b02597e8bcd42bf1c7ab3ab5b28756ab359a9fcca1aeb233a0255c78fcfdc8"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/ZBDGFGV2MWSWW5U7G2MFACYCCU/bundle.json","state_url":"https://pith.science/pith/ZBDGFGV2MWSWW5U7G2MFACYCCU/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/ZBDGFGV2MWSWW5U7G2MFACYCCU/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":"2026-08-03T08:03:23Z","links":{"resolver":"https://pith.science/pith/ZBDGFGV2MWSWW5U7G2MFACYCCU","bundle":"https://pith.science/pith/ZBDGFGV2MWSWW5U7G2MFACYCCU/bundle.json","state":"https://pith.science/pith/ZBDGFGV2MWSWW5U7G2MFACYCCU/state.json","well_known_bundle":"https://pith.science/.well-known/pith/ZBDGFGV2MWSWW5U7G2MFACYCCU/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2021:ZBDGFGV2MWSWW5U7G2MFACYCCU","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":"409f66dc038e136ad93927d9eac89e30a66f72025de7533912783e562a9e7d67","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2021-06-02T18:00:29Z","title_canon_sha256":"2ef3f5e440803c145f1fdc0025e0952b0af114727e004cb31ab4969ff6ed15da"},"schema_version":"1.0","source":{"id":"2106.01392","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2106.01392","created_at":"2026-07-05T03:21:50Z"},{"alias_kind":"arxiv_version","alias_value":"2106.01392v2","created_at":"2026-07-05T03:21:50Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2106.01392","created_at":"2026-07-05T03:21:50Z"},{"alias_kind":"pith_short_12","alias_value":"ZBDGFGV2MWSW","created_at":"2026-07-05T03:21:50Z"},{"alias_kind":"pith_short_16","alias_value":"ZBDGFGV2MWSWW5U7","created_at":"2026-07-05T03:21:50Z"},{"alias_kind":"pith_short_8","alias_value":"ZBDGFGV2","created_at":"2026-07-05T03:21:50Z"}],"graph_snapshots":[{"event_id":"sha256:09b02597e8bcd42bf1c7ab3ab5b28756ab359a9fcca1aeb233a0255c78fcfdc8","target":"graph","created_at":"2026-07-05T03:21:50Z","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/2106.01392/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We further exploit the relation between tropical Grassmannians and $\\operatorname{Gr}(4,n)$ cluster algebras in order to make and refine predictions for the singularities of scattering amplitudes in $\\mathcal{N}=4$ planar super Yang-Mills theory at higher multiplicity $n\\ge 8$. As a mathematical foundation that provides access to square-root symbol letters in principle for any $n$, we analyse infinite mutation sequences in cluster algebras with general coefficients. First specialising our analysis to the eight-particle amplitude, and comparing it with a recent, closely related approach based o","authors_text":"Georgios Papathanasiou, Niklas Henke","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2021-06-02T18:00:29Z","title":"Singularities of eight- and nine-particle amplitudes from cluster algebras and tropical geometry"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2106.01392","kind":"arxiv","version":2},"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:d4df4583647bb695c0a1ffa77c151bb92540a03aa4a1f3d2f60c339ba5e1431f","target":"record","created_at":"2026-07-05T03:21:50Z","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":"409f66dc038e136ad93927d9eac89e30a66f72025de7533912783e562a9e7d67","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2021-06-02T18:00:29Z","title_canon_sha256":"2ef3f5e440803c145f1fdc0025e0952b0af114727e004cb31ab4969ff6ed15da"},"schema_version":"1.0","source":{"id":"2106.01392","kind":"arxiv","version":2}},"canonical_sha256":"c846629aba65a56b769f3698500b0215150e01a43a496efe784bfa3fa4198213","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c846629aba65a56b769f3698500b0215150e01a43a496efe784bfa3fa4198213","first_computed_at":"2026-07-05T03:21:50.329477Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T03:21:50.329477Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"nAqSAZYlLCj3Xi0CCW0ujTsiN0UCGfCOW3PaAxkilD+ejjKh1FrtEBhZEiKOaI9J3jjZCUAocvo0vfy9Hg+iDw==","signature_status":"signed_v1","signed_at":"2026-07-05T03:21:50.330064Z","signed_message":"canonical_sha256_bytes"},"source_id":"2106.01392","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d4df4583647bb695c0a1ffa77c151bb92540a03aa4a1f3d2f60c339ba5e1431f","sha256:09b02597e8bcd42bf1c7ab3ab5b28756ab359a9fcca1aeb233a0255c78fcfdc8"],"state_sha256":"b910411b3035edb7d92ca8eab0d6773719f26578835bbcd0ad6ed39730059e84"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"IPNjTnosvuMwA7y7UOACblNwlQWX47LU1ofE3j6G0tMjvWT2Glxga+//9BHIG63wS/RHVJisSJLaWWGhmDpwDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-03T08:03:23.234468Z","bundle_sha256":"d292d3f16feab63dad2a99dbf76da199fb3d6b55dbefda3f3fc8ff31a71d3458"}}