{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2024:75K2RRSKZDJOXLII3RA44O2I3I","short_pith_number":"pith:75K2RRSK","schema_version":"1.0","canonical_sha256":"ff55a8c64ac8d2ebad08dc41ce3b48da04ef403d5d4d627179a0342b06dcb03f","source":{"kind":"arxiv","id":"2405.17332","version":2},"attestation_state":"computed","paper":{"title":"Moduli spaces in positive geometry","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["hep-th","math.CO"],"primary_cat":"math.AG","authors_text":"Thomas Lam","submitted_at":"2024-05-27T16:32:33Z","abstract_excerpt":"These are lecture notes for five lectures given at MPI Leipzig in May 2024. We study the moduli space M_{0,n} of n distinct points on P^1 as a positive geometry and a binary geometry. We develop mathematical formalism to study Cachazo-He-Yuan's scattering equations and the associated scalar and Yang-Mills amplitudes. We discuss open superstring amplitudes and relations to tropical geometry."},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"2405.17332","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2024-05-27T16:32:33Z","cross_cats_sorted":["hep-th","math.CO"],"title_canon_sha256":"6ade6035849d85aa63460359502d6bf86603d62c5cd0c773418845938c4592df","abstract_canon_sha256":"adca1d4b5fc3fa7fee1642c468c8c9b176fbdb58caa3b8d8cc1ca13a41cf1170"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:09:58.731983Z","signature_b64":"iamq9QPMw9NGdZcUKHa3bmMtxdCj9V941p+yAT8wX1o1VJPx2U21P+MerPJGla6iufol433yoDdul9B3fue9Bg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ff55a8c64ac8d2ebad08dc41ce3b48da04ef403d5d4d627179a0342b06dcb03f","last_reissued_at":"2026-07-05T11:09:58.731415Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:09:58.731415Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Moduli spaces in positive geometry","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["hep-th","math.CO"],"primary_cat":"math.AG","authors_text":"Thomas Lam","submitted_at":"2024-05-27T16:32:33Z","abstract_excerpt":"These are lecture notes for five lectures given at MPI Leipzig in May 2024. We study the moduli space M_{0,n} of n distinct points on P^1 as a positive geometry and a binary geometry. We develop mathematical formalism to study Cachazo-He-Yuan's scattering equations and the associated scalar and Yang-Mills amplitudes. We discuss open superstring amplitudes and relations to tropical geometry."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2405.17332","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/2405.17332/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"},"aliases":[{"alias_kind":"arxiv","alias_value":"2405.17332","created_at":"2026-07-05T11:09:58.731479+00:00"},{"alias_kind":"arxiv_version","alias_value":"2405.17332v2","created_at":"2026-07-05T11:09:58.731479+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2405.17332","created_at":"2026-07-05T11:09:58.731479+00:00"},{"alias_kind":"pith_short_12","alias_value":"75K2RRSKZDJO","created_at":"2026-07-05T11:09:58.731479+00:00"},{"alias_kind":"pith_short_16","alias_value":"75K2RRSKZDJOXLII","created_at":"2026-07-05T11:09:58.731479+00:00"},{"alias_kind":"pith_short_8","alias_value":"75K2RRSK","created_at":"2026-07-05T11:09:58.731479+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2501.03202","citing_title":"Positive geometries and canonical forms via mixed Hodge theory","ref_index":26,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/75K2RRSKZDJOXLII3RA44O2I3I","json":"https://pith.science/pith/75K2RRSKZDJOXLII3RA44O2I3I.json","graph_json":"https://pith.science/api/pith-number/75K2RRSKZDJOXLII3RA44O2I3I/graph.json","events_json":"https://pith.science/api/pith-number/75K2RRSKZDJOXLII3RA44O2I3I/events.json","paper":"https://pith.science/paper/75K2RRSK"},"agent_actions":{"view_html":"https://pith.science/pith/75K2RRSKZDJOXLII3RA44O2I3I","download_json":"https://pith.science/pith/75K2RRSKZDJOXLII3RA44O2I3I.json","view_paper":"https://pith.science/paper/75K2RRSK","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2405.17332&json=true","fetch_graph":"https://pith.science/api/pith-number/75K2RRSKZDJOXLII3RA44O2I3I/graph.json","fetch_events":"https://pith.science/api/pith-number/75K2RRSKZDJOXLII3RA44O2I3I/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/75K2RRSKZDJOXLII3RA44O2I3I/action/timestamp_anchor","attest_storage":"https://pith.science/pith/75K2RRSKZDJOXLII3RA44O2I3I/action/storage_attestation","attest_author":"https://pith.science/pith/75K2RRSKZDJOXLII3RA44O2I3I/action/author_attestation","sign_citation":"https://pith.science/pith/75K2RRSKZDJOXLII3RA44O2I3I/action/citation_signature","submit_replication":"https://pith.science/pith/75K2RRSKZDJOXLII3RA44O2I3I/action/replication_record"}},"created_at":"2026-07-05T11:09:58.731479+00:00","updated_at":"2026-07-05T11:09:58.731479+00:00"}