{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2021:P4HFFL3RLKSPLN7FXZXWRZDZE3","short_pith_number":"pith:P4HFFL3R","schema_version":"1.0","canonical_sha256":"7f0e52af715aa4f5b7e5be6f68e47926d4304ceaec0b4346e5f42026ef72f266","source":{"kind":"arxiv","id":"2108.11747","version":2},"attestation_state":"computed","paper":{"title":"Adjoints and Canonical Forms of Polypols","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Boris Shapiro, Felix Rydell, Kathl\\'en Kohn, Kristian Ranestad, Miruna-Stefana Sorea, Ragni Piene, Rainer Sinn, Simon Telen","submitted_at":"2021-08-26T12:42:21Z","abstract_excerpt":"Polypols are natural generalizations of polytopes, with boundaries given by nonlinear algebraic hypersurfaces. We describe polypols in the plane and in 3-space that admit a unique adjoint hypersurface and study them from an algebro-geometric perspective. We relate planar polypols to positive geometries introduced originally in particle physics, and identify the adjoint curve of a planar polypol with the numerator of the canonical differential form associated with the positive geometry. We settle several cases of a conjecture by Wachspress claiming that the adjoint curve of a regular planar pol"},"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":"2108.11747","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2021-08-26T12:42:21Z","cross_cats_sorted":[],"title_canon_sha256":"8617f2fe9dafef05fc75ab7cf4a42ba98eb14cb96e7a5df3d32b2fd53722b350","abstract_canon_sha256":"3c4099de347d255de6650c2ac599e6a0cba4e421e56c908d5a0d420bc6ec337f"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T10:35:28.239654Z","signature_b64":"33BdPOcXAKqgy1Rjm+V+ZWPoJQ0szb3OHAj6nXOK2O6kPIbkfF44JOpIQzZ/no9k7jBbpE0x1HCno4rg06HEAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7f0e52af715aa4f5b7e5be6f68e47926d4304ceaec0b4346e5f42026ef72f266","last_reissued_at":"2026-07-05T10:35:28.238954Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T10:35:28.238954Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Adjoints and Canonical Forms of Polypols","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Boris Shapiro, Felix Rydell, Kathl\\'en Kohn, Kristian Ranestad, Miruna-Stefana Sorea, Ragni Piene, Rainer Sinn, Simon Telen","submitted_at":"2021-08-26T12:42:21Z","abstract_excerpt":"Polypols are natural generalizations of polytopes, with boundaries given by nonlinear algebraic hypersurfaces. We describe polypols in the plane and in 3-space that admit a unique adjoint hypersurface and study them from an algebro-geometric perspective. We relate planar polypols to positive geometries introduced originally in particle physics, and identify the adjoint curve of a planar polypol with the numerator of the canonical differential form associated with the positive geometry. We settle several cases of a conjecture by Wachspress claiming that the adjoint curve of a regular planar pol"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2108.11747","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/2108.11747/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":"2108.11747","created_at":"2026-07-05T10:35:28.239067+00:00"},{"alias_kind":"arxiv_version","alias_value":"2108.11747v2","created_at":"2026-07-05T10:35:28.239067+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2108.11747","created_at":"2026-07-05T10:35:28.239067+00:00"},{"alias_kind":"pith_short_12","alias_value":"P4HFFL3RLKSP","created_at":"2026-07-05T10:35:28.239067+00:00"},{"alias_kind":"pith_short_16","alias_value":"P4HFFL3RLKSPLN7F","created_at":"2026-07-05T10:35:28.239067+00:00"},{"alias_kind":"pith_short_8","alias_value":"P4HFFL3R","created_at":"2026-07-05T10:35:28.239067+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2501.11819","citing_title":"Arrangements of circles supported by small chords and compatible with natural real algebraic functions","ref_index":8,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/P4HFFL3RLKSPLN7FXZXWRZDZE3","json":"https://pith.science/pith/P4HFFL3RLKSPLN7FXZXWRZDZE3.json","graph_json":"https://pith.science/api/pith-number/P4HFFL3RLKSPLN7FXZXWRZDZE3/graph.json","events_json":"https://pith.science/api/pith-number/P4HFFL3RLKSPLN7FXZXWRZDZE3/events.json","paper":"https://pith.science/paper/P4HFFL3R"},"agent_actions":{"view_html":"https://pith.science/pith/P4HFFL3RLKSPLN7FXZXWRZDZE3","download_json":"https://pith.science/pith/P4HFFL3RLKSPLN7FXZXWRZDZE3.json","view_paper":"https://pith.science/paper/P4HFFL3R","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2108.11747&json=true","fetch_graph":"https://pith.science/api/pith-number/P4HFFL3RLKSPLN7FXZXWRZDZE3/graph.json","fetch_events":"https://pith.science/api/pith-number/P4HFFL3RLKSPLN7FXZXWRZDZE3/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/P4HFFL3RLKSPLN7FXZXWRZDZE3/action/timestamp_anchor","attest_storage":"https://pith.science/pith/P4HFFL3RLKSPLN7FXZXWRZDZE3/action/storage_attestation","attest_author":"https://pith.science/pith/P4HFFL3RLKSPLN7FXZXWRZDZE3/action/author_attestation","sign_citation":"https://pith.science/pith/P4HFFL3RLKSPLN7FXZXWRZDZE3/action/citation_signature","submit_replication":"https://pith.science/pith/P4HFFL3RLKSPLN7FXZXWRZDZE3/action/replication_record"}},"created_at":"2026-07-05T10:35:28.239067+00:00","updated_at":"2026-07-05T10:35:28.239067+00:00"}