{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2023:JSL4ZUVBM3NJHRTCDWLPLWLHRE","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":"3209739172651578a68f3fbe896cb7a92f644efab1c226935f0e8e6114d73384","cross_cats_sorted":[],"license":"http://creativecommons.org/publicdomain/zero/1.0/","primary_cat":"math.MG","submitted_at":"2023-10-09T23:13:32Z","title_canon_sha256":"1ff72193ca336fef162f05ef4f60cfa8c92a027effaef7decf70f1d4007204a1"},"schema_version":"1.0","source":{"id":"2310.06206","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2310.06206","created_at":"2026-07-05T06:59:06Z"},{"alias_kind":"arxiv_version","alias_value":"2310.06206v1","created_at":"2026-07-05T06:59:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2310.06206","created_at":"2026-07-05T06:59:06Z"},{"alias_kind":"pith_short_12","alias_value":"JSL4ZUVBM3NJ","created_at":"2026-07-05T06:59:06Z"},{"alias_kind":"pith_short_16","alias_value":"JSL4ZUVBM3NJHRTC","created_at":"2026-07-05T06:59:06Z"},{"alias_kind":"pith_short_8","alias_value":"JSL4ZUVB","created_at":"2026-07-05T06:59:06Z"}],"graph_snapshots":[{"event_id":"sha256:3d97514c1195691e023999ba38c6516c9f1ef8bbc478c4b66ce5ae10ea7544b4","target":"graph","created_at":"2026-07-05T06:59:06Z","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/2310.06206/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We prove that two closed subsets of complex space $\\C^n$ with corresponding complex homothetic sections (projections) are complex homothetic. The proof uses a new Helly-type theorem for cosets of closed subgroups of $\\S ^1$.","authors_text":"Javier Bracho, Jorge Luis Arocha, Luis Montejano","cross_cats":[],"headline":"","license":"http://creativecommons.org/publicdomain/zero/1.0/","primary_cat":"math.MG","submitted_at":"2023-10-09T23:13:32Z","title":"Complex homothetic sections and projections through a Helly type Theorem for cosets of $\\S^1$"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2310.06206","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":"sha256:067ca1eb81b6d9120716a01174c47163ab0ef035babb6132700c2cfeafa98e60","target":"record","created_at":"2026-07-05T06:59:06Z","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":"3209739172651578a68f3fbe896cb7a92f644efab1c226935f0e8e6114d73384","cross_cats_sorted":[],"license":"http://creativecommons.org/publicdomain/zero/1.0/","primary_cat":"math.MG","submitted_at":"2023-10-09T23:13:32Z","title_canon_sha256":"1ff72193ca336fef162f05ef4f60cfa8c92a027effaef7decf70f1d4007204a1"},"schema_version":"1.0","source":{"id":"2310.06206","kind":"arxiv","version":1}},"canonical_sha256":"4c97ccd2a166da93c6621d96f5d9678928a642ff13ce9b9460c211914c1aaf71","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4c97ccd2a166da93c6621d96f5d9678928a642ff13ce9b9460c211914c1aaf71","first_computed_at":"2026-07-05T06:59:06.912845Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T06:59:06.912845Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"j4byRMnAB11OmaG8Tpo1O+VgscpLe6399kfBIbPwil+AdfYPI0+PiZfr1aa3uNJIgKXeOTEwFWPFyJ/uXPfDBA==","signature_status":"signed_v1","signed_at":"2026-07-05T06:59:06.913297Z","signed_message":"canonical_sha256_bytes"},"source_id":"2310.06206","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:067ca1eb81b6d9120716a01174c47163ab0ef035babb6132700c2cfeafa98e60","sha256:3d97514c1195691e023999ba38c6516c9f1ef8bbc478c4b66ce5ae10ea7544b4"],"state_sha256":"8a2143e4fa8022dbc110d2e7db72560e142241c2a005ca611b64617649db9e40"}