{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:VZW772MDQG47ZKLXFHNRFLSNVD","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":"9830b12fd1a6dc7e9faa9652924174a098d4a2a1eefed1cd84e3727958fc3abc","cross_cats_sorted":["cs.AI","cs.CV","math.DG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CG","submitted_at":"2026-05-24T16:19:27Z","title_canon_sha256":"d3482f915103fbf3003775c76ba0e4ba2028eaaf0b823e3583d2b7f10c677ecc"},"schema_version":"1.0","source":{"id":"2606.06505","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2606.06505","created_at":"2026-06-08T00:03:39Z"},{"alias_kind":"arxiv_version","alias_value":"2606.06505v1","created_at":"2026-06-08T00:03:39Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.06505","created_at":"2026-06-08T00:03:39Z"},{"alias_kind":"pith_short_12","alias_value":"VZW772MDQG47","created_at":"2026-06-08T00:03:39Z"},{"alias_kind":"pith_short_16","alias_value":"VZW772MDQG47ZKLX","created_at":"2026-06-08T00:03:39Z"},{"alias_kind":"pith_short_8","alias_value":"VZW772MD","created_at":"2026-06-08T00:03:39Z"}],"graph_snapshots":[{"event_id":"sha256:a70dd3d474a4361820f2dee2859b534c39695340d7bf729677cb4f2eb4079524","target":"graph","created_at":"2026-06-08T00:03:39Z","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/2606.06505/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We introduce a user defined probabilistic polygonal representation for plane curves. Given a curve, we select vertices on the curve and connect consecutive vertices by line segments to obtain a polygonal approximation. Each segment is equipped with a user defined uncertainty parameter in the normal direction. This yields a collection of thin probabilistic geometric primitives that retain the geometrz of the underlying curve while extending it beyond the idealized deterministic one dimensional formulation.\n  For each segment, we define a Random Variable that is uniform distributed in the tangen","authors_text":"Ali Darijani, Benedikt Stratmann, J\\\"urgen Beyerer","cross_cats":["cs.AI","cs.CV","math.DG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CG","submitted_at":"2026-05-24T16:19:27Z","title":"A Geometric Gaussian Mixture Representation of Plane Curves"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.06505","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":"sha256:822b817756319839346fd67ab2bae96a89fbe360aef8283a50e5dac03320288b","target":"record","created_at":"2026-06-08T00:03:39Z","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":"9830b12fd1a6dc7e9faa9652924174a098d4a2a1eefed1cd84e3727958fc3abc","cross_cats_sorted":["cs.AI","cs.CV","math.DG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CG","submitted_at":"2026-05-24T16:19:27Z","title_canon_sha256":"d3482f915103fbf3003775c76ba0e4ba2028eaaf0b823e3583d2b7f10c677ecc"},"schema_version":"1.0","source":{"id":"2606.06505","kind":"arxiv","version":1}},"canonical_sha256":"ae6dffe98381b9fca97729db12ae4da8d314dfeff60ad13b8c7fb4f563f57cf7","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ae6dffe98381b9fca97729db12ae4da8d314dfeff60ad13b8c7fb4f563f57cf7","first_computed_at":"2026-06-08T00:03:39.892593Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-08T00:03:39.892593Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"czVT9jesczamWJCBE3M1ovmz0BAVHufletecOUTgyMTBzGb4pcgmoFZUS8vj5VTIvkF6BKL7kiDEg++lMpPEBw==","signature_status":"signed_v1","signed_at":"2026-06-08T00:03:39.893521Z","signed_message":"canonical_sha256_bytes"},"source_id":"2606.06505","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:822b817756319839346fd67ab2bae96a89fbe360aef8283a50e5dac03320288b","sha256:a70dd3d474a4361820f2dee2859b534c39695340d7bf729677cb4f2eb4079524"],"state_sha256":"40e29290430ff07c0e935d0b8bc45aae63e77af7882117156b411d6d7b97d95c"}