{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:IZYQU7XTIXMKO6DFLMBODVX7HD","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":"b6d7cad931539ce0e5ecd3c65a50fd8a3c5470341d940c7695cf4040af5fbfe6","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CG","submitted_at":"2014-02-06T20:50:22Z","title_canon_sha256":"d259761b90dd3f476ab89d28c0f270c9fa3f3ce8db1ca5734e0936629ca8a00d"},"schema_version":"1.0","source":{"id":"1402.1484","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1402.1484","created_at":"2026-05-18T00:52:08Z"},{"alias_kind":"arxiv_version","alias_value":"1402.1484v2","created_at":"2026-05-18T00:52:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1402.1484","created_at":"2026-05-18T00:52:08Z"},{"alias_kind":"pith_short_12","alias_value":"IZYQU7XTIXMK","created_at":"2026-05-18T12:28:33Z"},{"alias_kind":"pith_short_16","alias_value":"IZYQU7XTIXMKO6DF","created_at":"2026-05-18T12:28:33Z"},{"alias_kind":"pith_short_8","alias_value":"IZYQU7XT","created_at":"2026-05-18T12:28:33Z"}],"graph_snapshots":[{"event_id":"sha256:a9ff62084ba08a7a136718f5f185bdc3f96277b0beff1e68aa2f6738da7d5a8a","target":"graph","created_at":"2026-05-18T00:52:08Z","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"},"paper":{"abstract_excerpt":"A graph is called (generically) rigid in $\\mathbb{R}^d$ if, for any choice of sufficiently generic edge lengths, it can be embedded in $\\mathbb{R}^d$ in a finite number of distinct ways, modulo rigid transformations. Here we deal with the problem of determining the maximum number of planar Euclidean embeddings as a function of the number of the vertices. We obtain polynomial systems which totally capture the structure of a given graph, by exploiting distance geometry theory. Consequently, counting the number of Euclidean embeddings of a given rigid graph, reduces to the problem of counting roo","authors_text":"Ioannis Psarros, Ioannis Z. Emiris","cross_cats":["math.CO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CG","submitted_at":"2014-02-06T20:50:22Z","title":"Counting Euclidean embeddings of rigid graphs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1402.1484","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":"sha256:88a666698974e00611bf9303f72379dacbfa9765e78653598e136fe58beaa1df","target":"record","created_at":"2026-05-18T00:52:08Z","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":"b6d7cad931539ce0e5ecd3c65a50fd8a3c5470341d940c7695cf4040af5fbfe6","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CG","submitted_at":"2014-02-06T20:50:22Z","title_canon_sha256":"d259761b90dd3f476ab89d28c0f270c9fa3f3ce8db1ca5734e0936629ca8a00d"},"schema_version":"1.0","source":{"id":"1402.1484","kind":"arxiv","version":2}},"canonical_sha256":"46710a7ef345d8a778655b02e1d6ff38ef15f8a6be361ad00d8a6e6020ac6b7b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"46710a7ef345d8a778655b02e1d6ff38ef15f8a6be361ad00d8a6e6020ac6b7b","first_computed_at":"2026-05-18T00:52:08.710649Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:52:08.710649Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"medQrlCbMDcBwswF7zPB++HciVV4/w1ec/XnDlWr/dGHs0cu1+93ksUXmJrCEc0/AeSkZdqgREGd2FVwkmXzAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:52:08.711207Z","signed_message":"canonical_sha256_bytes"},"source_id":"1402.1484","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:88a666698974e00611bf9303f72379dacbfa9765e78653598e136fe58beaa1df","sha256:a9ff62084ba08a7a136718f5f185bdc3f96277b0beff1e68aa2f6738da7d5a8a"],"state_sha256":"fbaf15b9a8e82d250579f952531e7f1cb3ff997129c632c60f26715d429af52e"}