{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:6U3JQVNFNGLDMQ64OKY3E7JM2I","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":"7a0af128ca5e3dac000df9afe2787d5254869beb7ec3ce3af82fd5f26a88b6ad","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CG","submitted_at":"2017-12-20T16:29:15Z","title_canon_sha256":"3a4b73ed42b03c864f220dcb674f35048f9ddee3ce834f1e50a9ae5fae379edc"},"schema_version":"1.0","source":{"id":"1712.07559","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1712.07559","created_at":"2026-05-18T00:27:34Z"},{"alias_kind":"arxiv_version","alias_value":"1712.07559v1","created_at":"2026-05-18T00:27:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1712.07559","created_at":"2026-05-18T00:27:34Z"},{"alias_kind":"pith_short_12","alias_value":"6U3JQVNFNGLD","created_at":"2026-05-18T12:31:03Z"},{"alias_kind":"pith_short_16","alias_value":"6U3JQVNFNGLDMQ64","created_at":"2026-05-18T12:31:03Z"},{"alias_kind":"pith_short_8","alias_value":"6U3JQVNF","created_at":"2026-05-18T12:31:03Z"}],"graph_snapshots":[{"event_id":"sha256:497838e9e22968d29088c601bb07aebda427d6986af35bcdd1aa4bda56e2f6b3","target":"graph","created_at":"2026-05-18T00:27:34Z","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":"Suppose we have an arrangement $\\mathcal{A}$ of $n$ geometric objects $x_1, \\dots, x_n \\subseteq \\mathbb{R}^2$ in the plane, with a distinguished point $p_i$ in each object $x_i$. The generalized transmission graph of $\\mathcal{A}$ has vertex set $\\{x_1, \\dots, x_n\\}$ and a directed edge $x_ix_j$ if and only if $p_j \\in x_i$. Generalized transmission graphs provide a generalized model of the connectivity in networks of directional antennas.\n  The complexity class $\\exists \\mathbb{R}$ contains all problems that can be reduced in polynomial time to an existential sentence of the form $\\exists x_","authors_text":"Katharina Klost, Wolfgang Mulzer","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CG","submitted_at":"2017-12-20T16:29:15Z","title":"Recognizing Generalized Transmission Graphs of Line Segments and Circular Sectors"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1712.07559","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:a6700e13c913a7628628a66a0d401104ea88de8a559a7f9e4329917375026c13","target":"record","created_at":"2026-05-18T00:27:34Z","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":"7a0af128ca5e3dac000df9afe2787d5254869beb7ec3ce3af82fd5f26a88b6ad","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CG","submitted_at":"2017-12-20T16:29:15Z","title_canon_sha256":"3a4b73ed42b03c864f220dcb674f35048f9ddee3ce834f1e50a9ae5fae379edc"},"schema_version":"1.0","source":{"id":"1712.07559","kind":"arxiv","version":1}},"canonical_sha256":"f5369855a569963643dc72b1b27d2cd2063c9369395f5af4e601a18ead5e1c49","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f5369855a569963643dc72b1b27d2cd2063c9369395f5af4e601a18ead5e1c49","first_computed_at":"2026-05-18T00:27:34.222257Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:27:34.222257Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"tymWvFyfAFBztNcOyAFCDVKceKmAabQvl8Ukd2sXemVKd/Civz0uFOIWLZuTY0Cekw4GU2rpTdmcPtPUNYszDg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:27:34.222806Z","signed_message":"canonical_sha256_bytes"},"source_id":"1712.07559","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a6700e13c913a7628628a66a0d401104ea88de8a559a7f9e4329917375026c13","sha256:497838e9e22968d29088c601bb07aebda427d6986af35bcdd1aa4bda56e2f6b3"],"state_sha256":"2c8b1518ccda146cb6d1dcf53ddb8fb02e234b93801e14ecb3cb7f8e66f23d89"}