{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:6U3JQVNFNGLDMQ64OKY3E7JM2I","short_pith_number":"pith:6U3JQVNF","canonical_record":{"source":{"id":"1712.07559","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CG","submitted_at":"2017-12-20T16:29:15Z","cross_cats_sorted":[],"title_canon_sha256":"3a4b73ed42b03c864f220dcb674f35048f9ddee3ce834f1e50a9ae5fae379edc","abstract_canon_sha256":"7a0af128ca5e3dac000df9afe2787d5254869beb7ec3ce3af82fd5f26a88b6ad"},"schema_version":"1.0"},"canonical_sha256":"f5369855a569963643dc72b1b27d2cd2063c9369395f5af4e601a18ead5e1c49","source":{"kind":"arxiv","id":"1712.07559","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"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:6U3JQVNFNGLDMQ64OKY3E7JM2I","target":"record","payload":{"canonical_record":{"source":{"id":"1712.07559","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CG","submitted_at":"2017-12-20T16:29:15Z","cross_cats_sorted":[],"title_canon_sha256":"3a4b73ed42b03c864f220dcb674f35048f9ddee3ce834f1e50a9ae5fae379edc","abstract_canon_sha256":"7a0af128ca5e3dac000df9afe2787d5254869beb7ec3ce3af82fd5f26a88b6ad"},"schema_version":"1.0"},"canonical_sha256":"f5369855a569963643dc72b1b27d2cd2063c9369395f5af4e601a18ead5e1c49","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:27:34.222806Z","signature_b64":"tymWvFyfAFBztNcOyAFCDVKceKmAabQvl8Ukd2sXemVKd/Civz0uFOIWLZuTY0Cekw4GU2rpTdmcPtPUNYszDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f5369855a569963643dc72b1b27d2cd2063c9369395f5af4e601a18ead5e1c49","last_reissued_at":"2026-05-18T00:27:34.222257Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:27:34.222257Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1712.07559","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:27:34Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"tWcOHu3UnWHg1kSouBixKE8lpcDVs9DO9UseaHziF/Z3LBi3Z44/jxdka4YMcrYsWosehXATTMMAxdlBHZAtBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T16:31:40.084556Z"},"content_sha256":"a6700e13c913a7628628a66a0d401104ea88de8a559a7f9e4329917375026c13","schema_version":"1.0","event_id":"sha256:a6700e13c913a7628628a66a0d401104ea88de8a559a7f9e4329917375026c13"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:6U3JQVNFNGLDMQ64OKY3E7JM2I","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Recognizing Generalized Transmission Graphs of Line Segments and Circular Sectors","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.CG","authors_text":"Katharina Klost, Wolfgang Mulzer","submitted_at":"2017-12-20T16:29:15Z","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_"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1712.07559","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:27:34Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"whtVmQhhucEKXgyICa7QAvuzdG/fj7/a9UxodQ6qO2b4P8D+0BD9TP7uCufwZ6m36e47xmD/Xnu+1mxHzg+zBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T16:31:40.085032Z"},"content_sha256":"497838e9e22968d29088c601bb07aebda427d6986af35bcdd1aa4bda56e2f6b3","schema_version":"1.0","event_id":"sha256:497838e9e22968d29088c601bb07aebda427d6986af35bcdd1aa4bda56e2f6b3"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/6U3JQVNFNGLDMQ64OKY3E7JM2I/bundle.json","state_url":"https://pith.science/pith/6U3JQVNFNGLDMQ64OKY3E7JM2I/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/6U3JQVNFNGLDMQ64OKY3E7JM2I/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-05-30T16:31:40Z","links":{"resolver":"https://pith.science/pith/6U3JQVNFNGLDMQ64OKY3E7JM2I","bundle":"https://pith.science/pith/6U3JQVNFNGLDMQ64OKY3E7JM2I/bundle.json","state":"https://pith.science/pith/6U3JQVNFNGLDMQ64OKY3E7JM2I/state.json","well_known_bundle":"https://pith.science/.well-known/pith/6U3JQVNFNGLDMQ64OKY3E7JM2I/bundle.json"},"state":{"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"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"jhuK5sDlyHCWz0GIxOmi/26jz1inwf3ki/JzmAEBvmk/c6at6g4rKABdTjz4GMweQpwhKqbFjYyBuUmcFJRHCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-30T16:31:40.087825Z","bundle_sha256":"148d612bfed80988cea7e781c6fbfea0bf0f9b93616092ea4b2be912f8c88a70"}}