{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:OUWGNIBOVVZAOALMSBJMR4KFR7","short_pith_number":"pith:OUWGNIBO","canonical_record":{"source":{"id":"1710.10112","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-10-27T13:00:49Z","cross_cats_sorted":["cs.DM"],"title_canon_sha256":"2d87d4a9561f7240be464a7a8786eadffdd157d4e138324919b0d2cfc0b33b65","abstract_canon_sha256":"8319bda1524793bcd095ab4237810a93cd6bdc75355169d32d716c5e595215fc"},"schema_version":"1.0"},"canonical_sha256":"752c66a02ead7207016c9052c8f1458fd3942c3b8939e6daed9156093962011e","source":{"kind":"arxiv","id":"1710.10112","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1710.10112","created_at":"2026-05-18T00:31:54Z"},{"alias_kind":"arxiv_version","alias_value":"1710.10112v1","created_at":"2026-05-18T00:31:54Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1710.10112","created_at":"2026-05-18T00:31:54Z"},{"alias_kind":"pith_short_12","alias_value":"OUWGNIBOVVZA","created_at":"2026-05-18T12:31:34Z"},{"alias_kind":"pith_short_16","alias_value":"OUWGNIBOVVZAOALM","created_at":"2026-05-18T12:31:34Z"},{"alias_kind":"pith_short_8","alias_value":"OUWGNIBO","created_at":"2026-05-18T12:31:34Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:OUWGNIBOVVZAOALMSBJMR4KFR7","target":"record","payload":{"canonical_record":{"source":{"id":"1710.10112","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-10-27T13:00:49Z","cross_cats_sorted":["cs.DM"],"title_canon_sha256":"2d87d4a9561f7240be464a7a8786eadffdd157d4e138324919b0d2cfc0b33b65","abstract_canon_sha256":"8319bda1524793bcd095ab4237810a93cd6bdc75355169d32d716c5e595215fc"},"schema_version":"1.0"},"canonical_sha256":"752c66a02ead7207016c9052c8f1458fd3942c3b8939e6daed9156093962011e","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:31:54.739121Z","signature_b64":"s5bnJy1vhRL24B68LF/661OHdZdET14nW9aBjNScL2sNc0jaF3TG8p+owutPs6Aid0kvKiyfAOVV5Iv10y3VBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"752c66a02ead7207016c9052c8f1458fd3942c3b8939e6daed9156093962011e","last_reissued_at":"2026-05-18T00:31:54.738728Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:31:54.738728Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1710.10112","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":"2026-05-18T00:31:54Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"j8jI0XvyRBa5FsvHuw1EljXvSjeId67uKMEKALeJreq9EtzquXSQPZQTtE6zP/9OYc5trqcejGLsN0FTbqT/Bw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T19:09:24.736962Z"},"content_sha256":"2f2756c2f4e275111e396355df51c902823a81b21c636319c18b71f16a45c1a6","schema_version":"1.0","event_id":"sha256:2f2756c2f4e275111e396355df51c902823a81b21c636319c18b71f16a45c1a6"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:OUWGNIBOVVZAOALMSBJMR4KFR7","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Hyperopic Cops and Robbers","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DM"],"primary_cat":"math.CO","authors_text":"A. Bonato, D. Cox, F. Mc Inerney, M.E. Messinger, N.E. Clarke, S. Finbow","submitted_at":"2017-10-27T13:00:49Z","abstract_excerpt":"We introduce a new variant of the game of Cops and Robbers played on graphs, where the robber is invisible unless outside the neighbor set of a cop. The hyperopic cop number is the corresponding analogue of the cop number, and we investigate bounds and other properties of this parameter. We characterize the cop-win graphs for this variant, along with graphs with the largest possible hyperopic cop number. We analyze the cases of graphs with diameter 2 or at least 3, focusing on when the hyperopic cop number is at most one greater than the cop number. We show that for planar graphs, as with the "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1710.10112","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":"2026-05-18T00:31:54Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"XqEjda18VUvRuOywKNb1490TTQQGdkpomGr7PCnmFsGC1yaxl67FOOpwJB31RYnv1prpoys+8j1t2Ubs0R9FCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T19:09:24.737724Z"},"content_sha256":"fff8793a63999c53014682419f666e14338c410fd614d2f3ca97f3c90d3d19f7","schema_version":"1.0","event_id":"sha256:fff8793a63999c53014682419f666e14338c410fd614d2f3ca97f3c90d3d19f7"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/OUWGNIBOVVZAOALMSBJMR4KFR7/bundle.json","state_url":"https://pith.science/pith/OUWGNIBOVVZAOALMSBJMR4KFR7/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/OUWGNIBOVVZAOALMSBJMR4KFR7/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":"2026-06-09T19:09:24Z","links":{"resolver":"https://pith.science/pith/OUWGNIBOVVZAOALMSBJMR4KFR7","bundle":"https://pith.science/pith/OUWGNIBOVVZAOALMSBJMR4KFR7/bundle.json","state":"https://pith.science/pith/OUWGNIBOVVZAOALMSBJMR4KFR7/state.json","well_known_bundle":"https://pith.science/.well-known/pith/OUWGNIBOVVZAOALMSBJMR4KFR7/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:OUWGNIBOVVZAOALMSBJMR4KFR7","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":"8319bda1524793bcd095ab4237810a93cd6bdc75355169d32d716c5e595215fc","cross_cats_sorted":["cs.DM"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-10-27T13:00:49Z","title_canon_sha256":"2d87d4a9561f7240be464a7a8786eadffdd157d4e138324919b0d2cfc0b33b65"},"schema_version":"1.0","source":{"id":"1710.10112","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1710.10112","created_at":"2026-05-18T00:31:54Z"},{"alias_kind":"arxiv_version","alias_value":"1710.10112v1","created_at":"2026-05-18T00:31:54Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1710.10112","created_at":"2026-05-18T00:31:54Z"},{"alias_kind":"pith_short_12","alias_value":"OUWGNIBOVVZA","created_at":"2026-05-18T12:31:34Z"},{"alias_kind":"pith_short_16","alias_value":"OUWGNIBOVVZAOALM","created_at":"2026-05-18T12:31:34Z"},{"alias_kind":"pith_short_8","alias_value":"OUWGNIBO","created_at":"2026-05-18T12:31:34Z"}],"graph_snapshots":[{"event_id":"sha256:fff8793a63999c53014682419f666e14338c410fd614d2f3ca97f3c90d3d19f7","target":"graph","created_at":"2026-05-18T00:31:54Z","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":"We introduce a new variant of the game of Cops and Robbers played on graphs, where the robber is invisible unless outside the neighbor set of a cop. The hyperopic cop number is the corresponding analogue of the cop number, and we investigate bounds and other properties of this parameter. We characterize the cop-win graphs for this variant, along with graphs with the largest possible hyperopic cop number. We analyze the cases of graphs with diameter 2 or at least 3, focusing on when the hyperopic cop number is at most one greater than the cop number. We show that for planar graphs, as with the ","authors_text":"A. Bonato, D. Cox, F. Mc Inerney, M.E. Messinger, N.E. Clarke, S. Finbow","cross_cats":["cs.DM"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-10-27T13:00:49Z","title":"Hyperopic Cops and Robbers"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1710.10112","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":"sha256:2f2756c2f4e275111e396355df51c902823a81b21c636319c18b71f16a45c1a6","target":"record","created_at":"2026-05-18T00:31:54Z","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":"8319bda1524793bcd095ab4237810a93cd6bdc75355169d32d716c5e595215fc","cross_cats_sorted":["cs.DM"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-10-27T13:00:49Z","title_canon_sha256":"2d87d4a9561f7240be464a7a8786eadffdd157d4e138324919b0d2cfc0b33b65"},"schema_version":"1.0","source":{"id":"1710.10112","kind":"arxiv","version":1}},"canonical_sha256":"752c66a02ead7207016c9052c8f1458fd3942c3b8939e6daed9156093962011e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"752c66a02ead7207016c9052c8f1458fd3942c3b8939e6daed9156093962011e","first_computed_at":"2026-05-18T00:31:54.738728Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:31:54.738728Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"s5bnJy1vhRL24B68LF/661OHdZdET14nW9aBjNScL2sNc0jaF3TG8p+owutPs6Aid0kvKiyfAOVV5Iv10y3VBw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:31:54.739121Z","signed_message":"canonical_sha256_bytes"},"source_id":"1710.10112","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2f2756c2f4e275111e396355df51c902823a81b21c636319c18b71f16a45c1a6","sha256:fff8793a63999c53014682419f666e14338c410fd614d2f3ca97f3c90d3d19f7"],"state_sha256":"1944aad499b5b5f11cc3accf06a38c62de2682ab746386277a2087f3c5d10aa0"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"b/j6Wsi5NUjl6/Iur8Ot3113+q+tc/+pl8RGuqMBfYQWvIQTwjxN48h642SwFH0xlsckjf/b4cwtitReFgGPAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-09T19:09:24.742231Z","bundle_sha256":"8aa2edbdc8aff267190a4148c2e1bd08b7a604962b823a8e348e9c11d57c73d7"}}