{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2019:WMWGCVX55ERVORJ3KMYOWT7GVX","short_pith_number":"pith:WMWGCVX5","canonical_record":{"source":{"id":"1903.11411","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2019-03-27T13:22:12Z","cross_cats_sorted":[],"title_canon_sha256":"27eb0c21e50f6dbc95bd6a1ebe811e765cf176e4aae06bd3844c009336be46c6","abstract_canon_sha256":"caf913ed70d3a1bc31313d6eccc754626ec915362fbe1715e43af7b53bc4fad0"},"schema_version":"1.0"},"canonical_sha256":"b32c6156fde92357453b5330eb4fe6adde8dc73b7f8d8c9d8b83b834c3637347","source":{"kind":"arxiv","id":"1903.11411","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1903.11411","created_at":"2026-05-17T23:50:03Z"},{"alias_kind":"arxiv_version","alias_value":"1903.11411v1","created_at":"2026-05-17T23:50:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1903.11411","created_at":"2026-05-17T23:50:03Z"},{"alias_kind":"pith_short_12","alias_value":"WMWGCVX55ERV","created_at":"2026-05-18T12:33:30Z"},{"alias_kind":"pith_short_16","alias_value":"WMWGCVX55ERVORJ3","created_at":"2026-05-18T12:33:30Z"},{"alias_kind":"pith_short_8","alias_value":"WMWGCVX5","created_at":"2026-05-18T12:33:30Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2019:WMWGCVX55ERVORJ3KMYOWT7GVX","target":"record","payload":{"canonical_record":{"source":{"id":"1903.11411","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2019-03-27T13:22:12Z","cross_cats_sorted":[],"title_canon_sha256":"27eb0c21e50f6dbc95bd6a1ebe811e765cf176e4aae06bd3844c009336be46c6","abstract_canon_sha256":"caf913ed70d3a1bc31313d6eccc754626ec915362fbe1715e43af7b53bc4fad0"},"schema_version":"1.0"},"canonical_sha256":"b32c6156fde92357453b5330eb4fe6adde8dc73b7f8d8c9d8b83b834c3637347","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:50:03.351323Z","signature_b64":"SzfWWSh2LF+VyqQNM3ZybWR4Ztxyf2HZr3czPyigFMl9Qynn084D7F2eknt3RQWdRjIeQr0iANFCc8HNQqT7Dg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b32c6156fde92357453b5330eb4fe6adde8dc73b7f8d8c9d8b83b834c3637347","last_reissued_at":"2026-05-17T23:50:03.350877Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:50:03.350877Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1903.11411","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":"2026-05-17T23:50:03Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"IIJUDxev0Q0MfZ8K1P8CfVOcgWrDfdlsRoi+pLYKrJRS+j8wvOOTMNNGMxJQ2fYfjBodetXsTal6YQcLVkmYDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T02:24:18.069082Z"},"content_sha256":"5ce1c73cc606aae829a19d77392ac2be0b923b9dd926ab754e0465eb301640ec","schema_version":"1.0","event_id":"sha256:5ce1c73cc606aae829a19d77392ac2be0b923b9dd926ab754e0465eb301640ec"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2019:WMWGCVX55ERVORJ3KMYOWT7GVX","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The Toucher-Isolator game","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Chris Dowden, Mihyun Kang, Milo\\v{s} Stojakovi\\'c, Mirjana Mikala\\v{c}ki","submitted_at":"2019-03-27T13:22:12Z","abstract_excerpt":"We introduce a new positional game called `Toucher-Isolator', which is a quantitative version of a Maker-Breaker type game. The playing board is the set of edges of a given graph G, and the two players, Toucher and Isolator, claim edges alternately. The aim of Toucher is to `touch' as many vertices as possible (i.e. to maximise the number of vertices that are incident to at least one of her chosen edges), and the aim of Isolator is to minimise the number of vertices that are so touched.\n  We analyse the number of untouched vertices u(G) at the end of the game when both Toucher and Isolator pla"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1903.11411","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":"2026-05-17T23:50:03Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"RHA0b8s4iZe+mZnUpFZTkvWKdXMsGocHTPnLs+bKfX7hqB2RWcIj70cOKhEOVvyuU43MgtLVHEYPPDY0duliAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T02:24:18.069885Z"},"content_sha256":"70cae97d9a0811a1daf7cb14b71464445b8409ba9af0c8db965d3893eaf23eda","schema_version":"1.0","event_id":"sha256:70cae97d9a0811a1daf7cb14b71464445b8409ba9af0c8db965d3893eaf23eda"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/WMWGCVX55ERVORJ3KMYOWT7GVX/bundle.json","state_url":"https://pith.science/pith/WMWGCVX55ERVORJ3KMYOWT7GVX/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/WMWGCVX55ERVORJ3KMYOWT7GVX/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":"2026-05-30T02:24:18Z","links":{"resolver":"https://pith.science/pith/WMWGCVX55ERVORJ3KMYOWT7GVX","bundle":"https://pith.science/pith/WMWGCVX55ERVORJ3KMYOWT7GVX/bundle.json","state":"https://pith.science/pith/WMWGCVX55ERVORJ3KMYOWT7GVX/state.json","well_known_bundle":"https://pith.science/.well-known/pith/WMWGCVX55ERVORJ3KMYOWT7GVX/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:WMWGCVX55ERVORJ3KMYOWT7GVX","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":"caf913ed70d3a1bc31313d6eccc754626ec915362fbe1715e43af7b53bc4fad0","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2019-03-27T13:22:12Z","title_canon_sha256":"27eb0c21e50f6dbc95bd6a1ebe811e765cf176e4aae06bd3844c009336be46c6"},"schema_version":"1.0","source":{"id":"1903.11411","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1903.11411","created_at":"2026-05-17T23:50:03Z"},{"alias_kind":"arxiv_version","alias_value":"1903.11411v1","created_at":"2026-05-17T23:50:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1903.11411","created_at":"2026-05-17T23:50:03Z"},{"alias_kind":"pith_short_12","alias_value":"WMWGCVX55ERV","created_at":"2026-05-18T12:33:30Z"},{"alias_kind":"pith_short_16","alias_value":"WMWGCVX55ERVORJ3","created_at":"2026-05-18T12:33:30Z"},{"alias_kind":"pith_short_8","alias_value":"WMWGCVX5","created_at":"2026-05-18T12:33:30Z"}],"graph_snapshots":[{"event_id":"sha256:70cae97d9a0811a1daf7cb14b71464445b8409ba9af0c8db965d3893eaf23eda","target":"graph","created_at":"2026-05-17T23:50:03Z","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 positional game called `Toucher-Isolator', which is a quantitative version of a Maker-Breaker type game. The playing board is the set of edges of a given graph G, and the two players, Toucher and Isolator, claim edges alternately. The aim of Toucher is to `touch' as many vertices as possible (i.e. to maximise the number of vertices that are incident to at least one of her chosen edges), and the aim of Isolator is to minimise the number of vertices that are so touched.\n  We analyse the number of untouched vertices u(G) at the end of the game when both Toucher and Isolator pla","authors_text":"Chris Dowden, Mihyun Kang, Milo\\v{s} Stojakovi\\'c, Mirjana Mikala\\v{c}ki","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2019-03-27T13:22:12Z","title":"The Toucher-Isolator game"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1903.11411","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":"sha256:5ce1c73cc606aae829a19d77392ac2be0b923b9dd926ab754e0465eb301640ec","target":"record","created_at":"2026-05-17T23:50:03Z","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":"caf913ed70d3a1bc31313d6eccc754626ec915362fbe1715e43af7b53bc4fad0","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2019-03-27T13:22:12Z","title_canon_sha256":"27eb0c21e50f6dbc95bd6a1ebe811e765cf176e4aae06bd3844c009336be46c6"},"schema_version":"1.0","source":{"id":"1903.11411","kind":"arxiv","version":1}},"canonical_sha256":"b32c6156fde92357453b5330eb4fe6adde8dc73b7f8d8c9d8b83b834c3637347","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b32c6156fde92357453b5330eb4fe6adde8dc73b7f8d8c9d8b83b834c3637347","first_computed_at":"2026-05-17T23:50:03.350877Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:50:03.350877Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"SzfWWSh2LF+VyqQNM3ZybWR4Ztxyf2HZr3czPyigFMl9Qynn084D7F2eknt3RQWdRjIeQr0iANFCc8HNQqT7Dg==","signature_status":"signed_v1","signed_at":"2026-05-17T23:50:03.351323Z","signed_message":"canonical_sha256_bytes"},"source_id":"1903.11411","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5ce1c73cc606aae829a19d77392ac2be0b923b9dd926ab754e0465eb301640ec","sha256:70cae97d9a0811a1daf7cb14b71464445b8409ba9af0c8db965d3893eaf23eda"],"state_sha256":"b0abc9f11032f162d0c4e7902b93bafbea96a39d2c420269ba2b9201d2c6ceac"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"gdVzpPlojp7L7Ba/BsZlD2le9juckzMnJYPbJa5rZi0Ilo+lMPhjkjqXMdMYRZRwh15R4yjK4eFPI4hqYvv5Bg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-30T02:24:18.073311Z","bundle_sha256":"1c481bd826fce620e05a86980bc2a237ae0b5052c6143f0fdd639765c5158f0c"}}