{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:ZVLP7YSQYX4FU7XRJKNRSAP6SO","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":"dab23ff6cbcb7a02bac4aa769b752c4e01b89623102a2ff0e73ecf7acd7789ca","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-07-30T11:48:43Z","title_canon_sha256":"b7bd79f5f65d4b3b0d9c78840abee895fd8dd973fd3e7bab375ab51262d92220"},"schema_version":"1.0","source":{"id":"1807.11297","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1807.11297","created_at":"2026-05-18T00:09:32Z"},{"alias_kind":"arxiv_version","alias_value":"1807.11297v1","created_at":"2026-05-18T00:09:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1807.11297","created_at":"2026-05-18T00:09:32Z"},{"alias_kind":"pith_short_12","alias_value":"ZVLP7YSQYX4F","created_at":"2026-05-18T12:33:07Z"},{"alias_kind":"pith_short_16","alias_value":"ZVLP7YSQYX4FU7XR","created_at":"2026-05-18T12:33:07Z"},{"alias_kind":"pith_short_8","alias_value":"ZVLP7YSQ","created_at":"2026-05-18T12:33:07Z"}],"graph_snapshots":[{"event_id":"sha256:2513708cca970e4e986cc022329ba0d49f06f727b83d916215a13d30b45d8c32","target":"graph","created_at":"2026-05-18T00:09:32Z","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":"This paper addresses several significant gaps in the theory of restricted mis\\`ere play (Plambeck, Siegel 2008), primarily in the well-studied universe of dead-ending games, $\\mathcal{E}$ (Milley, Renault 2013); if a player run out of moves in $X\\in \\mathcal E$, then they can never move again in any follower of $X$. A universe of games is a class of games which is closed under disjunctive sum, taking options and conjugates. We use novel results from absolute combinatorial game theory (Larsson, Nowakowski, Santos 2017) to show that $\\mathcal{E}$ and the universe $\\mathcal{D}\\subset \\mathcal{E}$","authors_text":"Carlos Santos, Gabriel Renault, Rebecca Milley, Richard Nowakowski, Urban Larsson","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-07-30T11:48:43Z","title":"Progress on mis\\`ere dead ends: game comparison, canonical form, and conjugate inverses"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1807.11297","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":"sha256:1b0eaca246a297f33a2a155a22d2c21b3b4741d97ef0140646396fbc4ca5c4d4","target":"record","created_at":"2026-05-18T00:09:32Z","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":"dab23ff6cbcb7a02bac4aa769b752c4e01b89623102a2ff0e73ecf7acd7789ca","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-07-30T11:48:43Z","title_canon_sha256":"b7bd79f5f65d4b3b0d9c78840abee895fd8dd973fd3e7bab375ab51262d92220"},"schema_version":"1.0","source":{"id":"1807.11297","kind":"arxiv","version":1}},"canonical_sha256":"cd56ffe250c5f85a7ef14a9b1901fe939bdeddd423becf0a1c69f88cbb866dc9","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"cd56ffe250c5f85a7ef14a9b1901fe939bdeddd423becf0a1c69f88cbb866dc9","first_computed_at":"2026-05-18T00:09:32.354402Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:09:32.354402Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"RxUGECKcap3VRTQBNTT4tYpzoZRU2OsBgD5CyBTLEgIO1Axwf1rU13aXB9y0IAq1TIqZG0o7i5K930FDvE48DQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:09:32.355122Z","signed_message":"canonical_sha256_bytes"},"source_id":"1807.11297","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1b0eaca246a297f33a2a155a22d2c21b3b4741d97ef0140646396fbc4ca5c4d4","sha256:2513708cca970e4e986cc022329ba0d49f06f727b83d916215a13d30b45d8c32"],"state_sha256":"9e620c2bfcca6571e03db411416b79cff2d396b9ccd7f31403f5be3479833d87"}