{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:65HVSPZKMACOJGNXAFT33MFPXW","short_pith_number":"pith:65HVSPZK","schema_version":"1.0","canonical_sha256":"f74f593f2a6004e499b70167bdb0afbd9164ca0a5d6dea10d41a04a500043a52","source":{"kind":"arxiv","id":"1707.07966","version":2},"attestation_state":"computed","paper":{"title":"The switch operators and push-the-button games: a sequential compound over rulesets","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DM","authors_text":"Aline Parreau (GOAL), Eric Duchene (GOAL), Marc Heinrich (GOAL), Urban Larsson","submitted_at":"2017-07-25T12:58:20Z","abstract_excerpt":"We study operators that combine combinatorial games. This field was initiated by Sprague-Grundy (1930s), Milnor (1950s) and Berlekamp-Conway-Guy (1970-80s) via the now classical disjunctive sum operator on (abstract) games. The new class consists in operators for rulesets, dubbed the switch-operators. The ordered pair of rulesets (R 1 , R 2) is compatible if, given any position in R 1 , there is a description of how to move in R 2. Given compatible (R 1 , R 2), we build the push-the-button game R 1 R 2 , where players start by playing according to the rules R 1 , but at some point during play,"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1707.07966","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2017-07-25T12:58:20Z","cross_cats_sorted":[],"title_canon_sha256":"fa6c3b1681c63dc24fc3c697fab3d912cf087a28631c179908d9ad58dda7eaac","abstract_canon_sha256":"90a54cbd1f84e26fa88d38627770f868a83c699f600dc8fe8332313d6fc83aab"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:27:30.264541Z","signature_b64":"aSywZ3Xxn4lSAJtg2QYvMrRpcspYaq6so8ujeLkXp5Gm2e8H+JvayBzJ0xZAlC+Gvl94fKoY96yLvx5fPCP5Cg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f74f593f2a6004e499b70167bdb0afbd9164ca0a5d6dea10d41a04a500043a52","last_reissued_at":"2026-05-18T00:27:30.263769Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:27:30.263769Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The switch operators and push-the-button games: a sequential compound over rulesets","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DM","authors_text":"Aline Parreau (GOAL), Eric Duchene (GOAL), Marc Heinrich (GOAL), Urban Larsson","submitted_at":"2017-07-25T12:58:20Z","abstract_excerpt":"We study operators that combine combinatorial games. This field was initiated by Sprague-Grundy (1930s), Milnor (1950s) and Berlekamp-Conway-Guy (1970-80s) via the now classical disjunctive sum operator on (abstract) games. The new class consists in operators for rulesets, dubbed the switch-operators. The ordered pair of rulesets (R 1 , R 2) is compatible if, given any position in R 1 , there is a description of how to move in R 2. Given compatible (R 1 , R 2), we build the push-the-button game R 1 R 2 , where players start by playing according to the rules R 1 , but at some point during play,"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1707.07966","kind":"arxiv","version":2},"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1707.07966","created_at":"2026-05-18T00:27:30.263900+00:00"},{"alias_kind":"arxiv_version","alias_value":"1707.07966v2","created_at":"2026-05-18T00:27:30.263900+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1707.07966","created_at":"2026-05-18T00:27:30.263900+00:00"},{"alias_kind":"pith_short_12","alias_value":"65HVSPZKMACO","created_at":"2026-05-18T12:31:03.183658+00:00"},{"alias_kind":"pith_short_16","alias_value":"65HVSPZKMACOJGNX","created_at":"2026-05-18T12:31:03.183658+00:00"},{"alias_kind":"pith_short_8","alias_value":"65HVSPZK","created_at":"2026-05-18T12:31:03.183658+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/65HVSPZKMACOJGNXAFT33MFPXW","json":"https://pith.science/pith/65HVSPZKMACOJGNXAFT33MFPXW.json","graph_json":"https://pith.science/api/pith-number/65HVSPZKMACOJGNXAFT33MFPXW/graph.json","events_json":"https://pith.science/api/pith-number/65HVSPZKMACOJGNXAFT33MFPXW/events.json","paper":"https://pith.science/paper/65HVSPZK"},"agent_actions":{"view_html":"https://pith.science/pith/65HVSPZKMACOJGNXAFT33MFPXW","download_json":"https://pith.science/pith/65HVSPZKMACOJGNXAFT33MFPXW.json","view_paper":"https://pith.science/paper/65HVSPZK","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1707.07966&json=true","fetch_graph":"https://pith.science/api/pith-number/65HVSPZKMACOJGNXAFT33MFPXW/graph.json","fetch_events":"https://pith.science/api/pith-number/65HVSPZKMACOJGNXAFT33MFPXW/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/65HVSPZKMACOJGNXAFT33MFPXW/action/timestamp_anchor","attest_storage":"https://pith.science/pith/65HVSPZKMACOJGNXAFT33MFPXW/action/storage_attestation","attest_author":"https://pith.science/pith/65HVSPZKMACOJGNXAFT33MFPXW/action/author_attestation","sign_citation":"https://pith.science/pith/65HVSPZKMACOJGNXAFT33MFPXW/action/citation_signature","submit_replication":"https://pith.science/pith/65HVSPZKMACOJGNXAFT33MFPXW/action/replication_record"}},"created_at":"2026-05-18T00:27:30.263900+00:00","updated_at":"2026-05-18T00:27:30.263900+00:00"}