{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2010:5OJIKXPYHLBY73PSO3DKZGOYNX","short_pith_number":"pith:5OJIKXPY","schema_version":"1.0","canonical_sha256":"eb92855df83ac38fedf276c6ac99d86df190a67d4a5db3e5beb160ba55e44ed2","source":{"kind":"arxiv","id":"1010.5846","version":3},"attestation_state":"computed","paper":{"title":"Two-lit trees for lit-only sigma-game","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Hau-wen Huang","submitted_at":"2010-10-28T03:23:21Z","abstract_excerpt":"A configuration of the lit-only $\\sigma$-game on a finite graph $\\Gamma$ is an assignment of one of two states, on or off, to all vertices of $\\Gamma.$ Given a configuration, a move of the lit-only $\\sigma$-game on $\\Gamma$ allows the player to choose an on vertex $s$ of $\\Gamma$ and change the states of all neighbors of $s.$ Given any integer $k$, we say that $\\Gamma$ is $k$-lit if, for any configuration, the number of on vertices can be reduced to at most $k$ by a finite sequence of moves. Assume that $\\Gamma$ is a tree with a perfect matching. We show that $\\Gamma$ is 1-lit and any tree obt"},"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":"1010.5846","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2010-10-28T03:23:21Z","cross_cats_sorted":[],"title_canon_sha256":"b121eeb398df2257c940b65fa06e93037fe3382ace3768aed75ed607ad89f9d7","abstract_canon_sha256":"f65f4db672739beff0af89d2de0e3a60e9978b28796bc6030e8048f9dad567e8"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:48:48.291770Z","signature_b64":"cbQkzHA1nIvdor7XfFenXK1e8BtIlQBhZgUC6HAq1/nANtdCGF044pqIQlIGjfCCDkfCVk4SKueLcd8JfaDvAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"eb92855df83ac38fedf276c6ac99d86df190a67d4a5db3e5beb160ba55e44ed2","last_reissued_at":"2026-05-18T03:48:48.291135Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:48:48.291135Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Two-lit trees for lit-only sigma-game","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Hau-wen Huang","submitted_at":"2010-10-28T03:23:21Z","abstract_excerpt":"A configuration of the lit-only $\\sigma$-game on a finite graph $\\Gamma$ is an assignment of one of two states, on or off, to all vertices of $\\Gamma.$ Given a configuration, a move of the lit-only $\\sigma$-game on $\\Gamma$ allows the player to choose an on vertex $s$ of $\\Gamma$ and change the states of all neighbors of $s.$ Given any integer $k$, we say that $\\Gamma$ is $k$-lit if, for any configuration, the number of on vertices can be reduced to at most $k$ by a finite sequence of moves. Assume that $\\Gamma$ is a tree with a perfect matching. We show that $\\Gamma$ is 1-lit and any tree obt"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1010.5846","kind":"arxiv","version":3},"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":"1010.5846","created_at":"2026-05-18T03:48:48.291224+00:00"},{"alias_kind":"arxiv_version","alias_value":"1010.5846v3","created_at":"2026-05-18T03:48:48.291224+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1010.5846","created_at":"2026-05-18T03:48:48.291224+00:00"},{"alias_kind":"pith_short_12","alias_value":"5OJIKXPYHLBY","created_at":"2026-05-18T12:26:04.259169+00:00"},{"alias_kind":"pith_short_16","alias_value":"5OJIKXPYHLBY73PS","created_at":"2026-05-18T12:26:04.259169+00:00"},{"alias_kind":"pith_short_8","alias_value":"5OJIKXPY","created_at":"2026-05-18T12:26:04.259169+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/5OJIKXPYHLBY73PSO3DKZGOYNX","json":"https://pith.science/pith/5OJIKXPYHLBY73PSO3DKZGOYNX.json","graph_json":"https://pith.science/api/pith-number/5OJIKXPYHLBY73PSO3DKZGOYNX/graph.json","events_json":"https://pith.science/api/pith-number/5OJIKXPYHLBY73PSO3DKZGOYNX/events.json","paper":"https://pith.science/paper/5OJIKXPY"},"agent_actions":{"view_html":"https://pith.science/pith/5OJIKXPYHLBY73PSO3DKZGOYNX","download_json":"https://pith.science/pith/5OJIKXPYHLBY73PSO3DKZGOYNX.json","view_paper":"https://pith.science/paper/5OJIKXPY","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1010.5846&json=true","fetch_graph":"https://pith.science/api/pith-number/5OJIKXPYHLBY73PSO3DKZGOYNX/graph.json","fetch_events":"https://pith.science/api/pith-number/5OJIKXPYHLBY73PSO3DKZGOYNX/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/5OJIKXPYHLBY73PSO3DKZGOYNX/action/timestamp_anchor","attest_storage":"https://pith.science/pith/5OJIKXPYHLBY73PSO3DKZGOYNX/action/storage_attestation","attest_author":"https://pith.science/pith/5OJIKXPYHLBY73PSO3DKZGOYNX/action/author_attestation","sign_citation":"https://pith.science/pith/5OJIKXPYHLBY73PSO3DKZGOYNX/action/citation_signature","submit_replication":"https://pith.science/pith/5OJIKXPYHLBY73PSO3DKZGOYNX/action/replication_record"}},"created_at":"2026-05-18T03:48:48.291224+00:00","updated_at":"2026-05-18T03:48:48.291224+00:00"}