{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:VDF33STGY2PF7ZF3RT2HSF6MMZ","short_pith_number":"pith:VDF33STG","canonical_record":{"source":{"id":"1802.05359","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-02-14T23:37:41Z","cross_cats_sorted":["math.RA"],"title_canon_sha256":"7cbf2587b735658266030db5fd0155369cb2b5a13ec6647ea7104d9c27f9afc7","abstract_canon_sha256":"e9145ba5d4820788cf1f32587813d82365f0c2cd99cfb8400fce90d1e5aac294"},"schema_version":"1.0"},"canonical_sha256":"a8cbbdca66c69e5fe4bb8cf47917cc66470619147d019b38df0c947913153b7a","source":{"kind":"arxiv","id":"1802.05359","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1802.05359","created_at":"2026-05-18T00:23:15Z"},{"alias_kind":"arxiv_version","alias_value":"1802.05359v1","created_at":"2026-05-18T00:23:15Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1802.05359","created_at":"2026-05-18T00:23:15Z"},{"alias_kind":"pith_short_12","alias_value":"VDF33STGY2PF","created_at":"2026-05-18T12:32:59Z"},{"alias_kind":"pith_short_16","alias_value":"VDF33STGY2PF7ZF3","created_at":"2026-05-18T12:32:59Z"},{"alias_kind":"pith_short_8","alias_value":"VDF33STG","created_at":"2026-05-18T12:32:59Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:VDF33STGY2PF7ZF3RT2HSF6MMZ","target":"record","payload":{"canonical_record":{"source":{"id":"1802.05359","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-02-14T23:37:41Z","cross_cats_sorted":["math.RA"],"title_canon_sha256":"7cbf2587b735658266030db5fd0155369cb2b5a13ec6647ea7104d9c27f9afc7","abstract_canon_sha256":"e9145ba5d4820788cf1f32587813d82365f0c2cd99cfb8400fce90d1e5aac294"},"schema_version":"1.0"},"canonical_sha256":"a8cbbdca66c69e5fe4bb8cf47917cc66470619147d019b38df0c947913153b7a","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:23:15.865089Z","signature_b64":"T6iA6+NdmLGhD/s0dJ6MZhWFaw/2kFZrRyvy9FrGP0VGCHS8D+w7yY+Yb8X5YPEp6waDIoCwGLYmFHzSLhqmDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a8cbbdca66c69e5fe4bb8cf47917cc66470619147d019b38df0c947913153b7a","last_reissued_at":"2026-05-18T00:23:15.864458Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:23:15.864458Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1802.05359","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":"2026-05-18T00:23:15Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Igl7VpmB1WxzsFwUosnGrB4Q0rJHgBMhOGCh+SeOrEtIGa83of2Zs+eNUhuOTkA3aLFJuQAMzDMhDWGbPPNHCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T16:06:43.199676Z"},"content_sha256":"2ed780554b9d1edb758cfad64a9d092a5fe71a23e7c41b24776ceec0f1c0a754","schema_version":"1.0","event_id":"sha256:2ed780554b9d1edb758cfad64a9d092a5fe71a23e7c41b24776ceec0f1c0a754"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:VDF33STGY2PF7ZF3RT2HSF6MMZ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Resolution of Conjectures Related to Lights Out! and Cartesian Products","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RA"],"primary_cat":"math.CO","authors_text":"Bryan Curtis, Bryan Shader, David Livingston, Jonathan Earl","submitted_at":"2018-02-14T23:37:41Z","abstract_excerpt":"Lights Out! is a game played on a $5 \\times 5$ grid of lights, or more generally on a graph. Pressing lights on the grid allows the player to turn off neighboring lights. The goal of the game is to start with a given initial configuration of lit lights and reach a state where all lights are out. Two conjectures posed in a recently published paper about Lights Out! on Cartesian products of graphs are resolved."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1802.05359","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":"2026-05-18T00:23:15Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"cUwabRrGunNzzFiYhBAbgMP3pHwN4EqxkKYSkOjOnaS/L+u79w00fTJa0P1y18fStdZ9TDs7PjMSrYTD5fXYBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T16:06:43.200395Z"},"content_sha256":"902bacad6d0d8e5c5d5bf3f49f6a0c3e33cfc48d1563a6c7d1d50db5c146e5c7","schema_version":"1.0","event_id":"sha256:902bacad6d0d8e5c5d5bf3f49f6a0c3e33cfc48d1563a6c7d1d50db5c146e5c7"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/VDF33STGY2PF7ZF3RT2HSF6MMZ/bundle.json","state_url":"https://pith.science/pith/VDF33STGY2PF7ZF3RT2HSF6MMZ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/VDF33STGY2PF7ZF3RT2HSF6MMZ/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":"2026-06-07T16:06:43Z","links":{"resolver":"https://pith.science/pith/VDF33STGY2PF7ZF3RT2HSF6MMZ","bundle":"https://pith.science/pith/VDF33STGY2PF7ZF3RT2HSF6MMZ/bundle.json","state":"https://pith.science/pith/VDF33STGY2PF7ZF3RT2HSF6MMZ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/VDF33STGY2PF7ZF3RT2HSF6MMZ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:VDF33STGY2PF7ZF3RT2HSF6MMZ","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":"e9145ba5d4820788cf1f32587813d82365f0c2cd99cfb8400fce90d1e5aac294","cross_cats_sorted":["math.RA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-02-14T23:37:41Z","title_canon_sha256":"7cbf2587b735658266030db5fd0155369cb2b5a13ec6647ea7104d9c27f9afc7"},"schema_version":"1.0","source":{"id":"1802.05359","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1802.05359","created_at":"2026-05-18T00:23:15Z"},{"alias_kind":"arxiv_version","alias_value":"1802.05359v1","created_at":"2026-05-18T00:23:15Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1802.05359","created_at":"2026-05-18T00:23:15Z"},{"alias_kind":"pith_short_12","alias_value":"VDF33STGY2PF","created_at":"2026-05-18T12:32:59Z"},{"alias_kind":"pith_short_16","alias_value":"VDF33STGY2PF7ZF3","created_at":"2026-05-18T12:32:59Z"},{"alias_kind":"pith_short_8","alias_value":"VDF33STG","created_at":"2026-05-18T12:32:59Z"}],"graph_snapshots":[{"event_id":"sha256:902bacad6d0d8e5c5d5bf3f49f6a0c3e33cfc48d1563a6c7d1d50db5c146e5c7","target":"graph","created_at":"2026-05-18T00:23:15Z","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":"Lights Out! is a game played on a $5 \\times 5$ grid of lights, or more generally on a graph. Pressing lights on the grid allows the player to turn off neighboring lights. The goal of the game is to start with a given initial configuration of lit lights and reach a state where all lights are out. Two conjectures posed in a recently published paper about Lights Out! on Cartesian products of graphs are resolved.","authors_text":"Bryan Curtis, Bryan Shader, David Livingston, Jonathan Earl","cross_cats":["math.RA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-02-14T23:37:41Z","title":"Resolution of Conjectures Related to Lights Out! and Cartesian Products"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1802.05359","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":"sha256:2ed780554b9d1edb758cfad64a9d092a5fe71a23e7c41b24776ceec0f1c0a754","target":"record","created_at":"2026-05-18T00:23:15Z","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":"e9145ba5d4820788cf1f32587813d82365f0c2cd99cfb8400fce90d1e5aac294","cross_cats_sorted":["math.RA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-02-14T23:37:41Z","title_canon_sha256":"7cbf2587b735658266030db5fd0155369cb2b5a13ec6647ea7104d9c27f9afc7"},"schema_version":"1.0","source":{"id":"1802.05359","kind":"arxiv","version":1}},"canonical_sha256":"a8cbbdca66c69e5fe4bb8cf47917cc66470619147d019b38df0c947913153b7a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a8cbbdca66c69e5fe4bb8cf47917cc66470619147d019b38df0c947913153b7a","first_computed_at":"2026-05-18T00:23:15.864458Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:23:15.864458Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"T6iA6+NdmLGhD/s0dJ6MZhWFaw/2kFZrRyvy9FrGP0VGCHS8D+w7yY+Yb8X5YPEp6waDIoCwGLYmFHzSLhqmDA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:23:15.865089Z","signed_message":"canonical_sha256_bytes"},"source_id":"1802.05359","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2ed780554b9d1edb758cfad64a9d092a5fe71a23e7c41b24776ceec0f1c0a754","sha256:902bacad6d0d8e5c5d5bf3f49f6a0c3e33cfc48d1563a6c7d1d50db5c146e5c7"],"state_sha256":"a49cea73bbbe2d35a190a9e4eb8143fde9c635360cf7498b4a09d41cbe4f3a84"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"jxWW+KGmxeA3I7f0q4wGmaBu69zGh8h0FkuATOUyufikcOa4688VbGfhKMJvEXbXXBskbUPyb4iLjEe1mV1KDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-07T16:06:43.204083Z","bundle_sha256":"08c290a03c247f07406bbf93fb3e89cbf807cf9bcfa0d06addda9d84e145cca6"}}