{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:F3VUVV32TLQBXLRN5XQL45YUYT","short_pith_number":"pith:F3VUVV32","canonical_record":{"source":{"id":"1507.06513","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-07-23T14:32:07Z","cross_cats_sorted":[],"title_canon_sha256":"2cf33dfbbc759ec0bb048f766d6638634fe4f97aae9200a68fee3ccd0ac4745e","abstract_canon_sha256":"31fbd4a4f077ab72edcc11c411dc26784739f3a74bead1eff5e130d9f96b1a53"},"schema_version":"1.0"},"canonical_sha256":"2eeb4ad77a9ae01bae2dede0be7714c4fb3116917ddc89dbbdb9c0d063d6e43b","source":{"kind":"arxiv","id":"1507.06513","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1507.06513","created_at":"2026-05-18T00:40:51Z"},{"alias_kind":"arxiv_version","alias_value":"1507.06513v2","created_at":"2026-05-18T00:40:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1507.06513","created_at":"2026-05-18T00:40:51Z"},{"alias_kind":"pith_short_12","alias_value":"F3VUVV32TLQB","created_at":"2026-05-18T12:29:19Z"},{"alias_kind":"pith_short_16","alias_value":"F3VUVV32TLQBXLRN","created_at":"2026-05-18T12:29:19Z"},{"alias_kind":"pith_short_8","alias_value":"F3VUVV32","created_at":"2026-05-18T12:29:19Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:F3VUVV32TLQBXLRN5XQL45YUYT","target":"record","payload":{"canonical_record":{"source":{"id":"1507.06513","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-07-23T14:32:07Z","cross_cats_sorted":[],"title_canon_sha256":"2cf33dfbbc759ec0bb048f766d6638634fe4f97aae9200a68fee3ccd0ac4745e","abstract_canon_sha256":"31fbd4a4f077ab72edcc11c411dc26784739f3a74bead1eff5e130d9f96b1a53"},"schema_version":"1.0"},"canonical_sha256":"2eeb4ad77a9ae01bae2dede0be7714c4fb3116917ddc89dbbdb9c0d063d6e43b","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:40:51.950973Z","signature_b64":"c6x2L4APL3+8VOS7nNHD+HAPk95oCnmDaV0kn8whr9gQQ3qiDFXxjpjqh4iNlVdO7nbDHRaS57AdHVSXtyJICQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2eeb4ad77a9ae01bae2dede0be7714c4fb3116917ddc89dbbdb9c0d063d6e43b","last_reissued_at":"2026-05-18T00:40:51.950294Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:40:51.950294Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1507.06513","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:40:51Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"iIg1dFISbQG5aI7sisAwm5jKOJTbJ6rN6NVg9z1qItK/xRjIT8+6qchMSbjGYtSt1vWEoxjc7cqp+7Io5nFlCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T18:32:29.232705Z"},"content_sha256":"c627d569a4afa2c27f7379ab61fdea6b5d904c50a12adb87d41fdc3000d442a0","schema_version":"1.0","event_id":"sha256:c627d569a4afa2c27f7379ab61fdea6b5d904c50a12adb87d41fdc3000d442a0"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:F3VUVV32TLQBXLRN5XQL45YUYT","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Online Paintability: The Slow-Coloring Game","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Douglas B. West, Gregory J. Puleo, Thomas Mahoney","submitted_at":"2015-07-23T14:32:07Z","abstract_excerpt":"The slow-coloring game is played by Lister and Painter on a graph $G$. On each round, Lister marks a nonempty subset $M$ of the uncolored vertices, scoring $|M|$ points. Painter then gives a color to a subset of $M$ that is independent in $G$. The game ends when all vertices are colored. Painter and Lister want to minimize and maximize the total score, respectively. The best score that each player can guarantee is the sum-color cost of $G$, written $\\mathring{\\mathrm{s}}(G)$. The game is an online variant of online sum list coloring.\n  We proe $\\frac{|V(G)|}{2\\alpha(G)} + \\frac{1}{2} \\leq \\fra"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1507.06513","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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:40:51Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"j5J9h+Vwwqy305MF3Jh0lgMC4en2kdrLQYCaPVTvfD4iFuM/He2mAOOH0pzvlFIumgIg/OR4vTAFbWMXniz1Bg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T18:32:29.233309Z"},"content_sha256":"8adac4e6786170ed2b4045bdb926c9763b74db06e37e409bfffd71d22ca52e84","schema_version":"1.0","event_id":"sha256:8adac4e6786170ed2b4045bdb926c9763b74db06e37e409bfffd71d22ca52e84"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/F3VUVV32TLQBXLRN5XQL45YUYT/bundle.json","state_url":"https://pith.science/pith/F3VUVV32TLQBXLRN5XQL45YUYT/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/F3VUVV32TLQBXLRN5XQL45YUYT/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":"2026-06-05T18:32:29Z","links":{"resolver":"https://pith.science/pith/F3VUVV32TLQBXLRN5XQL45YUYT","bundle":"https://pith.science/pith/F3VUVV32TLQBXLRN5XQL45YUYT/bundle.json","state":"https://pith.science/pith/F3VUVV32TLQBXLRN5XQL45YUYT/state.json","well_known_bundle":"https://pith.science/.well-known/pith/F3VUVV32TLQBXLRN5XQL45YUYT/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:F3VUVV32TLQBXLRN5XQL45YUYT","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":"31fbd4a4f077ab72edcc11c411dc26784739f3a74bead1eff5e130d9f96b1a53","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-07-23T14:32:07Z","title_canon_sha256":"2cf33dfbbc759ec0bb048f766d6638634fe4f97aae9200a68fee3ccd0ac4745e"},"schema_version":"1.0","source":{"id":"1507.06513","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1507.06513","created_at":"2026-05-18T00:40:51Z"},{"alias_kind":"arxiv_version","alias_value":"1507.06513v2","created_at":"2026-05-18T00:40:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1507.06513","created_at":"2026-05-18T00:40:51Z"},{"alias_kind":"pith_short_12","alias_value":"F3VUVV32TLQB","created_at":"2026-05-18T12:29:19Z"},{"alias_kind":"pith_short_16","alias_value":"F3VUVV32TLQBXLRN","created_at":"2026-05-18T12:29:19Z"},{"alias_kind":"pith_short_8","alias_value":"F3VUVV32","created_at":"2026-05-18T12:29:19Z"}],"graph_snapshots":[{"event_id":"sha256:8adac4e6786170ed2b4045bdb926c9763b74db06e37e409bfffd71d22ca52e84","target":"graph","created_at":"2026-05-18T00:40:51Z","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":"The slow-coloring game is played by Lister and Painter on a graph $G$. On each round, Lister marks a nonempty subset $M$ of the uncolored vertices, scoring $|M|$ points. Painter then gives a color to a subset of $M$ that is independent in $G$. The game ends when all vertices are colored. Painter and Lister want to minimize and maximize the total score, respectively. The best score that each player can guarantee is the sum-color cost of $G$, written $\\mathring{\\mathrm{s}}(G)$. The game is an online variant of online sum list coloring.\n  We proe $\\frac{|V(G)|}{2\\alpha(G)} + \\frac{1}{2} \\leq \\fra","authors_text":"Douglas B. West, Gregory J. Puleo, Thomas Mahoney","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-07-23T14:32:07Z","title":"Online Paintability: The Slow-Coloring Game"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1507.06513","kind":"arxiv","version":2},"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:c627d569a4afa2c27f7379ab61fdea6b5d904c50a12adb87d41fdc3000d442a0","target":"record","created_at":"2026-05-18T00:40:51Z","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":"31fbd4a4f077ab72edcc11c411dc26784739f3a74bead1eff5e130d9f96b1a53","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-07-23T14:32:07Z","title_canon_sha256":"2cf33dfbbc759ec0bb048f766d6638634fe4f97aae9200a68fee3ccd0ac4745e"},"schema_version":"1.0","source":{"id":"1507.06513","kind":"arxiv","version":2}},"canonical_sha256":"2eeb4ad77a9ae01bae2dede0be7714c4fb3116917ddc89dbbdb9c0d063d6e43b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2eeb4ad77a9ae01bae2dede0be7714c4fb3116917ddc89dbbdb9c0d063d6e43b","first_computed_at":"2026-05-18T00:40:51.950294Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:40:51.950294Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"c6x2L4APL3+8VOS7nNHD+HAPk95oCnmDaV0kn8whr9gQQ3qiDFXxjpjqh4iNlVdO7nbDHRaS57AdHVSXtyJICQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:40:51.950973Z","signed_message":"canonical_sha256_bytes"},"source_id":"1507.06513","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c627d569a4afa2c27f7379ab61fdea6b5d904c50a12adb87d41fdc3000d442a0","sha256:8adac4e6786170ed2b4045bdb926c9763b74db06e37e409bfffd71d22ca52e84"],"state_sha256":"0d9e5c67980e448c6190bd3ed24e0eab17fe2b62319c066910e68dc01238fa5c"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"lyIGCo8n0fFdbSOULbVCBzS2qry0bB3BRXf7BwrZUgst3G1OAFS2DoYcWRrMDp5gi3Z/NdBkI2E2YlLwBl3yAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-05T18:32:29.236395Z","bundle_sha256":"6f8e98812223901956f4086a6afacb1d3c31e0e98d8ee88b21ce43129587cad4"}}