{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:RPEEMLTW7GMI3VDALLCNW43YJB","short_pith_number":"pith:RPEEMLTW","canonical_record":{"source":{"id":"1105.3712","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2011-05-18T18:33:00Z","cross_cats_sorted":[],"title_canon_sha256":"d1e9ecb7646461d2405ed127d2928d58e5440eefc8255d6a9bd8c6be099c6646","abstract_canon_sha256":"c5c13017d46b90d55be1d39a25812d38de44462d6580bbdf5c5a7092a40dac57"},"schema_version":"1.0"},"canonical_sha256":"8bc8462e76f9988dd4605ac4db7378486f69dd32d32b986b8f2fd8281128e8b9","source":{"kind":"arxiv","id":"1105.3712","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1105.3712","created_at":"2026-05-18T04:21:52Z"},{"alias_kind":"arxiv_version","alias_value":"1105.3712v1","created_at":"2026-05-18T04:21:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1105.3712","created_at":"2026-05-18T04:21:52Z"},{"alias_kind":"pith_short_12","alias_value":"RPEEMLTW7GMI","created_at":"2026-05-18T12:26:41Z"},{"alias_kind":"pith_short_16","alias_value":"RPEEMLTW7GMI3VDA","created_at":"2026-05-18T12:26:41Z"},{"alias_kind":"pith_short_8","alias_value":"RPEEMLTW","created_at":"2026-05-18T12:26:41Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:RPEEMLTW7GMI3VDALLCNW43YJB","target":"record","payload":{"canonical_record":{"source":{"id":"1105.3712","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2011-05-18T18:33:00Z","cross_cats_sorted":[],"title_canon_sha256":"d1e9ecb7646461d2405ed127d2928d58e5440eefc8255d6a9bd8c6be099c6646","abstract_canon_sha256":"c5c13017d46b90d55be1d39a25812d38de44462d6580bbdf5c5a7092a40dac57"},"schema_version":"1.0"},"canonical_sha256":"8bc8462e76f9988dd4605ac4db7378486f69dd32d32b986b8f2fd8281128e8b9","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:21:52.037783Z","signature_b64":"LELluTW9vpMpffp5M6mpIZyuXp9yvs7ePQKtk1OltdUgnMRmOHERO/NWLtkjbZYutFHS5VkzIr0EXBSPpFP9Dg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8bc8462e76f9988dd4605ac4db7378486f69dd32d32b986b8f2fd8281128e8b9","last_reissued_at":"2026-05-18T04:21:52.037102Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:21:52.037102Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1105.3712","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":"2026-05-18T04:21:52Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"eHtegT2InaYWK3Q+OnXoOIgyb0KkU2DZXcNiP8SKGrazivSsEqSuM4W1BgW5OsSVRAguwtPrwYs2qHpblKl/Bg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-29T04:50:16.492521Z"},"content_sha256":"2f8452b5258a608fa183399fd709e9b2985a10fa8ac66ece128009cc5d5130ce","schema_version":"1.0","event_id":"sha256:2f8452b5258a608fa183399fd709e9b2985a10fa8ac66ece128009cc5d5130ce"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:RPEEMLTW7GMI3VDALLCNW43YJB","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Rainbow induced subgraphs in proper vertex colorings","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Andrzej Kisielewicz, Marek Szyku{\\l}a","submitted_at":"2011-05-18T18:33:00Z","abstract_excerpt":"For a given graph $H$ we define $\\rho(H)$ to be the minimum order of a graph $G$ such that every proper vertex coloring of $G$ contains a rainbow induced subgraph isomorphic to $H$. We give upper and lower bounds for $\\rho(H)$, compute the exact value for some classes of graphs, and consider an interesting combinatorial problem connected with computation of $\\rho(H)$ for paths. This research is motivated by some ideas in on-line graph coloring algorithms."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1105.3712","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":"2026-05-18T04:21:52Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"VNzF0AOPOTx25+JqOKNvvasTbSrV098JcKOZomPQbpm/pii12/re5oI9zIoXKvK6CIwak0DSRNyfk/oWUOc3Bw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-29T04:50:16.492852Z"},"content_sha256":"ddf5668e3f5fd9b3659a9c8fe3df1d46673799d589273f1ebf0f39a1ac8093b5","schema_version":"1.0","event_id":"sha256:ddf5668e3f5fd9b3659a9c8fe3df1d46673799d589273f1ebf0f39a1ac8093b5"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/RPEEMLTW7GMI3VDALLCNW43YJB/bundle.json","state_url":"https://pith.science/pith/RPEEMLTW7GMI3VDALLCNW43YJB/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/RPEEMLTW7GMI3VDALLCNW43YJB/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":"2026-06-29T04:50:16Z","links":{"resolver":"https://pith.science/pith/RPEEMLTW7GMI3VDALLCNW43YJB","bundle":"https://pith.science/pith/RPEEMLTW7GMI3VDALLCNW43YJB/bundle.json","state":"https://pith.science/pith/RPEEMLTW7GMI3VDALLCNW43YJB/state.json","well_known_bundle":"https://pith.science/.well-known/pith/RPEEMLTW7GMI3VDALLCNW43YJB/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:RPEEMLTW7GMI3VDALLCNW43YJB","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":"c5c13017d46b90d55be1d39a25812d38de44462d6580bbdf5c5a7092a40dac57","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2011-05-18T18:33:00Z","title_canon_sha256":"d1e9ecb7646461d2405ed127d2928d58e5440eefc8255d6a9bd8c6be099c6646"},"schema_version":"1.0","source":{"id":"1105.3712","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1105.3712","created_at":"2026-05-18T04:21:52Z"},{"alias_kind":"arxiv_version","alias_value":"1105.3712v1","created_at":"2026-05-18T04:21:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1105.3712","created_at":"2026-05-18T04:21:52Z"},{"alias_kind":"pith_short_12","alias_value":"RPEEMLTW7GMI","created_at":"2026-05-18T12:26:41Z"},{"alias_kind":"pith_short_16","alias_value":"RPEEMLTW7GMI3VDA","created_at":"2026-05-18T12:26:41Z"},{"alias_kind":"pith_short_8","alias_value":"RPEEMLTW","created_at":"2026-05-18T12:26:41Z"}],"graph_snapshots":[{"event_id":"sha256:ddf5668e3f5fd9b3659a9c8fe3df1d46673799d589273f1ebf0f39a1ac8093b5","target":"graph","created_at":"2026-05-18T04:21:52Z","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":"For a given graph $H$ we define $\\rho(H)$ to be the minimum order of a graph $G$ such that every proper vertex coloring of $G$ contains a rainbow induced subgraph isomorphic to $H$. We give upper and lower bounds for $\\rho(H)$, compute the exact value for some classes of graphs, and consider an interesting combinatorial problem connected with computation of $\\rho(H)$ for paths. This research is motivated by some ideas in on-line graph coloring algorithms.","authors_text":"Andrzej Kisielewicz, Marek Szyku{\\l}a","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2011-05-18T18:33:00Z","title":"Rainbow induced subgraphs in proper vertex colorings"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1105.3712","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":"sha256:2f8452b5258a608fa183399fd709e9b2985a10fa8ac66ece128009cc5d5130ce","target":"record","created_at":"2026-05-18T04:21:52Z","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":"c5c13017d46b90d55be1d39a25812d38de44462d6580bbdf5c5a7092a40dac57","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2011-05-18T18:33:00Z","title_canon_sha256":"d1e9ecb7646461d2405ed127d2928d58e5440eefc8255d6a9bd8c6be099c6646"},"schema_version":"1.0","source":{"id":"1105.3712","kind":"arxiv","version":1}},"canonical_sha256":"8bc8462e76f9988dd4605ac4db7378486f69dd32d32b986b8f2fd8281128e8b9","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8bc8462e76f9988dd4605ac4db7378486f69dd32d32b986b8f2fd8281128e8b9","first_computed_at":"2026-05-18T04:21:52.037102Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:21:52.037102Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"LELluTW9vpMpffp5M6mpIZyuXp9yvs7ePQKtk1OltdUgnMRmOHERO/NWLtkjbZYutFHS5VkzIr0EXBSPpFP9Dg==","signature_status":"signed_v1","signed_at":"2026-05-18T04:21:52.037783Z","signed_message":"canonical_sha256_bytes"},"source_id":"1105.3712","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2f8452b5258a608fa183399fd709e9b2985a10fa8ac66ece128009cc5d5130ce","sha256:ddf5668e3f5fd9b3659a9c8fe3df1d46673799d589273f1ebf0f39a1ac8093b5"],"state_sha256":"44782804fd9414c47fa03f5d14e204565c446cbee7cf436f491c521597948e32"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"mJPv6mXD81NuccN9a5hGrW3D/laqrHEN3vCnpJLIqLDRl30C+A9Sx68KA0g5RkvPNpB1R7kzQ5zD1WL8yHuMCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-29T04:50:16.494682Z","bundle_sha256":"495aa3a8f4578a2a4e4e3c81d5d322d7721a8aef450c53e8c52890bbcf6a3001"}}