{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:KAZ3I7FIYMOSKD6F4WHCRW6SNH","short_pith_number":"pith:KAZ3I7FI","canonical_record":{"source":{"id":"1712.02324","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GM","submitted_at":"2017-12-06T18:47:07Z","cross_cats_sorted":[],"title_canon_sha256":"18e09daee5bd45400486623b0fa1e9699a2b6a428776d86c18fc19bda64021ab","abstract_canon_sha256":"0e495df9e035eb7097367ed38e33e38e49d3767bea9309733ad7509a52d0586a"},"schema_version":"1.0"},"canonical_sha256":"5033b47ca8c31d250fc5e58e28dbd269d61a9ed5c8d76a5d762dc6b7b35f2ecc","source":{"kind":"arxiv","id":"1712.02324","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1712.02324","created_at":"2026-05-18T00:28:38Z"},{"alias_kind":"arxiv_version","alias_value":"1712.02324v1","created_at":"2026-05-18T00:28:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1712.02324","created_at":"2026-05-18T00:28:38Z"},{"alias_kind":"pith_short_12","alias_value":"KAZ3I7FIYMOS","created_at":"2026-05-18T12:31:24Z"},{"alias_kind":"pith_short_16","alias_value":"KAZ3I7FIYMOSKD6F","created_at":"2026-05-18T12:31:24Z"},{"alias_kind":"pith_short_8","alias_value":"KAZ3I7FI","created_at":"2026-05-18T12:31:24Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:KAZ3I7FIYMOSKD6F4WHCRW6SNH","target":"record","payload":{"canonical_record":{"source":{"id":"1712.02324","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GM","submitted_at":"2017-12-06T18:47:07Z","cross_cats_sorted":[],"title_canon_sha256":"18e09daee5bd45400486623b0fa1e9699a2b6a428776d86c18fc19bda64021ab","abstract_canon_sha256":"0e495df9e035eb7097367ed38e33e38e49d3767bea9309733ad7509a52d0586a"},"schema_version":"1.0"},"canonical_sha256":"5033b47ca8c31d250fc5e58e28dbd269d61a9ed5c8d76a5d762dc6b7b35f2ecc","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:28:38.485898Z","signature_b64":"1jPc9At3vLpWaGcdA0LHv2SeFyGCX/QdhF2Ew5vCN3P5ZPrEbzOLc3DBKBxYpA2kmw2D2LaJry5mNjEiGk3TCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5033b47ca8c31d250fc5e58e28dbd269d61a9ed5c8d76a5d762dc6b7b35f2ecc","last_reissued_at":"2026-05-18T00:28:38.485152Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:28:38.485152Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1712.02324","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":"2026-05-18T00:28:38Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"RvfgCTlWamxN9Fi7D8OhL0lkuF4XwrJ6KOyoeY64VnMzLQGWynv9tMeEku44cslEpK4MVmm5lg14/7nGCzsAAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T21:20:41.210303Z"},"content_sha256":"4e00436be9922e544d1034bb11d29894baf51a3ddfaee9325544a351fc8c8bb3","schema_version":"1.0","event_id":"sha256:4e00436be9922e544d1034bb11d29894baf51a3ddfaee9325544a351fc8c8bb3"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:KAZ3I7FIYMOSKD6F4WHCRW6SNH","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On the Rainbow Neighbourhood Number of Set-Graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GM","authors_text":"Johan Kok, Sudev Naduvath","submitted_at":"2017-12-06T18:47:07Z","abstract_excerpt":"In this paper, we present results for the rainbow neighbourhood numbers of set-graphs. It is also shown that set-graphs are perfect graphs. The intuitive colouring dilemma in respect of the rainbow neighbourhood convention is clarified as well. Finally, the new notion of the maximax independence, maximum proper colouring of a graph and a new graph parameter called the $i$-max number of $G$ are introduced as a new research direction."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1712.02324","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":"2026-05-18T00:28:38Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"QLdtRZ7VvlQsfNuoeo7ji5JZYcT3I7xDk3tFLLE+DhGVdjuAW8YMWECJ6J5xAlj6PqM5Bv+/ItBG+MLBdaaIAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T21:20:41.210664Z"},"content_sha256":"66c1b5c00f7d6c820cba2450c17e83b2324c43062d01ff7048673c8411738130","schema_version":"1.0","event_id":"sha256:66c1b5c00f7d6c820cba2450c17e83b2324c43062d01ff7048673c8411738130"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/KAZ3I7FIYMOSKD6F4WHCRW6SNH/bundle.json","state_url":"https://pith.science/pith/KAZ3I7FIYMOSKD6F4WHCRW6SNH/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/KAZ3I7FIYMOSKD6F4WHCRW6SNH/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":"2026-06-03T21:20:41Z","links":{"resolver":"https://pith.science/pith/KAZ3I7FIYMOSKD6F4WHCRW6SNH","bundle":"https://pith.science/pith/KAZ3I7FIYMOSKD6F4WHCRW6SNH/bundle.json","state":"https://pith.science/pith/KAZ3I7FIYMOSKD6F4WHCRW6SNH/state.json","well_known_bundle":"https://pith.science/.well-known/pith/KAZ3I7FIYMOSKD6F4WHCRW6SNH/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:KAZ3I7FIYMOSKD6F4WHCRW6SNH","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":"0e495df9e035eb7097367ed38e33e38e49d3767bea9309733ad7509a52d0586a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GM","submitted_at":"2017-12-06T18:47:07Z","title_canon_sha256":"18e09daee5bd45400486623b0fa1e9699a2b6a428776d86c18fc19bda64021ab"},"schema_version":"1.0","source":{"id":"1712.02324","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1712.02324","created_at":"2026-05-18T00:28:38Z"},{"alias_kind":"arxiv_version","alias_value":"1712.02324v1","created_at":"2026-05-18T00:28:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1712.02324","created_at":"2026-05-18T00:28:38Z"},{"alias_kind":"pith_short_12","alias_value":"KAZ3I7FIYMOS","created_at":"2026-05-18T12:31:24Z"},{"alias_kind":"pith_short_16","alias_value":"KAZ3I7FIYMOSKD6F","created_at":"2026-05-18T12:31:24Z"},{"alias_kind":"pith_short_8","alias_value":"KAZ3I7FI","created_at":"2026-05-18T12:31:24Z"}],"graph_snapshots":[{"event_id":"sha256:66c1b5c00f7d6c820cba2450c17e83b2324c43062d01ff7048673c8411738130","target":"graph","created_at":"2026-05-18T00:28:38Z","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":"In this paper, we present results for the rainbow neighbourhood numbers of set-graphs. It is also shown that set-graphs are perfect graphs. The intuitive colouring dilemma in respect of the rainbow neighbourhood convention is clarified as well. Finally, the new notion of the maximax independence, maximum proper colouring of a graph and a new graph parameter called the $i$-max number of $G$ are introduced as a new research direction.","authors_text":"Johan Kok, Sudev Naduvath","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GM","submitted_at":"2017-12-06T18:47:07Z","title":"On the Rainbow Neighbourhood Number of Set-Graphs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1712.02324","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":"sha256:4e00436be9922e544d1034bb11d29894baf51a3ddfaee9325544a351fc8c8bb3","target":"record","created_at":"2026-05-18T00:28:38Z","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":"0e495df9e035eb7097367ed38e33e38e49d3767bea9309733ad7509a52d0586a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GM","submitted_at":"2017-12-06T18:47:07Z","title_canon_sha256":"18e09daee5bd45400486623b0fa1e9699a2b6a428776d86c18fc19bda64021ab"},"schema_version":"1.0","source":{"id":"1712.02324","kind":"arxiv","version":1}},"canonical_sha256":"5033b47ca8c31d250fc5e58e28dbd269d61a9ed5c8d76a5d762dc6b7b35f2ecc","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5033b47ca8c31d250fc5e58e28dbd269d61a9ed5c8d76a5d762dc6b7b35f2ecc","first_computed_at":"2026-05-18T00:28:38.485152Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:28:38.485152Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"1jPc9At3vLpWaGcdA0LHv2SeFyGCX/QdhF2Ew5vCN3P5ZPrEbzOLc3DBKBxYpA2kmw2D2LaJry5mNjEiGk3TCA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:28:38.485898Z","signed_message":"canonical_sha256_bytes"},"source_id":"1712.02324","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4e00436be9922e544d1034bb11d29894baf51a3ddfaee9325544a351fc8c8bb3","sha256:66c1b5c00f7d6c820cba2450c17e83b2324c43062d01ff7048673c8411738130"],"state_sha256":"690d737711703d356cf6b55bd07ce521641107d5f8e3f4546c2fc49ada3210f0"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"R63C3qG55esRhdN0ZaE8G9dztInQgXVez9WOy8CRCaiT5XC/AcYFqkMm4E0wx4H2AGYowKGYDOA7e6T82hg+Bw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-03T21:20:41.212650Z","bundle_sha256":"d4f84711e4bd8972ebb76764c9be8595149edef2711d3f57dc3b65261e8d964e"}}