{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:LD3IRQXD4TLUK2C7CMG2SVG4NF","short_pith_number":"pith:LD3IRQXD","canonical_record":{"source":{"id":"1702.00103","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GM","submitted_at":"2017-02-01T01:57:25Z","cross_cats_sorted":[],"title_canon_sha256":"89aef8e1010826b04be156761631ebb30c0d91da89ddf2ef8bea20ae211f67cc","abstract_canon_sha256":"39b81a6f1f216e953d93cc5c8368263d8ac9b8f0a3f090ab892844c4451cd4e8"},"schema_version":"1.0"},"canonical_sha256":"58f688c2e3e4d745685f130da954dc6944c9ddafcbcce638912efa566886df17","source":{"kind":"arxiv","id":"1702.00103","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1702.00103","created_at":"2026-05-18T00:51:22Z"},{"alias_kind":"arxiv_version","alias_value":"1702.00103v1","created_at":"2026-05-18T00:51:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1702.00103","created_at":"2026-05-18T00:51:22Z"},{"alias_kind":"pith_short_12","alias_value":"LD3IRQXD4TLU","created_at":"2026-05-18T12:31:28Z"},{"alias_kind":"pith_short_16","alias_value":"LD3IRQXD4TLUK2C7","created_at":"2026-05-18T12:31:28Z"},{"alias_kind":"pith_short_8","alias_value":"LD3IRQXD","created_at":"2026-05-18T12:31:28Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:LD3IRQXD4TLUK2C7CMG2SVG4NF","target":"record","payload":{"canonical_record":{"source":{"id":"1702.00103","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GM","submitted_at":"2017-02-01T01:57:25Z","cross_cats_sorted":[],"title_canon_sha256":"89aef8e1010826b04be156761631ebb30c0d91da89ddf2ef8bea20ae211f67cc","abstract_canon_sha256":"39b81a6f1f216e953d93cc5c8368263d8ac9b8f0a3f090ab892844c4451cd4e8"},"schema_version":"1.0"},"canonical_sha256":"58f688c2e3e4d745685f130da954dc6944c9ddafcbcce638912efa566886df17","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:51:22.349875Z","signature_b64":"OxNYwDsOUntMvyA6/vaRbyQ9XHn1JXgDfSGyFllDKBpFiqRvf38tztZAIFM9+czUi1fTPtDcWiz4KYcrTtouBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"58f688c2e3e4d745685f130da954dc6944c9ddafcbcce638912efa566886df17","last_reissued_at":"2026-05-18T00:51:22.349084Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:51:22.349084Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1702.00103","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":"2026-05-18T00:51:22Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"VkNGaFkZ1iA5Bu+Kygw630S5SA3jkt2qgCjXZYnmf+RuW+Qk7+Xem//NtPR0xy4YsBhQ5uOwm/IQQLFa3aciAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T23:14:02.272354Z"},"content_sha256":"f3e95e1e0f7a0a2950037e9b0cdd29d7de3ba348d91432f3b75025b930e10437","schema_version":"1.0","event_id":"sha256:f3e95e1e0f7a0a2950037e9b0cdd29d7de3ba348d91432f3b75025b930e10437"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:LD3IRQXD4TLUK2C7CMG2SVG4NF","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A note on chromatic blending of colour clusters","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GM","authors_text":"Johan Kok, Muhammad Kamran Jamil, Naduvath Sudev","submitted_at":"2017-02-01T01:57:25Z","abstract_excerpt":"For a colour cluster $\\C =(\\mathcal{C}_1,\\mathcal{C}_2, \\mathcal{C}_3,\\dots,\\mathcal{C}_\\ell)$, $\\mathcal{C}_i$ is a colour class, and $|\\mathcal{C}_i|=r_i \\geq 1$, we investigate a simple connected graph structure $G^{\\C}$, which represents a graphical embodiment of the colour cluster such that the chromatic number $\\chi(G^{\\C})= \\ell,$ and the number of edges is a maximum, denoted $\\varepsilon^+(G^{\\C})$. We also extend the study by inducing new colour clusters recursively by blending the colours of all pairs of adjacent vertices. Recursion repeats until a maximal homogeneous blend between a"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1702.00103","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":"2026-05-18T00:51:22Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"VQRun8SA6+p7EzmpyNxROb7Mr+W/cmSsiM38TOj5wtYuC1Z9qMjqfRbZFtEBEjtjkFDc3ytQqEPz23LLJm3eAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T23:14:02.272698Z"},"content_sha256":"7e2c4dbf3518b68934b083c327e296d63032949733cb760e4bb366ec01bd2b5f","schema_version":"1.0","event_id":"sha256:7e2c4dbf3518b68934b083c327e296d63032949733cb760e4bb366ec01bd2b5f"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/LD3IRQXD4TLUK2C7CMG2SVG4NF/bundle.json","state_url":"https://pith.science/pith/LD3IRQXD4TLUK2C7CMG2SVG4NF/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/LD3IRQXD4TLUK2C7CMG2SVG4NF/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":"2026-06-03T23:14:02Z","links":{"resolver":"https://pith.science/pith/LD3IRQXD4TLUK2C7CMG2SVG4NF","bundle":"https://pith.science/pith/LD3IRQXD4TLUK2C7CMG2SVG4NF/bundle.json","state":"https://pith.science/pith/LD3IRQXD4TLUK2C7CMG2SVG4NF/state.json","well_known_bundle":"https://pith.science/.well-known/pith/LD3IRQXD4TLUK2C7CMG2SVG4NF/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:LD3IRQXD4TLUK2C7CMG2SVG4NF","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":"39b81a6f1f216e953d93cc5c8368263d8ac9b8f0a3f090ab892844c4451cd4e8","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GM","submitted_at":"2017-02-01T01:57:25Z","title_canon_sha256":"89aef8e1010826b04be156761631ebb30c0d91da89ddf2ef8bea20ae211f67cc"},"schema_version":"1.0","source":{"id":"1702.00103","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1702.00103","created_at":"2026-05-18T00:51:22Z"},{"alias_kind":"arxiv_version","alias_value":"1702.00103v1","created_at":"2026-05-18T00:51:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1702.00103","created_at":"2026-05-18T00:51:22Z"},{"alias_kind":"pith_short_12","alias_value":"LD3IRQXD4TLU","created_at":"2026-05-18T12:31:28Z"},{"alias_kind":"pith_short_16","alias_value":"LD3IRQXD4TLUK2C7","created_at":"2026-05-18T12:31:28Z"},{"alias_kind":"pith_short_8","alias_value":"LD3IRQXD","created_at":"2026-05-18T12:31:28Z"}],"graph_snapshots":[{"event_id":"sha256:7e2c4dbf3518b68934b083c327e296d63032949733cb760e4bb366ec01bd2b5f","target":"graph","created_at":"2026-05-18T00:51:22Z","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 colour cluster $\\C =(\\mathcal{C}_1,\\mathcal{C}_2, \\mathcal{C}_3,\\dots,\\mathcal{C}_\\ell)$, $\\mathcal{C}_i$ is a colour class, and $|\\mathcal{C}_i|=r_i \\geq 1$, we investigate a simple connected graph structure $G^{\\C}$, which represents a graphical embodiment of the colour cluster such that the chromatic number $\\chi(G^{\\C})= \\ell,$ and the number of edges is a maximum, denoted $\\varepsilon^+(G^{\\C})$. We also extend the study by inducing new colour clusters recursively by blending the colours of all pairs of adjacent vertices. Recursion repeats until a maximal homogeneous blend between a","authors_text":"Johan Kok, Muhammad Kamran Jamil, Naduvath Sudev","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GM","submitted_at":"2017-02-01T01:57:25Z","title":"A note on chromatic blending of colour clusters"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1702.00103","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:f3e95e1e0f7a0a2950037e9b0cdd29d7de3ba348d91432f3b75025b930e10437","target":"record","created_at":"2026-05-18T00:51:22Z","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":"39b81a6f1f216e953d93cc5c8368263d8ac9b8f0a3f090ab892844c4451cd4e8","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GM","submitted_at":"2017-02-01T01:57:25Z","title_canon_sha256":"89aef8e1010826b04be156761631ebb30c0d91da89ddf2ef8bea20ae211f67cc"},"schema_version":"1.0","source":{"id":"1702.00103","kind":"arxiv","version":1}},"canonical_sha256":"58f688c2e3e4d745685f130da954dc6944c9ddafcbcce638912efa566886df17","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"58f688c2e3e4d745685f130da954dc6944c9ddafcbcce638912efa566886df17","first_computed_at":"2026-05-18T00:51:22.349084Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:51:22.349084Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"OxNYwDsOUntMvyA6/vaRbyQ9XHn1JXgDfSGyFllDKBpFiqRvf38tztZAIFM9+czUi1fTPtDcWiz4KYcrTtouBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:51:22.349875Z","signed_message":"canonical_sha256_bytes"},"source_id":"1702.00103","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f3e95e1e0f7a0a2950037e9b0cdd29d7de3ba348d91432f3b75025b930e10437","sha256:7e2c4dbf3518b68934b083c327e296d63032949733cb760e4bb366ec01bd2b5f"],"state_sha256":"a990f212fb671b63c554de48d1e59577239ad63093f8ee17b5ae1c4e2c5ea506"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"A6sD9eNZ0wKPE/wbY2W7Z+je5NZHAzMR/tzWV9b1WFDQdLoPbt0nVTmrRyCG5kpSLftPBrTbtjO8d8/WUpsPAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-03T23:14:02.274566Z","bundle_sha256":"a1de5958aefc12d7bd8db94c6bebda72e875bf1fd0326330980a1e81174b8296"}}