{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:PGXFYG66NEPIDMKY3NW4L76QES","short_pith_number":"pith:PGXFYG66","schema_version":"1.0","canonical_sha256":"79ae5c1bde691e81b158db6dc5ffd024b7007ffd5bef3cd1d19e001411c13601","source":{"kind":"arxiv","id":"1705.02097","version":1},"attestation_state":"computed","paper":{"title":"An Essay on Comp\\^onent\\u{a} Analysis of 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":"2017-05-01T15:11:56Z","abstract_excerpt":"In most studies related to colouring of graphs and perhaps in the study of other invariants and variants of graphs, the restrictions of non-triviality and connectedness are placed upon graphs. For the introduction to comp\\^{o}nent\\u{a} analysis, these restrictions are relaxed. In particular, this essay focuses on comp\\^{o}nent\\u{a} analysis in respect of the recently introduced $J$-colouring. The concept of $J^c$-rainbow connectivity is also introduced in this paper."},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1705.02097","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GM","submitted_at":"2017-05-01T15:11:56Z","cross_cats_sorted":[],"title_canon_sha256":"0afbca7fa66b4b620b86a14ccf307ad4420e9cc7679ea547b9c6e2319a5fec75","abstract_canon_sha256":"5e50fc2f0702e7dbd0972d4460980eb9def62410975e6c5bc50ea8432e58d947"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:45:00.635296Z","signature_b64":"W9U+YotvYNvaku1zFHHrog/Ol/V30urN1o3E9GXxKiOx9by9Np4Y8O9+RUkT97IQV5q8ByWPqUDeOtz9KBSMCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"79ae5c1bde691e81b158db6dc5ffd024b7007ffd5bef3cd1d19e001411c13601","last_reissued_at":"2026-05-18T00:45:00.634885Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:45:00.634885Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"An Essay on Comp\\^onent\\u{a} Analysis of 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":"2017-05-01T15:11:56Z","abstract_excerpt":"In most studies related to colouring of graphs and perhaps in the study of other invariants and variants of graphs, the restrictions of non-triviality and connectedness are placed upon graphs. For the introduction to comp\\^{o}nent\\u{a} analysis, these restrictions are relaxed. In particular, this essay focuses on comp\\^{o}nent\\u{a} analysis in respect of the recently introduced $J$-colouring. The concept of $J^c$-rainbow connectivity is also introduced in this paper."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1705.02097","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1705.02097","created_at":"2026-05-18T00:45:00.634946+00:00"},{"alias_kind":"arxiv_version","alias_value":"1705.02097v1","created_at":"2026-05-18T00:45:00.634946+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1705.02097","created_at":"2026-05-18T00:45:00.634946+00:00"},{"alias_kind":"pith_short_12","alias_value":"PGXFYG66NEPI","created_at":"2026-05-18T12:31:37.085036+00:00"},{"alias_kind":"pith_short_16","alias_value":"PGXFYG66NEPIDMKY","created_at":"2026-05-18T12:31:37.085036+00:00"},{"alias_kind":"pith_short_8","alias_value":"PGXFYG66","created_at":"2026-05-18T12:31:37.085036+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/PGXFYG66NEPIDMKY3NW4L76QES","json":"https://pith.science/pith/PGXFYG66NEPIDMKY3NW4L76QES.json","graph_json":"https://pith.science/api/pith-number/PGXFYG66NEPIDMKY3NW4L76QES/graph.json","events_json":"https://pith.science/api/pith-number/PGXFYG66NEPIDMKY3NW4L76QES/events.json","paper":"https://pith.science/paper/PGXFYG66"},"agent_actions":{"view_html":"https://pith.science/pith/PGXFYG66NEPIDMKY3NW4L76QES","download_json":"https://pith.science/pith/PGXFYG66NEPIDMKY3NW4L76QES.json","view_paper":"https://pith.science/paper/PGXFYG66","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1705.02097&json=true","fetch_graph":"https://pith.science/api/pith-number/PGXFYG66NEPIDMKY3NW4L76QES/graph.json","fetch_events":"https://pith.science/api/pith-number/PGXFYG66NEPIDMKY3NW4L76QES/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/PGXFYG66NEPIDMKY3NW4L76QES/action/timestamp_anchor","attest_storage":"https://pith.science/pith/PGXFYG66NEPIDMKY3NW4L76QES/action/storage_attestation","attest_author":"https://pith.science/pith/PGXFYG66NEPIDMKY3NW4L76QES/action/author_attestation","sign_citation":"https://pith.science/pith/PGXFYG66NEPIDMKY3NW4L76QES/action/citation_signature","submit_replication":"https://pith.science/pith/PGXFYG66NEPIDMKY3NW4L76QES/action/replication_record"}},"created_at":"2026-05-18T00:45:00.634946+00:00","updated_at":"2026-05-18T00:45:00.634946+00:00"}