{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:DSJPPPU3NFI6Q7IJUT5NKCGITI","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":"7c3327dbb2af2f2304d2bda71f7377306b8b2fba6cf9404f9ebd6010644d2167","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-01-05T15:51:43Z","title_canon_sha256":"17bcd32b57bc4cf2ef22dbec5a481075e578e797a7f2b674a8d7624b6a119d13"},"schema_version":"1.0","source":{"id":"1801.01802","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1801.01802","created_at":"2026-05-18T00:26:40Z"},{"alias_kind":"arxiv_version","alias_value":"1801.01802v1","created_at":"2026-05-18T00:26:40Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1801.01802","created_at":"2026-05-18T00:26:40Z"},{"alias_kind":"pith_short_12","alias_value":"DSJPPPU3NFI6","created_at":"2026-05-18T12:32:19Z"},{"alias_kind":"pith_short_16","alias_value":"DSJPPPU3NFI6Q7IJ","created_at":"2026-05-18T12:32:19Z"},{"alias_kind":"pith_short_8","alias_value":"DSJPPPU3","created_at":"2026-05-18T12:32:19Z"}],"graph_snapshots":[{"event_id":"sha256:3a7890cb42b8fd3f0e4115c76fa8c0a24c26078b3c3b6813bcfaed2738172e01","target":"graph","created_at":"2026-05-18T00:26:40Z","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":"A neighborhood-prime labeling of a graph is a variation of a prime labeling in which the vertices are assigned labels from $1$ to $|V(G)|$ such that the $\\gcd$ of the labels in the neighborhood of each non-degree $1$ vertex is equal to $1$. In this paper, we examine neighborhood-prime labelings of several classes of graphs such as polygonal snakes and books, with a focus on trees including caterpillars, spiders, and firecrackers.","authors_text":"Malori Cloys, N. Bradley Fox","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-01-05T15:51:43Z","title":"Neighborhood-Prime Labelings of Trees and Other Classes of Graphs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1801.01802","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":"sha256:9ed4f168429921dca10fef631307bba3fe791e8af1d7592b5c6d2e7b50546cd5","target":"record","created_at":"2026-05-18T00:26:40Z","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":"7c3327dbb2af2f2304d2bda71f7377306b8b2fba6cf9404f9ebd6010644d2167","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-01-05T15:51:43Z","title_canon_sha256":"17bcd32b57bc4cf2ef22dbec5a481075e578e797a7f2b674a8d7624b6a119d13"},"schema_version":"1.0","source":{"id":"1801.01802","kind":"arxiv","version":1}},"canonical_sha256":"1c92f7be9b6951e87d09a4fad508c89a2b58c4f90f036997c629087f1c1bf4ed","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1c92f7be9b6951e87d09a4fad508c89a2b58c4f90f036997c629087f1c1bf4ed","first_computed_at":"2026-05-18T00:26:40.945391Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:26:40.945391Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Fm7Dv9Ptl0jI/Cr4QCMAQme3l6h8b5cTvAVe3F/2nrb0l4EzWXMEm8nfGwK72SUdwY5vHVQZqUCIZCg6ocHdBg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:26:40.946003Z","signed_message":"canonical_sha256_bytes"},"source_id":"1801.01802","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9ed4f168429921dca10fef631307bba3fe791e8af1d7592b5c6d2e7b50546cd5","sha256:3a7890cb42b8fd3f0e4115c76fa8c0a24c26078b3c3b6813bcfaed2738172e01"],"state_sha256":"55f3e08bc596b198e2231e0c059bbe8571f4a9356ca6c6f03cb6210307ac3172"}