{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:NH7T2PWXVRC4KQGR5WD6EWYP46","short_pith_number":"pith:NH7T2PWX","canonical_record":{"source":{"id":"1608.02332","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-08-08T06:38:10Z","cross_cats_sorted":[],"title_canon_sha256":"029d42d0bbf7354e34e8d8c9ee12cec2b969cb1da24d940b3ea1eca43d711c18","abstract_canon_sha256":"75ba1af91d1a1394a7adbb623b587e3ae54dfe8d8da09c82150aeeaf6b56f381"},"schema_version":"1.0"},"canonical_sha256":"69ff3d3ed7ac45c540d1ed87e25b0fe79e56ed8972c1fd16a6099db0f2c15e20","source":{"kind":"arxiv","id":"1608.02332","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1608.02332","created_at":"2026-05-18T01:09:40Z"},{"alias_kind":"arxiv_version","alias_value":"1608.02332v1","created_at":"2026-05-18T01:09:40Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1608.02332","created_at":"2026-05-18T01:09:40Z"},{"alias_kind":"pith_short_12","alias_value":"NH7T2PWXVRC4","created_at":"2026-05-18T12:30:32Z"},{"alias_kind":"pith_short_16","alias_value":"NH7T2PWXVRC4KQGR","created_at":"2026-05-18T12:30:32Z"},{"alias_kind":"pith_short_8","alias_value":"NH7T2PWX","created_at":"2026-05-18T12:30:32Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:NH7T2PWXVRC4KQGR5WD6EWYP46","target":"record","payload":{"canonical_record":{"source":{"id":"1608.02332","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-08-08T06:38:10Z","cross_cats_sorted":[],"title_canon_sha256":"029d42d0bbf7354e34e8d8c9ee12cec2b969cb1da24d940b3ea1eca43d711c18","abstract_canon_sha256":"75ba1af91d1a1394a7adbb623b587e3ae54dfe8d8da09c82150aeeaf6b56f381"},"schema_version":"1.0"},"canonical_sha256":"69ff3d3ed7ac45c540d1ed87e25b0fe79e56ed8972c1fd16a6099db0f2c15e20","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:09:40.456505Z","signature_b64":"5sXt9/FsaWZYi7s3DfiFMXqnMKlgovnnfj4lNU8bnoLFFLQSih64nazgoq7e5ESS+tkXpGImA4lnB4N3iP6bCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"69ff3d3ed7ac45c540d1ed87e25b0fe79e56ed8972c1fd16a6099db0f2c15e20","last_reissued_at":"2026-05-18T01:09:40.456100Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:09:40.456100Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1608.02332","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":"2026-05-18T01:09:40Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"vk6rj1KwX4h0dAkAu5yjYRTmaQQ9S+LFD7egyEmiZS5OSRwMD65vzl2qYK+kIIH6Hn2iks9fMQXl2t/QQwe0Dg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-22T20:56:15.671692Z"},"content_sha256":"d5e3382f1425a7db8c2c29b77177ef50d230e753eccd7e423cb9cc12122f02ce","schema_version":"1.0","event_id":"sha256:d5e3382f1425a7db8c2c29b77177ef50d230e753eccd7e423cb9cc12122f02ce"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:NH7T2PWXVRC4KQGR5WD6EWYP46","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Threshold Colorings of Prisms and the Petersen Graph","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Gasper Fijavz, Matthias Kriesell","submitted_at":"2016-08-08T06:38:10Z","abstract_excerpt":"Let $G$ be a graph, $r \\geq t$ integers, and $N \\subseteq E(G)$. An $(r,t)$-threshold-coloring of $G$ with respect to $N$ is a mapping $c: V(G) \\rightarrow \\{0,\\ldots,r-1\\}$ such that $|c(u)-c(v)| \\leq t$ for every $uv \\in N$ and $|c(u)-c(v)|>t$ for every $uv \\in E(G) \\setminus N$. A graph is total threshold colorable if there exist integers $r,t$ such that for every $N \\subseteq E(G)$, $G$ admits an $(r,t)$-threshold-coloring with respect to $N$. We show that every prism is total threshold colorable, and that the Petersen graph is total threshold colorable. In contrast to this fact we show th"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1608.02332","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":"2026-05-18T01:09:40Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Sk14ScnxY1RcXCI14kz68+4D6v6mExoFecXzafC6dEE1iU0VDJDBmA2Ls0Mk7yqcUmCbv4/tWmlZJmSaFU0vAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-22T20:56:15.672576Z"},"content_sha256":"166ead58dd5673efbf4c4ebf3a64c4966dd01de6c92b69bf0cda0a98dce6f774","schema_version":"1.0","event_id":"sha256:166ead58dd5673efbf4c4ebf3a64c4966dd01de6c92b69bf0cda0a98dce6f774"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/NH7T2PWXVRC4KQGR5WD6EWYP46/bundle.json","state_url":"https://pith.science/pith/NH7T2PWXVRC4KQGR5WD6EWYP46/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/NH7T2PWXVRC4KQGR5WD6EWYP46/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":"2026-06-22T20:56:15Z","links":{"resolver":"https://pith.science/pith/NH7T2PWXVRC4KQGR5WD6EWYP46","bundle":"https://pith.science/pith/NH7T2PWXVRC4KQGR5WD6EWYP46/bundle.json","state":"https://pith.science/pith/NH7T2PWXVRC4KQGR5WD6EWYP46/state.json","well_known_bundle":"https://pith.science/.well-known/pith/NH7T2PWXVRC4KQGR5WD6EWYP46/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:NH7T2PWXVRC4KQGR5WD6EWYP46","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":"75ba1af91d1a1394a7adbb623b587e3ae54dfe8d8da09c82150aeeaf6b56f381","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-08-08T06:38:10Z","title_canon_sha256":"029d42d0bbf7354e34e8d8c9ee12cec2b969cb1da24d940b3ea1eca43d711c18"},"schema_version":"1.0","source":{"id":"1608.02332","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1608.02332","created_at":"2026-05-18T01:09:40Z"},{"alias_kind":"arxiv_version","alias_value":"1608.02332v1","created_at":"2026-05-18T01:09:40Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1608.02332","created_at":"2026-05-18T01:09:40Z"},{"alias_kind":"pith_short_12","alias_value":"NH7T2PWXVRC4","created_at":"2026-05-18T12:30:32Z"},{"alias_kind":"pith_short_16","alias_value":"NH7T2PWXVRC4KQGR","created_at":"2026-05-18T12:30:32Z"},{"alias_kind":"pith_short_8","alias_value":"NH7T2PWX","created_at":"2026-05-18T12:30:32Z"}],"graph_snapshots":[{"event_id":"sha256:166ead58dd5673efbf4c4ebf3a64c4966dd01de6c92b69bf0cda0a98dce6f774","target":"graph","created_at":"2026-05-18T01:09:40Z","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":"Let $G$ be a graph, $r \\geq t$ integers, and $N \\subseteq E(G)$. An $(r,t)$-threshold-coloring of $G$ with respect to $N$ is a mapping $c: V(G) \\rightarrow \\{0,\\ldots,r-1\\}$ such that $|c(u)-c(v)| \\leq t$ for every $uv \\in N$ and $|c(u)-c(v)|>t$ for every $uv \\in E(G) \\setminus N$. A graph is total threshold colorable if there exist integers $r,t$ such that for every $N \\subseteq E(G)$, $G$ admits an $(r,t)$-threshold-coloring with respect to $N$. We show that every prism is total threshold colorable, and that the Petersen graph is total threshold colorable. In contrast to this fact we show th","authors_text":"Gasper Fijavz, Matthias Kriesell","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-08-08T06:38:10Z","title":"Threshold Colorings of Prisms and the Petersen Graph"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1608.02332","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:d5e3382f1425a7db8c2c29b77177ef50d230e753eccd7e423cb9cc12122f02ce","target":"record","created_at":"2026-05-18T01:09:40Z","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":"75ba1af91d1a1394a7adbb623b587e3ae54dfe8d8da09c82150aeeaf6b56f381","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-08-08T06:38:10Z","title_canon_sha256":"029d42d0bbf7354e34e8d8c9ee12cec2b969cb1da24d940b3ea1eca43d711c18"},"schema_version":"1.0","source":{"id":"1608.02332","kind":"arxiv","version":1}},"canonical_sha256":"69ff3d3ed7ac45c540d1ed87e25b0fe79e56ed8972c1fd16a6099db0f2c15e20","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"69ff3d3ed7ac45c540d1ed87e25b0fe79e56ed8972c1fd16a6099db0f2c15e20","first_computed_at":"2026-05-18T01:09:40.456100Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:09:40.456100Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"5sXt9/FsaWZYi7s3DfiFMXqnMKlgovnnfj4lNU8bnoLFFLQSih64nazgoq7e5ESS+tkXpGImA4lnB4N3iP6bCg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:09:40.456505Z","signed_message":"canonical_sha256_bytes"},"source_id":"1608.02332","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d5e3382f1425a7db8c2c29b77177ef50d230e753eccd7e423cb9cc12122f02ce","sha256:166ead58dd5673efbf4c4ebf3a64c4966dd01de6c92b69bf0cda0a98dce6f774"],"state_sha256":"c29d1b9fe8dcd2c5e9deb5c65515e8703982c8c87f8962e8d9415e69acae5779"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"UQwXRmRtf69zk9bWtix8dGaryFD9u+6s2FmSjSy929PpjVZrqrSOYyv//XKkCcgUlJo1Cf4/TXCXQco+cOAdAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-22T20:56:15.674559Z","bundle_sha256":"e295c4f61b4c79b1f56d7073e795b1d8d337893d15da0971b864e81176fdfd32"}}