{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:TLUVJ54EXAEFJE7SHM6PDHJUBJ","short_pith_number":"pith:TLUVJ54E","canonical_record":{"source":{"id":"1708.04406","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-08-15T06:02:54Z","cross_cats_sorted":[],"title_canon_sha256":"25a7687f2f6db3bc2a0024497ea18a693d3fe981894596f87dd23f7eb3ff7992","abstract_canon_sha256":"91079de6a0f56a6d66b5469ef6b291f4ac44e94249f5fc925c6462661028ba69"},"schema_version":"1.0"},"canonical_sha256":"9ae954f784b8085493f23b3cf19d340a5120b06c15cf5374353133dd7830f86d","source":{"kind":"arxiv","id":"1708.04406","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1708.04406","created_at":"2026-05-18T00:37:59Z"},{"alias_kind":"arxiv_version","alias_value":"1708.04406v1","created_at":"2026-05-18T00:37:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1708.04406","created_at":"2026-05-18T00:37:59Z"},{"alias_kind":"pith_short_12","alias_value":"TLUVJ54EXAEF","created_at":"2026-05-18T12:31:46Z"},{"alias_kind":"pith_short_16","alias_value":"TLUVJ54EXAEFJE7S","created_at":"2026-05-18T12:31:46Z"},{"alias_kind":"pith_short_8","alias_value":"TLUVJ54E","created_at":"2026-05-18T12:31:46Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:TLUVJ54EXAEFJE7SHM6PDHJUBJ","target":"record","payload":{"canonical_record":{"source":{"id":"1708.04406","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-08-15T06:02:54Z","cross_cats_sorted":[],"title_canon_sha256":"25a7687f2f6db3bc2a0024497ea18a693d3fe981894596f87dd23f7eb3ff7992","abstract_canon_sha256":"91079de6a0f56a6d66b5469ef6b291f4ac44e94249f5fc925c6462661028ba69"},"schema_version":"1.0"},"canonical_sha256":"9ae954f784b8085493f23b3cf19d340a5120b06c15cf5374353133dd7830f86d","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:37:59.397345Z","signature_b64":"1jaNJQP9o3o/QzJkPwbFnvk7NGkqZFl65SbIvMX4VngsEvKTsm2KO/QqKKMFMMoTC12vPWHJxwC+RV+C1GLeCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9ae954f784b8085493f23b3cf19d340a5120b06c15cf5374353133dd7830f86d","last_reissued_at":"2026-05-18T00:37:59.396846Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:37:59.396846Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1708.04406","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":"2026-05-18T00:37:59Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"V6VlpOW9lAPnzHdn9IRhdBHVb9rI+PiAqHZKoDLDvUqssMWmmklONm8BGU+9E7I7wQmLVTrO0Z51H2yyEcgeAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T13:07:38.369569Z"},"content_sha256":"2fe7d1b59d450f73c48179ab27692796e1cb5d0f5a45cfae0585a77b6660ef37","schema_version":"1.0","event_id":"sha256:2fe7d1b59d450f73c48179ab27692796e1cb5d0f5a45cfae0585a77b6660ef37"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:TLUVJ54EXAEFJE7SHM6PDHJUBJ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The square of a planar cubic graph is $7$-colorable","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Carsten Thomassen","submitted_at":"2017-08-15T06:02:54Z","abstract_excerpt":"We prove the conjecture made by G.Wegner in 1977 that the square of every planar, cubic graph is $7$-colorable. Here, $7$ cannot be replaced by $6$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1708.04406","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":"2026-05-18T00:37:59Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"HFxbm027ch/wCse7zP9ktXikXV7DiBSklGwUs9FDCKhoAWgD3XSSAg3/RXDIUE3qQRuA49mYuaeT4bRmatyZDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T13:07:38.369914Z"},"content_sha256":"79164729bf97475029903a1953242c8967c48f2775032a4fb3b05cd4cd473da8","schema_version":"1.0","event_id":"sha256:79164729bf97475029903a1953242c8967c48f2775032a4fb3b05cd4cd473da8"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/TLUVJ54EXAEFJE7SHM6PDHJUBJ/bundle.json","state_url":"https://pith.science/pith/TLUVJ54EXAEFJE7SHM6PDHJUBJ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/TLUVJ54EXAEFJE7SHM6PDHJUBJ/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":"2026-06-03T13:07:38Z","links":{"resolver":"https://pith.science/pith/TLUVJ54EXAEFJE7SHM6PDHJUBJ","bundle":"https://pith.science/pith/TLUVJ54EXAEFJE7SHM6PDHJUBJ/bundle.json","state":"https://pith.science/pith/TLUVJ54EXAEFJE7SHM6PDHJUBJ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/TLUVJ54EXAEFJE7SHM6PDHJUBJ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:TLUVJ54EXAEFJE7SHM6PDHJUBJ","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":"91079de6a0f56a6d66b5469ef6b291f4ac44e94249f5fc925c6462661028ba69","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-08-15T06:02:54Z","title_canon_sha256":"25a7687f2f6db3bc2a0024497ea18a693d3fe981894596f87dd23f7eb3ff7992"},"schema_version":"1.0","source":{"id":"1708.04406","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1708.04406","created_at":"2026-05-18T00:37:59Z"},{"alias_kind":"arxiv_version","alias_value":"1708.04406v1","created_at":"2026-05-18T00:37:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1708.04406","created_at":"2026-05-18T00:37:59Z"},{"alias_kind":"pith_short_12","alias_value":"TLUVJ54EXAEF","created_at":"2026-05-18T12:31:46Z"},{"alias_kind":"pith_short_16","alias_value":"TLUVJ54EXAEFJE7S","created_at":"2026-05-18T12:31:46Z"},{"alias_kind":"pith_short_8","alias_value":"TLUVJ54E","created_at":"2026-05-18T12:31:46Z"}],"graph_snapshots":[{"event_id":"sha256:79164729bf97475029903a1953242c8967c48f2775032a4fb3b05cd4cd473da8","target":"graph","created_at":"2026-05-18T00:37:59Z","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":"We prove the conjecture made by G.Wegner in 1977 that the square of every planar, cubic graph is $7$-colorable. Here, $7$ cannot be replaced by $6$.","authors_text":"Carsten Thomassen","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-08-15T06:02:54Z","title":"The square of a planar cubic graph is $7$-colorable"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1708.04406","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":"sha256:2fe7d1b59d450f73c48179ab27692796e1cb5d0f5a45cfae0585a77b6660ef37","target":"record","created_at":"2026-05-18T00:37:59Z","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":"91079de6a0f56a6d66b5469ef6b291f4ac44e94249f5fc925c6462661028ba69","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-08-15T06:02:54Z","title_canon_sha256":"25a7687f2f6db3bc2a0024497ea18a693d3fe981894596f87dd23f7eb3ff7992"},"schema_version":"1.0","source":{"id":"1708.04406","kind":"arxiv","version":1}},"canonical_sha256":"9ae954f784b8085493f23b3cf19d340a5120b06c15cf5374353133dd7830f86d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9ae954f784b8085493f23b3cf19d340a5120b06c15cf5374353133dd7830f86d","first_computed_at":"2026-05-18T00:37:59.396846Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:37:59.396846Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"1jaNJQP9o3o/QzJkPwbFnvk7NGkqZFl65SbIvMX4VngsEvKTsm2KO/QqKKMFMMoTC12vPWHJxwC+RV+C1GLeCw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:37:59.397345Z","signed_message":"canonical_sha256_bytes"},"source_id":"1708.04406","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2fe7d1b59d450f73c48179ab27692796e1cb5d0f5a45cfae0585a77b6660ef37","sha256:79164729bf97475029903a1953242c8967c48f2775032a4fb3b05cd4cd473da8"],"state_sha256":"dede0d1be3a89b9b4f1f770ef1e270bc3b4d1e5aa5ae4c0dbbecfe0f58b2bc9b"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"OksZPx/uLafFXHiQ66nxomIe1hBnlWQK5w6lWeW/hQya8SbCSPnGPb42UpwxpS8m1cSdia4puBBbHl7O3bWiDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-03T13:07:38.371935Z","bundle_sha256":"a6accb1f178615b7c6e2bb370e2fa05e586f9bee1d82a75b39560df28da453c2"}}