{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:ZCSCDH4JMULYNUAHJRYS5JNRXS","short_pith_number":"pith:ZCSCDH4J","canonical_record":{"source":{"id":"1804.00850","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-04-03T07:23:25Z","cross_cats_sorted":[],"title_canon_sha256":"1b4cd35e6def97d2a52f71913268bb99e0276f52295eeb65a12d695ed1c521b3","abstract_canon_sha256":"fd9eaa0d76331ae3b616fc8a58ac3aa510be462eb5f21d86843bf311facab025"},"schema_version":"1.0"},"canonical_sha256":"c8a4219f89651786d0074c712ea5b1bcb65efdfac3698d7ef21bc1fc55cb95fc","source":{"kind":"arxiv","id":"1804.00850","version":4},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1804.00850","created_at":"2026-05-17T23:56:05Z"},{"alias_kind":"arxiv_version","alias_value":"1804.00850v4","created_at":"2026-05-17T23:56:05Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1804.00850","created_at":"2026-05-17T23:56:05Z"},{"alias_kind":"pith_short_12","alias_value":"ZCSCDH4JMULY","created_at":"2026-05-18T12:33:04Z"},{"alias_kind":"pith_short_16","alias_value":"ZCSCDH4JMULYNUAH","created_at":"2026-05-18T12:33:04Z"},{"alias_kind":"pith_short_8","alias_value":"ZCSCDH4J","created_at":"2026-05-18T12:33:04Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:ZCSCDH4JMULYNUAHJRYS5JNRXS","target":"record","payload":{"canonical_record":{"source":{"id":"1804.00850","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-04-03T07:23:25Z","cross_cats_sorted":[],"title_canon_sha256":"1b4cd35e6def97d2a52f71913268bb99e0276f52295eeb65a12d695ed1c521b3","abstract_canon_sha256":"fd9eaa0d76331ae3b616fc8a58ac3aa510be462eb5f21d86843bf311facab025"},"schema_version":"1.0"},"canonical_sha256":"c8a4219f89651786d0074c712ea5b1bcb65efdfac3698d7ef21bc1fc55cb95fc","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:56:05.416789Z","signature_b64":"yhV5jzqi6ojHN2dNzHHJRGjtW4qE4G+mgEaAFAppDSbg+GvGWWHqeRvABpKdR/2HizbdYlfL9s65JL2WF9FzAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c8a4219f89651786d0074c712ea5b1bcb65efdfac3698d7ef21bc1fc55cb95fc","last_reissued_at":"2026-05-17T23:56:05.416140Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:56:05.416140Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1804.00850","source_version":4,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-17T23:56:05Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"jKIfTJeuLFzzgmK825gB1ngYiV7XUveanT3cnO1+800mhFUE72YpZAIf94D72sEfZBw5hPy8XFNNzU/JY2IjAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T17:32:22.169170Z"},"content_sha256":"63449e5d6819b9c53fe2d4272184c8b5536651e51b7c51bcd78cc04bd9c5ae9b","schema_version":"1.0","event_id":"sha256:63449e5d6819b9c53fe2d4272184c8b5536651e51b7c51bcd78cc04bd9c5ae9b"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:ZCSCDH4JMULYNUAHJRYS5JNRXS","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Boxicity, poset dimension, and excluded minors","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Louis Esperet, Veit Wiechert","submitted_at":"2018-04-03T07:23:25Z","abstract_excerpt":"In this short note, we relate the boxicity of graphs (and the dimension of posets) with their generalized coloring parameters. In particular, together with known estimates, our results imply that any graph with no $K_t$-minor can be represented as the intersection of $O(t^2\\log t)$ interval graphs (improving the previous bound of $O(t^4)$), and as the intersection of $\\tfrac{15}2 t^2$ circular-arc graphs."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1804.00850","kind":"arxiv","version":4},"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":"2026-05-17T23:56:05Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"0/ojvpHXnMX49hDehRRIktFphReZEtiVSOHI6pGrYr1BmKpouAg9eS9Lw00Kxtr5GYRZ/c+94cvr3Oxtc0r7Bg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T17:32:22.169542Z"},"content_sha256":"e0cfb7001fb6ec587ee63d5cbab36dec4acbbdb9b2066976d875b6a901a59f48","schema_version":"1.0","event_id":"sha256:e0cfb7001fb6ec587ee63d5cbab36dec4acbbdb9b2066976d875b6a901a59f48"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/ZCSCDH4JMULYNUAHJRYS5JNRXS/bundle.json","state_url":"https://pith.science/pith/ZCSCDH4JMULYNUAHJRYS5JNRXS/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/ZCSCDH4JMULYNUAHJRYS5JNRXS/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":"2026-06-01T17:32:22Z","links":{"resolver":"https://pith.science/pith/ZCSCDH4JMULYNUAHJRYS5JNRXS","bundle":"https://pith.science/pith/ZCSCDH4JMULYNUAHJRYS5JNRXS/bundle.json","state":"https://pith.science/pith/ZCSCDH4JMULYNUAHJRYS5JNRXS/state.json","well_known_bundle":"https://pith.science/.well-known/pith/ZCSCDH4JMULYNUAHJRYS5JNRXS/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:ZCSCDH4JMULYNUAHJRYS5JNRXS","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":"fd9eaa0d76331ae3b616fc8a58ac3aa510be462eb5f21d86843bf311facab025","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-04-03T07:23:25Z","title_canon_sha256":"1b4cd35e6def97d2a52f71913268bb99e0276f52295eeb65a12d695ed1c521b3"},"schema_version":"1.0","source":{"id":"1804.00850","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1804.00850","created_at":"2026-05-17T23:56:05Z"},{"alias_kind":"arxiv_version","alias_value":"1804.00850v4","created_at":"2026-05-17T23:56:05Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1804.00850","created_at":"2026-05-17T23:56:05Z"},{"alias_kind":"pith_short_12","alias_value":"ZCSCDH4JMULY","created_at":"2026-05-18T12:33:04Z"},{"alias_kind":"pith_short_16","alias_value":"ZCSCDH4JMULYNUAH","created_at":"2026-05-18T12:33:04Z"},{"alias_kind":"pith_short_8","alias_value":"ZCSCDH4J","created_at":"2026-05-18T12:33:04Z"}],"graph_snapshots":[{"event_id":"sha256:e0cfb7001fb6ec587ee63d5cbab36dec4acbbdb9b2066976d875b6a901a59f48","target":"graph","created_at":"2026-05-17T23:56:05Z","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":"In this short note, we relate the boxicity of graphs (and the dimension of posets) with their generalized coloring parameters. In particular, together with known estimates, our results imply that any graph with no $K_t$-minor can be represented as the intersection of $O(t^2\\log t)$ interval graphs (improving the previous bound of $O(t^4)$), and as the intersection of $\\tfrac{15}2 t^2$ circular-arc graphs.","authors_text":"Louis Esperet, Veit Wiechert","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-04-03T07:23:25Z","title":"Boxicity, poset dimension, and excluded minors"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1804.00850","kind":"arxiv","version":4},"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":"sha256:63449e5d6819b9c53fe2d4272184c8b5536651e51b7c51bcd78cc04bd9c5ae9b","target":"record","created_at":"2026-05-17T23:56:05Z","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":"fd9eaa0d76331ae3b616fc8a58ac3aa510be462eb5f21d86843bf311facab025","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-04-03T07:23:25Z","title_canon_sha256":"1b4cd35e6def97d2a52f71913268bb99e0276f52295eeb65a12d695ed1c521b3"},"schema_version":"1.0","source":{"id":"1804.00850","kind":"arxiv","version":4}},"canonical_sha256":"c8a4219f89651786d0074c712ea5b1bcb65efdfac3698d7ef21bc1fc55cb95fc","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c8a4219f89651786d0074c712ea5b1bcb65efdfac3698d7ef21bc1fc55cb95fc","first_computed_at":"2026-05-17T23:56:05.416140Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:56:05.416140Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"yhV5jzqi6ojHN2dNzHHJRGjtW4qE4G+mgEaAFAppDSbg+GvGWWHqeRvABpKdR/2HizbdYlfL9s65JL2WF9FzAQ==","signature_status":"signed_v1","signed_at":"2026-05-17T23:56:05.416789Z","signed_message":"canonical_sha256_bytes"},"source_id":"1804.00850","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:63449e5d6819b9c53fe2d4272184c8b5536651e51b7c51bcd78cc04bd9c5ae9b","sha256:e0cfb7001fb6ec587ee63d5cbab36dec4acbbdb9b2066976d875b6a901a59f48"],"state_sha256":"89b3617458bb5247cacc4eacb20a8c7614223471c981af558ae3d7c441841350"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"K7CD246Uu9R1NTi8clBA6a40dyIcmS3KmQScc6BOm42SF5YgVPsJ7WhgmjGL4dknOTEgG7lLiiapu8gpIbE3Ag==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-01T17:32:22.171484Z","bundle_sha256":"eef30224f4fd3990c911dd838972bfb251ef15050ca10396664defe06079f8d2"}}