{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:U2FDWXFE3CYQKDJKF2ECQLKCLJ","short_pith_number":"pith:U2FDWXFE","canonical_record":{"source":{"id":"1404.6278","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-04-24T21:45:43Z","cross_cats_sorted":[],"title_canon_sha256":"2c3cf7363365c26314e92a785332dfdf9e73623336dfe9cc1a02af174efdb7b8","abstract_canon_sha256":"6cd5f83f6e6682dc1996ec6a1b6eedf3e84eed2df5a05ae3d9ba8c78222aa76a"},"schema_version":"1.0"},"canonical_sha256":"a68a3b5ca4d8b1050d2a2e88282d425a4894468736559925a8da3262e03aa547","source":{"kind":"arxiv","id":"1404.6278","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1404.6278","created_at":"2026-05-18T02:53:16Z"},{"alias_kind":"arxiv_version","alias_value":"1404.6278v1","created_at":"2026-05-18T02:53:16Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1404.6278","created_at":"2026-05-18T02:53:16Z"},{"alias_kind":"pith_short_12","alias_value":"U2FDWXFE3CYQ","created_at":"2026-05-18T12:28:52Z"},{"alias_kind":"pith_short_16","alias_value":"U2FDWXFE3CYQKDJK","created_at":"2026-05-18T12:28:52Z"},{"alias_kind":"pith_short_8","alias_value":"U2FDWXFE","created_at":"2026-05-18T12:28:52Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:U2FDWXFE3CYQKDJKF2ECQLKCLJ","target":"record","payload":{"canonical_record":{"source":{"id":"1404.6278","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-04-24T21:45:43Z","cross_cats_sorted":[],"title_canon_sha256":"2c3cf7363365c26314e92a785332dfdf9e73623336dfe9cc1a02af174efdb7b8","abstract_canon_sha256":"6cd5f83f6e6682dc1996ec6a1b6eedf3e84eed2df5a05ae3d9ba8c78222aa76a"},"schema_version":"1.0"},"canonical_sha256":"a68a3b5ca4d8b1050d2a2e88282d425a4894468736559925a8da3262e03aa547","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:53:16.971261Z","signature_b64":"b87JQMdi4C+8SmggeVs11Ut9WqlJTNp+/tm9hfGETpVByQg06OdhzzABBmDyzHB7AeUMYUpn6VwKC5ESeDB1AA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a68a3b5ca4d8b1050d2a2e88282d425a4894468736559925a8da3262e03aa547","last_reissued_at":"2026-05-18T02:53:16.970517Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:53:16.970517Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1404.6278","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":"2026-05-18T02:53:16Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"flDnRB4bzMBiPuTZcCl7Mwm/qIhr3Zvr+OKUmxyMi4unvHgteFX5C2H4DQgMlgA4NaWhdHim3KInmZjFs2qqAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T15:22:11.181070Z"},"content_sha256":"2472f1a415165d5201207a9441bceda57f9bf38678031f6104aad3846bc91afc","schema_version":"1.0","event_id":"sha256:2472f1a415165d5201207a9441bceda57f9bf38678031f6104aad3846bc91afc"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:U2FDWXFE3CYQKDJKF2ECQLKCLJ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On Coupon Colorings of Graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Bob Chen, Jacques Verstraete, Jeong Han Kim, Michael Tait","submitted_at":"2014-04-24T21:45:43Z","abstract_excerpt":"Let $G$ be a graph with no isolated vertices. A {\\em $k$-coupon coloring} of $G$ is an assignment of colors from $[k] := \\{1,2,\\dots,k\\}$ to the vertices of $G$ such that the neighborhood of every vertex of $G$ contains vertices of all colors from $[k]$. The maximum $k$ for which a $k$-coupon coloring exists is called the {\\em coupon coloring number} of $G$, and is denoted $\\chi_{c}(G)$. In this paper, we prove that every $d$-regular graph $G$ has $\\chi_{c}(G) \\geq (1 - o(1))d/\\log d$ as $d \\rightarrow \\infty$, and the proportion of $d$-regular graphs $G$ for which $\\chi_c(G) \\leq (1 + o(1))d/"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1404.6278","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":"2026-05-18T02:53:16Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"0Nr/0zivzac0+vwD2VdO9uuVi+LwFeBcLWCWiEiFRpzNtLyQV0w0PRtOrUoUidq0iPRdwpUFqX+iQntyCKcUDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T15:22:11.181769Z"},"content_sha256":"209c7b12119cf87316dc2f51dbdcf83dc53f56b424174a5ea0228905b246bccb","schema_version":"1.0","event_id":"sha256:209c7b12119cf87316dc2f51dbdcf83dc53f56b424174a5ea0228905b246bccb"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/U2FDWXFE3CYQKDJKF2ECQLKCLJ/bundle.json","state_url":"https://pith.science/pith/U2FDWXFE3CYQKDJKF2ECQLKCLJ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/U2FDWXFE3CYQKDJKF2ECQLKCLJ/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":"2026-05-28T15:22:11Z","links":{"resolver":"https://pith.science/pith/U2FDWXFE3CYQKDJKF2ECQLKCLJ","bundle":"https://pith.science/pith/U2FDWXFE3CYQKDJKF2ECQLKCLJ/bundle.json","state":"https://pith.science/pith/U2FDWXFE3CYQKDJKF2ECQLKCLJ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/U2FDWXFE3CYQKDJKF2ECQLKCLJ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:U2FDWXFE3CYQKDJKF2ECQLKCLJ","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":"6cd5f83f6e6682dc1996ec6a1b6eedf3e84eed2df5a05ae3d9ba8c78222aa76a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-04-24T21:45:43Z","title_canon_sha256":"2c3cf7363365c26314e92a785332dfdf9e73623336dfe9cc1a02af174efdb7b8"},"schema_version":"1.0","source":{"id":"1404.6278","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1404.6278","created_at":"2026-05-18T02:53:16Z"},{"alias_kind":"arxiv_version","alias_value":"1404.6278v1","created_at":"2026-05-18T02:53:16Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1404.6278","created_at":"2026-05-18T02:53:16Z"},{"alias_kind":"pith_short_12","alias_value":"U2FDWXFE3CYQ","created_at":"2026-05-18T12:28:52Z"},{"alias_kind":"pith_short_16","alias_value":"U2FDWXFE3CYQKDJK","created_at":"2026-05-18T12:28:52Z"},{"alias_kind":"pith_short_8","alias_value":"U2FDWXFE","created_at":"2026-05-18T12:28:52Z"}],"graph_snapshots":[{"event_id":"sha256:209c7b12119cf87316dc2f51dbdcf83dc53f56b424174a5ea0228905b246bccb","target":"graph","created_at":"2026-05-18T02:53:16Z","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 with no isolated vertices. A {\\em $k$-coupon coloring} of $G$ is an assignment of colors from $[k] := \\{1,2,\\dots,k\\}$ to the vertices of $G$ such that the neighborhood of every vertex of $G$ contains vertices of all colors from $[k]$. The maximum $k$ for which a $k$-coupon coloring exists is called the {\\em coupon coloring number} of $G$, and is denoted $\\chi_{c}(G)$. In this paper, we prove that every $d$-regular graph $G$ has $\\chi_{c}(G) \\geq (1 - o(1))d/\\log d$ as $d \\rightarrow \\infty$, and the proportion of $d$-regular graphs $G$ for which $\\chi_c(G) \\leq (1 + o(1))d/","authors_text":"Bob Chen, Jacques Verstraete, Jeong Han Kim, Michael Tait","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-04-24T21:45:43Z","title":"On Coupon Colorings of Graphs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1404.6278","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":"sha256:2472f1a415165d5201207a9441bceda57f9bf38678031f6104aad3846bc91afc","target":"record","created_at":"2026-05-18T02:53:16Z","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":"6cd5f83f6e6682dc1996ec6a1b6eedf3e84eed2df5a05ae3d9ba8c78222aa76a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-04-24T21:45:43Z","title_canon_sha256":"2c3cf7363365c26314e92a785332dfdf9e73623336dfe9cc1a02af174efdb7b8"},"schema_version":"1.0","source":{"id":"1404.6278","kind":"arxiv","version":1}},"canonical_sha256":"a68a3b5ca4d8b1050d2a2e88282d425a4894468736559925a8da3262e03aa547","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a68a3b5ca4d8b1050d2a2e88282d425a4894468736559925a8da3262e03aa547","first_computed_at":"2026-05-18T02:53:16.970517Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:53:16.970517Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"b87JQMdi4C+8SmggeVs11Ut9WqlJTNp+/tm9hfGETpVByQg06OdhzzABBmDyzHB7AeUMYUpn6VwKC5ESeDB1AA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:53:16.971261Z","signed_message":"canonical_sha256_bytes"},"source_id":"1404.6278","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2472f1a415165d5201207a9441bceda57f9bf38678031f6104aad3846bc91afc","sha256:209c7b12119cf87316dc2f51dbdcf83dc53f56b424174a5ea0228905b246bccb"],"state_sha256":"63efb43f644dd7c92ac7253bdde6257413fd6fdd84b1d14bbc18100dc8d4595f"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"KABc/6iWkIpWmEpYQN8J1z/42ZZDWMMYXWZEKVxeFXniq1d0QtzlmJLXfEKxLWQOUDFtczPSJuwGTIvwxr5HCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-28T15:22:11.185732Z","bundle_sha256":"55adb6fba55d2e3437621724724c9a774e688468a38b3393fc8464d7d2999cf0"}}