Pith Number

pith:OG5IEDGZ

pith:2026:OG5IEDGZ5W4FJ5QLPCJXCPDUCE

not attested not anchored not stored refs pending

Improved bounds for lines and $1$-separated sets in Euclidean Ramsey theory

Gabriel Currier, Jiaming Zhang, Param Mody, Zehan Xie

arxiv:2606.17194 v1 · 2026-06-15 · math.CO

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{OG5IEDGZ5W4FJ5QLPCJXCPDUCE}

Prints a linked badge after your title and injects PDF metadata. Compiles on arXiv. Learn more · Embed verified badge

Record completeness

1 Bitcoin timestamp

2 Internet Archive

3 Author claim open · sign in to claim

4 Citations open

5 Replications open

✓ Portable graph bundle live · download bundle · merged state

The bundle contains the canonical record plus signed events. A mirror can host it anywhere and recompute the same current state with the deterministic merge algorithm.

Receipt and verification

First computed	2026-06-19T16:10:05.574600Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

71ba820cd9edb854f60b7893713c74113334cdfce98f8733cf04f92b45f67c02

Aliases

arxiv: 2606.17194 · arxiv_version: 2606.17194v1 · doi: 10.48550/arxiv.2606.17194 · pith_short_12: OG5IEDGZ5W4F · pith_short_16: OG5IEDGZ5W4FJ5QL · pith_short_8: OG5IEDGZ

Agent API

Resolver JSON Graph JSON Events JSON Schema Signing key

Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/OG5IEDGZ5W4FJ5QLPCJXCPDUCE \
  | jq -c '.canonical_record' \
  | python3 -c "import sys,json,hashlib; b=json.dumps(json.loads(sys.stdin.read()), sort_keys=True, separators=(',',':'), ensure_ascii=False).encode(); print(hashlib.sha256(b).hexdigest())"
# expect: 71ba820cd9edb854f60b7893713c74113334cdfce98f8733cf04f92b45f67c02

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "dd6beb46b415746cf89f223a55e7c9c78628d81195283c541fa7a650ffa4222a",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2026-06-15T18:34:02Z",
    "title_canon_sha256": "244cc56b6cd9dfc73ed0e0ef43271090b675b48cacd293fa618b43910c16b15b"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2606.17194",
    "kind": "arxiv",
    "version": 1
  }
}