Pith Number

pith:RFWYWJJO

pith:2026:RFWYWJJOMWPBDIOX2KJKVWGABO

not attested not anchored not stored refs pending

Toward a KKL Theorem for any HDX

Max Hopkins

arxiv:2606.29449 v1 · 2026-06-28 · math.CO · cs.CC · cs.DM

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{RFWYWJJOMWPBDIOX2KJKVWGABO}

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	2026-06-30T01:18:06.996144Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

896d8b252e659e11a1d7d292aad8c00b810bccfd8ba563509fd2425514952832

Aliases

arxiv: 2606.29449 · arxiv_version: 2606.29449v1 · doi: 10.48550/arxiv.2606.29449 · pith_short_12: RFWYWJJOMWPB · pith_short_16: RFWYWJJOMWPBDIOX · pith_short_8: RFWYWJJO

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/RFWYWJJOMWPBDIOX2KJKVWGABO \
  | 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: 896d8b252e659e11a1d7d292aad8c00b810bccfd8ba563509fd2425514952832

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "963bdc97713b73b7624bda20c9eb939ce9cd6ba8308dc5d8b192b401820ea387",
    "cross_cats_sorted": [
      "cs.CC",
      "cs.DM"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2026-06-28T15:13:41Z",
    "title_canon_sha256": "c702cc13b1e8a16795b9431f8d8f985ff2aec9000b45d3d8899954a6e0f3fd59"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2606.29449",
    "kind": "arxiv",
    "version": 1
  }
}