Pith Number

pith:6WH6Z3FR

pith:2026:6WH6Z3FRY7PUB7BP2VKTXXB7ID

not attested not anchored not stored refs pending

On the maximum density of $r$-graphs in which every $(r+1)$-set spans $0$ or $2$ edges

Dhruv Mubayi, Haoran Luo, Vishesh Jain

arxiv:2606.20367 v1 · 2026-06-18 · 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{6WH6Z3FRY7PUB7BP2VKTXXB7ID}

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	2026-06-19T16:13:10.178087Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

f58fececb1c7df40fc2fd5553bdc3f40d54b6f3213c57f17d1e66bbf96f13ad2

Aliases

arxiv: 2606.20367 · arxiv_version: 2606.20367v1 · doi: 10.48550/arxiv.2606.20367 · pith_short_12: 6WH6Z3FRY7PU · pith_short_16: 6WH6Z3FRY7PUB7BP · pith_short_8: 6WH6Z3FR

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/6WH6Z3FRY7PUB7BP2VKTXXB7ID \
  | 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: f58fececb1c7df40fc2fd5553bdc3f40d54b6f3213c57f17d1e66bbf96f13ad2

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "0798b02083bf6394a68accb0f9c71db9f377375b7f36b2f6a4ae01e364dfef44",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by-nc-sa/4.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2026-06-18T15:30:49Z",
    "title_canon_sha256": "71484471253a24c0f506939a77146668f2017fc311586b5a0f26414889ed7e04"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2606.20367",
    "kind": "arxiv",
    "version": 1
  }
}