Pith Number

pith:OO7XAJ2L

pith:2015:OO7XAJ2LNZNM4UPIO6JCZ7KEHH

not attested not anchored not stored refs pending

On the number of unit-area triangles spanned by convex grids in the plane

Ilya D. Shkredov, Micha Sharir, Orit E. Raz

arxiv:1504.06989 v1 · 2015-04-27 · 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{OO7XAJ2LNZNM4UPIO6JCZ7KEHH}

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	2026-05-18T02:17:43.956292Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

73bf70274b6e5ace51e877922cfd4439ce3190ded6fb320261e9b39ee3b9ece7

Aliases

arxiv: 1504.06989 · arxiv_version: 1504.06989v1 · doi: 10.48550/arxiv.1504.06989 · pith_short_12: OO7XAJ2LNZNM · pith_short_16: OO7XAJ2LNZNM4UPI · pith_short_8: OO7XAJ2L

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/OO7XAJ2LNZNM4UPIO6JCZ7KEHH \
  | 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: 73bf70274b6e5ace51e877922cfd4439ce3190ded6fb320261e9b39ee3b9ece7

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "a3469c0c7e44ab89c662b6853a21146cea76984cdf4ed69026d93422d975770a",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2015-04-27T09:25:59Z",
    "title_canon_sha256": "a3d975ce476513708cec3a89655ca807ace161619d73d3e6530bfa32136155a1"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1504.06989",
    "kind": "arxiv",
    "version": 1
  }
}