Pith Number

pith:KXZTWQZP

pith:2007:KXZTWQZP7INFWJSXY3ZL7NFBD7

not attested not anchored not stored refs pending

Extremal problems on triangle areas in two and three dimensions

Adrian Dumitrescu, Csaba D. Toth, Micha Sharir

arxiv:0710.4109 v1 · 2007-10-22 · 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{KXZTWQZP7INFWJSXY3ZL7NFBD7}

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	2026-05-18T03:04:47.012876Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

55f33b432ffa1a5b2657c6f2bfb4a11fe1464e318046997b3da5a08c05a1ce39

Aliases

arxiv: 0710.4109 · arxiv_version: 0710.4109v1 · doi: 10.48550/arxiv.0710.4109 · pith_short_12: KXZTWQZP7INF · pith_short_16: KXZTWQZP7INFWJSX · pith_short_8: KXZTWQZP

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/KXZTWQZP7INFWJSXY3ZL7NFBD7 \
  | 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: 55f33b432ffa1a5b2657c6f2bfb4a11fe1464e318046997b3da5a08c05a1ce39

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "be1c0ac1a3ed9f58ee591b5b5aa41dd42a3b44ba48eb6288cdbf43a110d27173",
    "cross_cats_sorted": [],
    "license": "",
    "primary_cat": "math.CO",
    "submitted_at": "2007-10-22T17:12:08Z",
    "title_canon_sha256": "c37e2db77fd51ed20136df4d30b9f459f50650e5f04505c3a9882ffd67022095"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0710.4109",
    "kind": "arxiv",
    "version": 1
  }
}