Pith Number

pith:PKPF52N6

pith:2010:PKPF52N6BDVX3EHDINGF55ZMBE

not attested not anchored not stored refs pending

The 2-Center Problem in Three Dimensions

Micha Sharir, Pankaj K. Agarwal, Rinat Ben Avraham

arxiv:1012.2694 v1 · 2010-12-13 · cs.CG

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{PKPF52N6BDVX3EHDINGF55ZMBE}

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	2026-05-18T04:33:27.987668Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

7a9e5ee9be08eb7d90e3434c5ef72c091ea5a88cefe171657a1e939fb6126725

Aliases

arxiv: 1012.2694 · arxiv_version: 1012.2694v1 · doi: 10.48550/arxiv.1012.2694 · pith_short_12: PKPF52N6BDVX · pith_short_16: PKPF52N6BDVX3EHD · pith_short_8: PKPF52N6

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/PKPF52N6BDVX3EHDINGF55ZMBE \
  | 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: 7a9e5ee9be08eb7d90e3434c5ef72c091ea5a88cefe171657a1e939fb6126725

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "76f3820cda87ac168d50960a34881d2864ed0c87545facf39383860f58f2df98",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "cs.CG",
    "submitted_at": "2010-12-13T11:17:35Z",
    "title_canon_sha256": "22e55dab8ef38ed5121188fe8506865c86d6a26280eabd2617633402ed6e9c37"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1012.2694",
    "kind": "arxiv",
    "version": 1
  }
}