Pith Number

pith:PQH2TADW

pith:2026:PQH2TADWI6Y6WCXUPXW7S4YKSG

not attested not anchored not stored refs pending

Minimum enclosing Bregman balls made easy

Frank Nielsen

arxiv:2607.24197 v1 · 2026-07-27 · cs.IT · cs.CG · math.IT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{PQH2TADWI6Y6WCXUPXW7S4YKSG}

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	2026-07-28T02:23:50.369185Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

7c0fa9807647b1eb0af47dedf9730a91b5b2cc53ac4d0d8a5f1bf5956bb461eb

Aliases

arxiv: 2607.24197 · arxiv_version: 2607.24197v1 · doi: 10.48550/arxiv.2607.24197 · pith_short_12: PQH2TADWI6Y6 · pith_short_16: PQH2TADWI6Y6WCXU · pith_short_8: PQH2TADW

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/PQH2TADWI6Y6WCXUPXW7S4YKSG \
  | 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: 7c0fa9807647b1eb0af47dedf9730a91b5b2cc53ac4d0d8a5f1bf5956bb461eb

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "3a5f0d4648d002de6f66ce4f55b2c219af10cb17db9cbaa648acaaae7cbf148a",
    "cross_cats_sorted": [
      "cs.CG",
      "math.IT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "cs.IT",
    "submitted_at": "2026-07-27T09:18:47Z",
    "title_canon_sha256": "08eb90a356511cf1fd31a2e2dc70f86c8ba8d9048b15813464d8952b5db7bbb7"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2607.24197",
    "kind": "arxiv",
    "version": 1
  }
}