Pith Number

pith:O7OQXCVK

pith:2026:O7OQXCVKRENID3GNH6O5O2K3UP

not attested not anchored not stored refs pending

Minimizing clusters with prescribed asymptotic geometry

Anna Skorobogatova, Michael Novack, Robin Neumayer

arxiv:2606.07468 v1 · 2026-06-05 · math.AP · math.DG

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{O7OQXCVKRENID3GNH6O5O2K3UP}

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	2026-06-08T01:05:28.886217Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

77dd0b8aaa891a81eccd3f9dd7695ba3e8c8f4ea06853f2b7c31e59830bb3708

Aliases

arxiv: 2606.07468 · arxiv_version: 2606.07468v1 · doi: 10.48550/arxiv.2606.07468 · pith_short_12: O7OQXCVKRENI · pith_short_16: O7OQXCVKRENID3GN · pith_short_8: O7OQXCVK

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/O7OQXCVKRENID3GNH6O5O2K3UP \
  | 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: 77dd0b8aaa891a81eccd3f9dd7695ba3e8c8f4ea06853f2b7c31e59830bb3708

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "ec468963ab97ab0d087100b54450945cc9de1e580d11011acd0a3ae14d72fa6c",
    "cross_cats_sorted": [
      "math.DG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2026-06-05T17:21:08Z",
    "title_canon_sha256": "f48188fbef35d5d78d3136e26369b1dfc1bd3a76a9ae412bb48947f22053416d"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2606.07468",
    "kind": "arxiv",
    "version": 1
  }
}