Pith Number

pith:OOJLCPLZ

pith:2025:OOJLCPLZLGSRWYNTBDRRT3TL4X

not attested not anchored not stored refs pending

Potential Theory and the Boundary of Combinatorial Graphs

Stefan Steinerberger

arxiv:2507.20833 v1 · 2025-07-28 · math.CA · math.AP · math.CO · math.PR

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{OOJLCPLZLGSRWYNTBDRRT3TL4X}

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	2026-07-05T11:44:26.723173Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

7392b13d7959a51b61b308e319ee6be5cfcc7cfdecb24d1f54850ed400c974be

Aliases

arxiv: 2507.20833 · arxiv_version: 2507.20833v1 · doi: 10.48550/arxiv.2507.20833 · pith_short_12: OOJLCPLZLGSR · pith_short_16: OOJLCPLZLGSRWYNT · pith_short_8: OOJLCPLZ

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/OOJLCPLZLGSRWYNTBDRRT3TL4X \
  | 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: 7392b13d7959a51b61b308e319ee6be5cfcc7cfdecb24d1f54850ed400c974be

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "737b8eaa4fde6454026324713dfbe83b02dba5bda1e6113c051602b944a6fc44",
    "cross_cats_sorted": [
      "math.AP",
      "math.CO",
      "math.PR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CA",
    "submitted_at": "2025-07-28T13:40:06Z",
    "title_canon_sha256": "c956c833bef69a87f7271d5074ea8e9c0424dc6a808b748b2c927f48ba44a19c"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2507.20833",
    "kind": "arxiv",
    "version": 1
  }
}