Pith Number

pith:5NZMMZVC

pith:2017:5NZMMZVCJ57B2PI7JNBQ2SCNMD

not attested not anchored not stored refs pending

A discrete harmonic function bounded on a large portion of $\mathbb{Z}^2$ is constant

Alexander Logunov, Eugenia Malinnikova, Lev Buhovsky, Mikhail Sodin

arxiv:1712.07902 v1 · 2017-12-21 · math.CA · math.AP

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{5NZMMZVCJ57B2PI7JNBQ2SCNMD}

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	2026-05-18T00:27:29.402525Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

eb72c666a24f7e1d3d1f4b430d484d60f724f4721e4e87fdd4b66588d5d3ba2a

Aliases

arxiv: 1712.07902 · arxiv_version: 1712.07902v1 · doi: 10.48550/arxiv.1712.07902 · pith_short_12: 5NZMMZVCJ57B · pith_short_16: 5NZMMZVCJ57B2PI7 · pith_short_8: 5NZMMZVC

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/5NZMMZVCJ57B2PI7JNBQ2SCNMD \
  | 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: eb72c666a24f7e1d3d1f4b430d484d60f724f4721e4e87fdd4b66588d5d3ba2a

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "2abda8e6ebd6d08635b1fa49993c75232b1f92e9ffa5df63eece6ef84419eeb0",
    "cross_cats_sorted": [
      "math.AP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CA",
    "submitted_at": "2017-12-21T12:26:51Z",
    "title_canon_sha256": "e737cc8b1b9ebc531e7555b28a06d4ef1c1328812271fa981f08ed465d819a68"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1712.07902",
    "kind": "arxiv",
    "version": 1
  }
}