Pith Number

pith:5EWN4O2X

pith:2013:5EWN4O2XPRKXPWAH2DG5XIKAOS

not attested not anchored not stored refs pending

On harmonic functions and the linear-growth case of Gromov's theorem

Matthew Tointon

arxiv:1301.1566 v3 · 2013-01-08 · math.GR · math.CO · math.MG

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{5EWN4O2XPRKXPWAH2DG5XIKAOS}

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	2026-05-18T03:06:51.673379Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e92cde3b577c5577d807d0cddba14074a512d9cc1abce6b6d1a00c3ec6786176

Aliases

arxiv: 1301.1566 · arxiv_version: 1301.1566v3 · doi: 10.48550/arxiv.1301.1566 · pith_short_12: 5EWN4O2XPRKX · pith_short_16: 5EWN4O2XPRKXPWAH · pith_short_8: 5EWN4O2X

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/5EWN4O2XPRKXPWAH2DG5XIKAOS \
  | 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: e92cde3b577c5577d807d0cddba14074a512d9cc1abce6b6d1a00c3ec6786176

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "098b757038fac33f77e54e1234b8c88d653c9706fba4e1df88c248e2056c6fb5",
    "cross_cats_sorted": [
      "math.CO",
      "math.MG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2013-01-08T15:40:52Z",
    "title_canon_sha256": "90eb2696b67df2e5226983b158ee0883f1051809317e39437a38e813a402cecd"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1301.1566",
    "kind": "arxiv",
    "version": 3
  }
}