Pith Number

pith:WIB4MZSZ

pith:2010:WIB4MZSZMPQ7TIUXIN6VU5XS4C

not attested not anchored not stored refs pending

Some results concerning the $p$-Royden and $p$-harmonic boundaries of a graph of bounded degree

Michael Puls

arxiv:1012.2473 v2 · 2010-12-11 · math.FA · 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{WIB4MZSZMPQ7TIUXIN6VU5XS4C}

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	2026-05-18T04:15:50.161945Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b203c6665963e1f9a297437d5a76f2e0a18a7d8b359d0ac40c6f34487e91a833

Aliases

arxiv: 1012.2473 · arxiv_version: 1012.2473v2 · doi: 10.48550/arxiv.1012.2473 · pith_short_12: WIB4MZSZMPQ7 · pith_short_16: WIB4MZSZMPQ7TIUX · pith_short_8: WIB4MZSZ

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/WIB4MZSZMPQ7TIUXIN6VU5XS4C \
  | 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: b203c6665963e1f9a297437d5a76f2e0a18a7d8b359d0ac40c6f34487e91a833

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "dae247268a9634e39e7877aacb403ccbae7092461870ce7445c81b174c374c15",
    "cross_cats_sorted": [
      "math.MG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.FA",
    "submitted_at": "2010-12-11T17:12:59Z",
    "title_canon_sha256": "a6ba949288880715c588c59ac246fc2ef59b658ceea8f3907c4bc7f4522a4c9b"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1012.2473",
    "kind": "arxiv",
    "version": 2
  }
}