Pith Number

pith:2B7G25U6

pith:2008:2B7G25U6WCJIO6NFQJS4KPRLCC

not attested not anchored not stored refs pending

Graphs of bounded degree and the $p$-harmonic boundary

Michael J. Puls

arxiv:0806.3073 v3 · 2008-06-18 · math.FA · 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{2B7G25U6WCJIO6NFQJS4KPRLCC}

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	2026-05-18T04:40:46.571745Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

d07e6d769eb0928779a58265c53e2b10b56b7210316267933fa02aa7dfbe3da3

Aliases

arxiv: 0806.3073 · arxiv_version: 0806.3073v3 · doi: 10.48550/arxiv.0806.3073 · pith_short_12: 2B7G25U6WCJI · pith_short_16: 2B7G25U6WCJIO6NF · pith_short_8: 2B7G25U6

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/2B7G25U6WCJIO6NFQJS4KPRLCC \
  | 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: d07e6d769eb0928779a58265c53e2b10b56b7210316267933fa02aa7dfbe3da3

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "28390620a3c5b36f4ebff356ba0d0e1f230b1ea8c53f56c49e6c7c842ae4bd1a",
    "cross_cats_sorted": [
      "math.DG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.FA",
    "submitted_at": "2008-06-18T19:45:34Z",
    "title_canon_sha256": "40b62ee32c0516816354d603e5afe2224840641f9607c93e5b67d7e6f46dddc4"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0806.3073",
    "kind": "arxiv",
    "version": 3
  }
}