Pith Number

pith:R6UDZNPC

pith:2005:R6UDZNPCR7GDM2FXMQKKJ7GKXO

not attested not anchored not stored refs pending

Spectral asymptotics of the Laplacian on supercritical bond-percolation graphs

Peter M\"uller, Peter Stollmann

arxiv:math-ph/0506053 v2 · 2005-06-21 · math-ph · cond-mat.dis-nn · math.MP · math.PR · math.SP

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{R6UDZNPCR7GDM2FXMQKKJ7GKXO}

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	2026-05-18T04:08:43.359155Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

8fa83cb5e28fcc3668b76414a4fccabb88ec12b4d090e3cd49ea4d8481a682f6

Aliases

arxiv: math-ph/0506053 · arxiv_version: math-ph/0506053v2 · doi: 10.48550/arxiv.math-ph/0506053 · pith_short_12: R6UDZNPCR7GD · pith_short_16: R6UDZNPCR7GDM2FX · pith_short_8: R6UDZNPC

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/R6UDZNPCR7GDM2FXMQKKJ7GKXO \
  | 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: 8fa83cb5e28fcc3668b76414a4fccabb88ec12b4d090e3cd49ea4d8481a682f6

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "9b187cc8fbf5669f6e9d5f0d7c74865b7c782e2ce7a5068d78212a8950c744e7",
    "cross_cats_sorted": [
      "cond-mat.dis-nn",
      "math.MP",
      "math.PR",
      "math.SP"
    ],
    "license": "",
    "primary_cat": "math-ph",
    "submitted_at": "2005-06-21T03:19:39Z",
    "title_canon_sha256": "8e8f24b6274c6a4828d8b0aae5dc9fb9ce959b29043172d70e5180e42b6bf551"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math-ph/0506053",
    "kind": "arxiv",
    "version": 2
  }
}