Pith Number

pith:MSBHRNRW

pith:2005:MSBHRNRWYXIJE2AHRV7UNMI72T

not attested not anchored not stored refs pending

Percolation theory

Vincent Beffara (UMPA-ENSL), Vladas Sidoravicius (IMPA)

arxiv:math/0507220 v1 · 2005-07-11 · math.PR

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{MSBHRNRWYXIJE2AHRV7UNMI72T}

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	2026-05-18T01:05:23.319951Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

648278b636c5d09268078d7f46b11fd4ddcd378bbed9cdea63813ffb10ca24c3

Aliases

arxiv: math/0507220 · arxiv_version: math/0507220v1 · doi: 10.48550/arxiv.math/0507220 · pith_short_12: MSBHRNRWYXIJ · pith_short_16: MSBHRNRWYXIJE2AH · pith_short_8: MSBHRNRW

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/MSBHRNRWYXIJE2AHRV7UNMI72T \
  | 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: 648278b636c5d09268078d7f46b11fd4ddcd378bbed9cdea63813ffb10ca24c3

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "36f9cfb3a1cdb37df1e286cfb455f4de5d43101788fd3a5e937026ef4b7e2b44",
    "cross_cats_sorted": [],
    "license": "",
    "primary_cat": "math.PR",
    "submitted_at": "2005-07-11T14:20:10Z",
    "title_canon_sha256": "d4d828dd742a6a82f4ecff6d85f1ae9063c65d02054c54a8d3d2370cd3f3f5fc"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0507220",
    "kind": "arxiv",
    "version": 1
  }
}