Pith Number

pith:UPVJIWTF

pith:2012:UPVJIWTF2SEAJ3BLKNLF65WFZJ

not attested not anchored not stored refs pending

Percolation on infinite graphs and isoperimetric inequalities

Aldo Procacci, Remy Sanchis, Rog\'erio G. Alves

arxiv:1211.0948 v1 · 2012-11-05 · math-ph · math.MP

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{UPVJIWTF2SEAJ3BLKNLF65WFZJ}

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	2026-05-18T01:53:25.706081Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

a3ea945a65d48804ec2b53565f76c5ca6567bedee15c282ea007956bdf28d4cc

Aliases

arxiv: 1211.0948 · arxiv_version: 1211.0948v1 · doi: 10.48550/arxiv.1211.0948 · pith_short_12: UPVJIWTF2SEA · pith_short_16: UPVJIWTF2SEAJ3BL · pith_short_8: UPVJIWTF

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/UPVJIWTF2SEAJ3BLKNLF65WFZJ \
  | 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: a3ea945a65d48804ec2b53565f76c5ca6567bedee15c282ea007956bdf28d4cc

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "d8b1f11bbce769ebc18c78790a2841b390ef74d9b88b01723ec06ed7373099e2",
    "cross_cats_sorted": [
      "math.MP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math-ph",
    "submitted_at": "2012-11-05T17:51:24Z",
    "title_canon_sha256": "f29d2d7409f9a27d1739a34a2f384494deb2014e839661a676b49c328f161440"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1211.0948",
    "kind": "arxiv",
    "version": 1
  }
}