Pith Number

pith:QPNQFVDT

pith:2016:QPNQFVDTZYALL3VKTDJFG7KSYU

not attested not anchored not stored refs pending

Sharpness of the phase transition and lower bounds for the critical intensity in continuum percolation on $\mathbb{R}^d$

Sebastian Ziesche

arxiv:1607.06211 v1 · 2016-07-21 · math.PR · cond-mat.stat-mech

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{QPNQFVDTZYALL3VKTDJFG7KSYU}

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	2026-05-18T01:10:42.246114Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

83db02d473ce00b5eeaa98d2537d52c53bad0f0d688e9b34439768faa37cb944

Aliases

arxiv: 1607.06211 · arxiv_version: 1607.06211v1 · doi: 10.48550/arxiv.1607.06211 · pith_short_12: QPNQFVDTZYAL · pith_short_16: QPNQFVDTZYALL3VK · pith_short_8: QPNQFVDT

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/QPNQFVDTZYALL3VKTDJFG7KSYU \
  | 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: 83db02d473ce00b5eeaa98d2537d52c53bad0f0d688e9b34439768faa37cb944

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "0f7435ffe95b8660c0c577f9b7d230dada889a80346dcb2fadc5bb0a2dde959f",
    "cross_cats_sorted": [
      "cond-mat.stat-mech"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2016-07-21T07:00:11Z",
    "title_canon_sha256": "c219d2965951079ca91bcbbc4032139deb744fffe3eb3b36f6f8f3c2dd5cbf0c"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1607.06211",
    "kind": "arxiv",
    "version": 1
  }
}