Pith Number

pith:U3JIJRXE

pith:2017:U3JIJRXESSQXA7OHZXIYSFRVLQ

not attested not anchored not stored refs pending

Non-triviality of the vacancy phase transition for the Boolean model

Mathew D. Penrose

arxiv:1706.02197 v2 · 2017-06-07 · 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{U3JIJRXESSQXA7OHZXIYSFRVLQ}

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	2026-05-18T00:10:13.669861Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

a6d284c6e494a1707dc7cdd18916355c00d3f3f15d1c0f831da646154a230c37

Aliases

arxiv: 1706.02197 · arxiv_version: 1706.02197v2 · doi: 10.48550/arxiv.1706.02197 · pith_short_12: U3JIJRXESSQX · pith_short_16: U3JIJRXESSQXA7OH · pith_short_8: U3JIJRXE

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/U3JIJRXESSQXA7OHZXIYSFRVLQ \
  | 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: a6d284c6e494a1707dc7cdd18916355c00d3f3f15d1c0f831da646154a230c37

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "06604f5297034667123b206271353a923c55418e1fd9367dde600d26734be175",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2017-06-07T14:07:50Z",
    "title_canon_sha256": "8abd9df831118a4f1a35c766c297ae4ca095231119e7bd6869f481bad33d1ca9"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1706.02197",
    "kind": "arxiv",
    "version": 2
  }
}