Pith Number

pith:PCAVDS3S

pith:2009:PCAVDS3S4N75W72P5ZAATTB32P

not attested not anchored not stored refs pending

Zero Range Condensation at Criticality

In\'es Armend\'ariz, Michail Loulakis, Stefan Grosskinsky

arxiv:0912.1793 v2 · 2009-12-09 · 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{PCAVDS3S4N75W72P5ZAATTB32P}

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	2026-05-18T03:21:43.857965Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

788151cb72e37fdb7f4fee4009cc3bd3c3755f10d710c1bec2b91820afe98bd8

Aliases

arxiv: 0912.1793 · arxiv_version: 0912.1793v2 · doi: 10.48550/arxiv.0912.1793 · pith_short_12: PCAVDS3S4N75 · pith_short_16: PCAVDS3S4N75W72P · pith_short_8: PCAVDS3S

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/PCAVDS3S4N75W72P5ZAATTB32P \
  | 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: 788151cb72e37fdb7f4fee4009cc3bd3c3755f10d710c1bec2b91820afe98bd8

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "faffca7d5b0eb03f64bcdfdc8267e0a96dce2e3670f0a32ac27e3656dd8d0ef1",
    "cross_cats_sorted": [
      "cond-mat.stat-mech"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2009-12-09T19:39:19Z",
    "title_canon_sha256": "7905c54360bdba83b90a7dc6c689bb689fc826fcfdbfdc36c0b0f34394837eb6"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0912.1793",
    "kind": "arxiv",
    "version": 2
  }
}