Pith Number

pith:VZFA4BZN

pith:2010:VZFA4BZNDUSCPRAHF7SV4MPNDQ

not attested not anchored not stored refs pending

On invariant Gibbs measures conditioned on mass and momentum

Jeremy Quastel, Tadahiro Oh

arxiv:1012.3432 v2 · 2010-12-15 · math.PR · math.AP

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{VZFA4BZNDUSCPRAHF7SV4MPNDQ}

Prints a linked badge after your title and injects PDF metadata. Compiles on arXiv. Learn more

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	2026-05-18T04:17:04.437721Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ae4a0e072d1d2427c4072fe55e31ed1c2e1dfd45a3062aeb65b47922fb1110f3

Aliases

arxiv: 1012.3432 · arxiv_version: 1012.3432v2 · doi: 10.48550/arxiv.1012.3432 · pith_short_12: VZFA4BZNDUSC · pith_short_16: VZFA4BZNDUSCPRAH · pith_short_8: VZFA4BZN

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/VZFA4BZNDUSCPRAHF7SV4MPNDQ \
  | 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: ae4a0e072d1d2427c4072fe55e31ed1c2e1dfd45a3062aeb65b47922fb1110f3

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "b6e30fd9f3d22f9947015c7611d28b1a78b360fe818e0fe52c1a5baf78a55cb9",
    "cross_cats_sorted": [
      "math.AP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2010-12-15T19:27:27Z",
    "title_canon_sha256": "89991ea34b5b828bf355fcc0e864e0f745ddb7cfa3fbc4c753acb1a663b2cf44"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1012.3432",
    "kind": "arxiv",
    "version": 2
  }
}