Pith Number

pith:JRZQVCO5

pith:2008:JRZQVCO55INTVDSHN3OMQTYB6Y

not attested not anchored not stored refs pending

Chaos, concentration, and multiple valleys

Sourav Chatterjee

arxiv:0810.4221 v2 · 2008-10-23 · math.PR · 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{JRZQVCO55INTVDSHN3OMQTYB6Y}

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.

Cited by

1 paper in Pith

Limit theorems for the number of sign and level-set clusters of the Gaussian free field

Receipt and verification

First computed	2026-07-04T15:33:44.275701Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

4c730a89ddea1b3a8e476edcc84f01f602792eaa17e7b4df3d2a9bedf6110e3e

Aliases

arxiv: 0810.4221 · arxiv_version: 0810.4221v2 · doi: 10.48550/arxiv.0810.4221 · pith_short_12: JRZQVCO55INT · pith_short_16: JRZQVCO55INTVDSH · pith_short_8: JRZQVCO5

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/JRZQVCO55INTVDSHN3OMQTYB6Y \
  | 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: 4c730a89ddea1b3a8e476edcc84f01f602792eaa17e7b4df3d2a9bedf6110e3e

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "67b715a87b2dac1cb1db66d4c0410497a028e393f48410a65a8b4015174a5e06",
    "cross_cats_sorted": [
      "math-ph",
      "math.MP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2008-10-23T07:51:15Z",
    "title_canon_sha256": "2fd04ee493bcdb33e0d9d901ebf05be426f2cb2d605ad30172e07c77702f0073"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0810.4221",
    "kind": "arxiv",
    "version": 2
  }
}