Pith Number

pith:HRQYYDAB

pith:2011:HRQYYDABMTRJLTRV46XWQLEGYP

not attested not anchored not stored refs pending

On the Furstenberg measure and density of states for the Anderson-Bernoulli model at small disorder

Jean Bourgain

arxiv:1101.2148 v1 · 2011-01-11 · math.AP

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{HRQYYDABMTRJLTRV46XWQLEGYP}

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	2026-05-18T04:31:50.775988Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

3c618c0c0164e295ce35e7af682c86c3fdd05887be451b77a40e6c44000e8d37

Aliases

arxiv: 1101.2148 · arxiv_version: 1101.2148v1 · doi: 10.48550/arxiv.1101.2148 · pith_short_12: HRQYYDABMTRJ · pith_short_16: HRQYYDABMTRJLTRV · pith_short_8: HRQYYDAB

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/HRQYYDABMTRJLTRV46XWQLEGYP \
  | 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: 3c618c0c0164e295ce35e7af682c86c3fdd05887be451b77a40e6c44000e8d37

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "e8c5aa4444abec64f0a56b08ce722238e9c8f077be2e82b7a7ea7fa16740bbd0",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2011-01-11T15:48:01Z",
    "title_canon_sha256": "70a46178b2e173dc42508688ea4070efda93d2c2ad6dbd3f3017c1d7c15aa23e"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1101.2148",
    "kind": "arxiv",
    "version": 1
  }
}