Pith Number

pith:47N4BUGI

pith:2012:47N4BUGINB6GFF26TCCNVI3TEL

not attested not anchored not stored refs pending

Thin shell implies spectral gap up to polylog via a stochastic localization scheme

Ronen Eldan

arxiv:1203.0893 v5 · 2012-03-05 · math.MG · math.FA · 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{47N4BUGINB6GFF26TCCNVI3TEL}

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

A Mathematical Introduction to Diffusion Models

Receipt and verification

First computed	2026-05-18T03:25:59.552435Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e7dbc0d0c8687c62975e9884daa37322d54249fc21072681031e1b8f12d3c7e2

Aliases

arxiv: 1203.0893 · arxiv_version: 1203.0893v5 · doi: 10.48550/arxiv.1203.0893 · pith_short_12: 47N4BUGINB6G · pith_short_16: 47N4BUGINB6GFF26 · pith_short_8: 47N4BUGI

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/47N4BUGINB6GFF26TCCNVI3TEL \
  | 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: e7dbc0d0c8687c62975e9884daa37322d54249fc21072681031e1b8f12d3c7e2

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "a16efaca417fdb20e6ed88ae0e5993ea68646fc642260ac8af0513bb243afd18",
    "cross_cats_sorted": [
      "math.FA",
      "math.PR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.MG",
    "submitted_at": "2012-03-05T12:54:51Z",
    "title_canon_sha256": "9c728c37700e084aa7ec674affc76fa9a1fadbe722cd700529e84e9877948d9f"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1203.0893",
    "kind": "arxiv",
    "version": 5
  }
}