Pith Number

pith:JJN4N7ZZ

pith:2003:JJN4N7ZZJT2QUTTQUCVLF4SCGS

not attested not anchored not stored refs pending

Pinched exponential volume growth implies an infinite dimensional isoperimetric inequality

Itai Benjamini, Oded Schramm

arxiv:math/0303127 v1 · 2003-03-11 · math.MG

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{JJN4N7ZZJT2QUTTQUCVLF4SCGS}

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	2026-07-04T14:37:08.427505Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

4a5bc6ff394cf50a4e70a0aab2f24234b2a47af0b707586dfde7bca5cbef7073

Aliases

arxiv: math/0303127 · arxiv_version: math/0303127v1 · doi: 10.48550/arxiv.math/0303127 · pith_short_12: JJN4N7ZZJT2Q · pith_short_16: JJN4N7ZZJT2QUTTQ · pith_short_8: JJN4N7ZZ

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/JJN4N7ZZJT2QUTTQUCVLF4SCGS \
  | 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: 4a5bc6ff394cf50a4e70a0aab2f24234b2a47af0b707586dfde7bca5cbef7073

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "3a8545c989353401da6e8c1c03a6d2a69bbdefb949ca9a1924c99dba60d29a2a",
    "cross_cats_sorted": [],
    "license": "",
    "primary_cat": "math.MG",
    "submitted_at": "2003-03-11T18:12:37Z",
    "title_canon_sha256": "bd61181f2bcbbfc3ed6590e8a5869c4a45e635c3af5c067be2356b59e317e03b"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0303127",
    "kind": "arxiv",
    "version": 1
  }
}