Pith Number

pith:ZYA5GPVJ

pith:2012:ZYA5GPVJBHDFGDVYTE2EFHCDBS

not attested not anchored not stored refs pending

Lipschitz Functions on Expanders are Typically Flat

Amir Yehudayoff, Ron Peled, Wojciech Samotij

arxiv:1203.3930 v1 · 2012-03-18 · math.PR

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{ZYA5GPVJBHDFGDVYTE2EFHCDBS}

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	2026-05-18T00:48:55.559799Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ce01d33ea909c6530eb89934429c430cb7d23ffeede369b6b8846817e9ce7640

Aliases

arxiv: 1203.3930 · arxiv_version: 1203.3930v1 · doi: 10.48550/arxiv.1203.3930 · pith_short_12: ZYA5GPVJBHDF · pith_short_16: ZYA5GPVJBHDFGDVY · pith_short_8: ZYA5GPVJ

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/ZYA5GPVJBHDFGDVYTE2EFHCDBS \
  | 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: ce01d33ea909c6530eb89934429c430cb7d23ffeede369b6b8846817e9ce7640

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "db4ab13e447458f3859386e5450029cc48601f434e0efeaaa5ab6771a532fa2c",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2012-03-18T08:07:17Z",
    "title_canon_sha256": "f89721e9411aef9659be8ce54f4d33d878c5963c5ead9e8ae0c6c3abd07e0b72"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1203.3930",
    "kind": "arxiv",
    "version": 1
  }
}