Pith Number

pith:YPJKQTJG

pith:2011:YPJKQTJGLFIZ3P73E3RL65HSDB

not attested not anchored not stored refs pending

$\ell^p$-distortion and $p$-spectral gap of finite regular graphs

Alain Valette, Pierre-Nicolas Jolissaint

arxiv:1110.0909 v2 · 2011-10-05 · math.MG · math.CO

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{YPJKQTJGLFIZ3P73E3RL65HSDB}

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	2026-05-18T00:44:30.515438Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

c3d2a84d2659519dbffb26e2bf74f21866d6b90e5bb51e0af7968abfce3b1dfc

Aliases

arxiv: 1110.0909 · arxiv_version: 1110.0909v2 · doi: 10.48550/arxiv.1110.0909 · pith_short_12: YPJKQTJGLFIZ · pith_short_16: YPJKQTJGLFIZ3P73 · pith_short_8: YPJKQTJG

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/YPJKQTJGLFIZ3P73E3RL65HSDB \
  | 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: c3d2a84d2659519dbffb26e2bf74f21866d6b90e5bb51e0af7968abfce3b1dfc

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "548aee8a893d9efedd67e529d95c4dbada32e84c8b2f1ba19d9730dd98e5a717",
    "cross_cats_sorted": [
      "math.CO"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.MG",
    "submitted_at": "2011-10-05T07:07:40Z",
    "title_canon_sha256": "b8abf435556876660999ae2c95a448b7afb12c1201829bcbb65976070d30a339"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1110.0909",
    "kind": "arxiv",
    "version": 2
  }
}