Pith Number

pith:CQBWIZW6

pith:2011:CQBWIZW6C3UHZPMAI5MPKNRN5D

not attested not anchored not stored refs pending

Low-distortion embeddings of graphs with large girth

Mikhail I. Ostrovskii

arxiv:1108.2542 v2 · 2011-08-12 · math.MG · math.CO · math.FA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{CQBWIZW6C3UHZPMAI5MPKNRN5D}

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	2026-05-18T03:32:45.580389Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

14036466de16e87cbd804758f5362de8e02e9ccdbc9f7bfdb1f095a03b7cdb97

Aliases

arxiv: 1108.2542 · arxiv_version: 1108.2542v2 · doi: 10.48550/arxiv.1108.2542 · pith_short_12: CQBWIZW6C3UH · pith_short_16: CQBWIZW6C3UHZPMA · pith_short_8: CQBWIZW6

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/CQBWIZW6C3UHZPMAI5MPKNRN5D \
  | 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: 14036466de16e87cbd804758f5362de8e02e9ccdbc9f7bfdb1f095a03b7cdb97

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "eec3c9177c498835b295ad84d6788a0220dd536f1b584b4be5ef12cf7270ac5d",
    "cross_cats_sorted": [
      "math.CO",
      "math.FA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.MG",
    "submitted_at": "2011-08-12T00:42:17Z",
    "title_canon_sha256": "f2ae2148fd02ed5f82ce851e88ba0724e882ef4bc6ea091b1be2e366b7d08813"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1108.2542",
    "kind": "arxiv",
    "version": 2
  }
}