Pith Number

pith:Q3QUU2HQ

pith:2000:Q3QUU2HQ35RM3OM3QTLNHR5LY2

not attested not anchored not stored refs pending

On asymptotic dimension of groups

A. Dranishnikov, G. Bell

arxiv:math/0012006 v2 · 2000-12-02 · math.GR · math.GT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{Q3QUU2HQ35RM3OM3QTLNHR5LY2}

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	2026-05-18T02:41:33.372211Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

86e14a68f0df62cdb99b84d6d3c7abc699113c19b3b0dd2a5eeedb47cfa09196

Aliases

arxiv: math/0012006 · arxiv_version: math/0012006v2 · doi: 10.48550/arxiv.math/0012006 · pith_short_12: Q3QUU2HQ35RM · pith_short_16: Q3QUU2HQ35RM3OM3 · pith_short_8: Q3QUU2HQ

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/Q3QUU2HQ35RM3OM3QTLNHR5LY2 \
  | 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: 86e14a68f0df62cdb99b84d6d3c7abc699113c19b3b0dd2a5eeedb47cfa09196

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "7a472dabdbd0b155373356252c241082a300b83ea095e5ef77f1afbd33fed22a",
    "cross_cats_sorted": [
      "math.GT"
    ],
    "license": "",
    "primary_cat": "math.GR",
    "submitted_at": "2000-12-02T00:13:32Z",
    "title_canon_sha256": "82f8bf96be0bc3cb1d425b1f831698ec7ae01cc511f9b89409247edcf8fa1744"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0012006",
    "kind": "arxiv",
    "version": 2
  }
}