Pith Number

pith:4QFGBLVK

pith:2011:4QFGBLVKVJCFQ7NVJSGZ5PB4DG

not attested not anchored not stored refs pending

Injective hulls of certain discrete metric spaces and groups

Urs Lang

arxiv:1107.5971 v2 · 2011-07-29 · math.GR · 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{4QFGBLVKVJCFQ7NVJSGZ5PB4DG}

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	2026-05-18T03:52:26.381675Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e40a60aeaaaa44587db54c8d9ebc3c19a3a506280d5579f8556dbf9f878d7954

Aliases

arxiv: 1107.5971 · arxiv_version: 1107.5971v2 · doi: 10.48550/arxiv.1107.5971 · pith_short_12: 4QFGBLVKVJCF · pith_short_16: 4QFGBLVKVJCFQ7NV · pith_short_8: 4QFGBLVK

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/4QFGBLVKVJCFQ7NVJSGZ5PB4DG \
  | 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: e40a60aeaaaa44587db54c8d9ebc3c19a3a506280d5579f8556dbf9f878d7954

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "51d04e7ba39a90455778d09928212b0d03eae0df76993940fb842ed0c894c85d",
    "cross_cats_sorted": [
      "math.MG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2011-07-29T13:52:23Z",
    "title_canon_sha256": "b0291a4b81d8b9615ed1de31307edc217b7832681f38353aeee4ba38152aab13"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1107.5971",
    "kind": "arxiv",
    "version": 2
  }
}