Pith Number

pith:WCIACUPS

pith:2015:WCIACUPSKRUBW7UR2XZKHKGUFI

not attested not anchored not stored refs pending

The distortion dimension of $\mathbb Q$--rank $1$ lattices

Enrico Leuzinger, Robert Young

arxiv:1509.09224 v1 · 2015-09-30 · 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{WCIACUPSKRUBW7UR2XZKHKGUFI}

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	2026-05-18T01:31:26.792040Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b0900151f254681b7e91d5f2a3a8d42a0f9d0b5b7df5bfa8d4cc0f50b5ce4d84

Aliases

arxiv: 1509.09224 · arxiv_version: 1509.09224v1 · doi: 10.48550/arxiv.1509.09224 · pith_short_12: WCIACUPSKRUB · pith_short_16: WCIACUPSKRUBW7UR · pith_short_8: WCIACUPS

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/WCIACUPSKRUBW7UR2XZKHKGUFI \
  | 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: b0900151f254681b7e91d5f2a3a8d42a0f9d0b5b7df5bfa8d4cc0f50b5ce4d84

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "7e0dac2049f3094b03a30e97af6fb768b168425712a4be071e8c03b2b701ea33",
    "cross_cats_sorted": [
      "math.GT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2015-09-30T15:33:23Z",
    "title_canon_sha256": "04fc92d6f0b048d7dcb1f705d2cfb4a9e8c281e55aa26653c2a0d96d5146ed9a"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1509.09224",
    "kind": "arxiv",
    "version": 1
  }
}