Pith Number

pith:3LEBHFQC

pith:2012:3LEBHFQCNZ2LHQ6JQY7AGRDQ4R

not attested not anchored not stored refs pending

Lipschitz homotopy groups of the Heisenberg groups

Robert Young, Stefan Wenger

arxiv:1210.6943 v3 · 2012-10-25 · math.GT · 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{3LEBHFQCNZ2LHQ6JQY7AGRDQ4R}

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	2026-05-18T03:04:06.794225Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

dac81396026e74b3c3c9863e034470e456fb3b0618608271c676918e15c495b6

Aliases

arxiv: 1210.6943 · arxiv_version: 1210.6943v3 · doi: 10.48550/arxiv.1210.6943 · pith_short_12: 3LEBHFQCNZ2L · pith_short_16: 3LEBHFQCNZ2LHQ6J · pith_short_8: 3LEBHFQC

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/3LEBHFQCNZ2LHQ6JQY7AGRDQ4R \
  | 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: dac81396026e74b3c3c9863e034470e456fb3b0618608271c676918e15c495b6

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "b96afb55892308e0867f45bb4cb2b669135de4d43c6df6e6c5495102db127873",
    "cross_cats_sorted": [
      "math.MG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GT",
    "submitted_at": "2012-10-25T18:48:12Z",
    "title_canon_sha256": "beccc221b72a6a7b33f0000afe0db4dc8f23740eac1d95c89d380106a9ef0b2c"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1210.6943",
    "kind": "arxiv",
    "version": 3
  }
}