Pith Number

pith:VHF2ZZLQ

pith:2012:VHF2ZZLQQKBQ5D5XRYQHAOIZRS

not attested not anchored not stored refs pending

Sharp geometric rigidity of isometries on Heisenberg groups

D. V. Isangulova, S. K. Vodopyanov

arxiv:1204.3441 v1 · 2012-04-16 · math.MG · 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{VHF2ZZLQQKBQ5D5XRYQHAOIZRS}

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	2026-05-18T03:57:51.530069Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

a9cbace57082830e8fb78e207039198c8f125f0704d29e2a3f1aee767c406c88

Aliases

arxiv: 1204.3441 · arxiv_version: 1204.3441v1 · doi: 10.48550/arxiv.1204.3441 · pith_short_12: VHF2ZZLQQKBQ · pith_short_16: VHF2ZZLQQKBQ5D5X · pith_short_8: VHF2ZZLQ

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/VHF2ZZLQQKBQ5D5XRYQHAOIZRS \
  | 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: a9cbace57082830e8fb78e207039198c8f125f0704d29e2a3f1aee767c406c88

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "df2b89c6c0a9bd98021d52dae7f01c3750d3a50d08ac34f3ae343aa0a80fd26b",
    "cross_cats_sorted": [
      "math.FA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.MG",
    "submitted_at": "2012-04-16T11:15:25Z",
    "title_canon_sha256": "118c11ff436385f0e235480925bb39d93cfcbb635f07bfc09f00e9296aace525"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1204.3441",
    "kind": "arxiv",
    "version": 1
  }
}