Pith Number

pith:ZKG2AULP

pith:2016:ZKG2AULPS3FYV6AJSQ4LGNXGUR

not attested not anchored not stored refs pending

Mini-course: property of rapid decay

{\L}ukasz Garncarek

arxiv:1603.06730 v3 · 2016-03-22 · math.GR

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{ZKG2AULPS3FYV6AJSQ4LGNXGUR}

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	2026-05-18T00:39:13.631257Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ca8da0516f96cb8af8099438b336e6a4628554fbc43e308092e196434f90979f

Aliases

arxiv: 1603.06730 · arxiv_version: 1603.06730v3 · doi: 10.48550/arxiv.1603.06730 · pith_short_12: ZKG2AULPS3FY · pith_short_16: ZKG2AULPS3FYV6AJ · pith_short_8: ZKG2AULP

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/ZKG2AULPS3FYV6AJSQ4LGNXGUR \
  | 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: ca8da0516f96cb8af8099438b336e6a4628554fbc43e308092e196434f90979f

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "c8f56db01a6ccc7770d498d56e8724bbe041e209e4364a337066ac40bcea5ca6",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2016-03-22T10:47:33Z",
    "title_canon_sha256": "60177e9c3d5720eba1650f6565d9c7e13249bb4f9ef91bf249a9513ca5230d9f"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1603.06730",
    "kind": "arxiv",
    "version": 3
  }
}