Pith Number

pith:X4CR3M3K

pith:2014:X4CR3M3K36I5S7AA7DTQNKEL2I

not attested not anchored not stored refs pending

Growth Tight Actions of Product Groups

Christopher H. Cashen, Jing Tao

arxiv:1404.4335 v2 · 2014-04-16 · 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{X4CR3M3K36I5S7AA7DTQNKEL2I}

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	2026-05-18T01:12:01.997149Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

bf051db36adf91d97c00f8e706a88bd21a37a6bcdb091dbf202f88288bce3f84

Aliases

arxiv: 1404.4335 · arxiv_version: 1404.4335v2 · doi: 10.48550/arxiv.1404.4335 · pith_short_12: X4CR3M3K36I5 · pith_short_16: X4CR3M3K36I5S7AA · pith_short_8: X4CR3M3K

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/X4CR3M3K36I5S7AA7DTQNKEL2I \
  | 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: bf051db36adf91d97c00f8e706a88bd21a37a6bcdb091dbf202f88288bce3f84

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "5408c2ae16858474bdd81bde8627b560d50f1985b7074c959253a5ce211319d0",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2014-04-16T18:18:40Z",
    "title_canon_sha256": "1ac11d9cdf2240c5fecf629e6add10748a25346e580d486edda72749f34fbba7"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1404.4335",
    "kind": "arxiv",
    "version": 2
  }
}