Pith Number

pith:UUGCKZM3

pith:2019:UUGCKZM3OY524LEK5L3TH4E2BJ

not attested not anchored not stored refs pending

Stability for product groups and property $(\tau)$

Adrian Ioana

arxiv:1909.00282 v1 · 2019-08-31 · math.GR · math.OA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{UUGCKZM3OY524LEK5L3TH4E2BJ}

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	2026-07-05T00:01:07.526934Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

a50c25659b763bae2c8aeaf733f09a0a635e34c3fc16d7401b5f492c2a4bf34a

Aliases

arxiv: 1909.00282 · arxiv_version: 1909.00282v1 · doi: 10.48550/arxiv.1909.00282 · pith_short_12: UUGCKZM3OY52 · pith_short_16: UUGCKZM3OY524LEK · pith_short_8: UUGCKZM3

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/UUGCKZM3OY524LEK5L3TH4E2BJ \
  | 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: a50c25659b763bae2c8aeaf733f09a0a635e34c3fc16d7401b5f492c2a4bf34a

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "ddb5c0dae447b58149ad0ed1e0c2391c5a6a86051251a68850ec9aacb25c065e",
    "cross_cats_sorted": [
      "math.OA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2019-08-31T20:33:50Z",
    "title_canon_sha256": "b32c20747bda6679c37f6ba1a2a61a592d5ce3ed1c507aa4de68aa08723bbfb6"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1909.00282",
    "kind": "arxiv",
    "version": 1
  }
}