Pith Number

pith:ZGZ75YNR

pith:2010:ZGZ75YNRII4LP4F6SW4DQJSMNY

not attested not anchored not stored refs pending

Isomorphism in expanding families of indistinguishable groups

James B. Wilson, Mark L. Lewis

arxiv:1010.5466 v4 · 2010-10-26 · math.GR · math.RA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{ZGZ75YNRII4LP4F6SW4DQJSMNY}

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	2026-05-18T02:28:55.540809Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

c9b3fee1b14238b7f0be95b838264c6e182310523b701ef8186b4b0113c39824

Aliases

arxiv: 1010.5466 · arxiv_version: 1010.5466v4 · doi: 10.48550/arxiv.1010.5466 · pith_short_12: ZGZ75YNRII4L · pith_short_16: ZGZ75YNRII4LP4F6 · pith_short_8: ZGZ75YNR

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/ZGZ75YNRII4LP4F6SW4DQJSMNY \
  | 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: c9b3fee1b14238b7f0be95b838264c6e182310523b701ef8186b4b0113c39824

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "a40cd17f6f34d2d6aa53aaec4b972f019a03f07c157e0deb5977c2e604de6ed2",
    "cross_cats_sorted": [
      "math.RA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2010-10-26T17:23:50Z",
    "title_canon_sha256": "a0d8e084983138b7448a31100c8b01da4960a3252bf4b7c5d6381ecfff2e9e4f"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1010.5466",
    "kind": "arxiv",
    "version": 4
  }
}