Pith Number

pith:ZEOIYARY

pith:2012:ZEOIYARY6UMXXUWMOADSXBPGHI

not attested not anchored not stored refs pending

The space of bi-invariant orders on a nilpotent group

Dave Witte Morris

arxiv:1204.0454 v2 · 2012-04-02 · 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{ZEOIYARY6UMXXUWMOADSXBPGHI}

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	2026-05-18T03:57:52.688739Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

c91c8c0238f5197bd2cc70072b85e63a3ba98010f7c35e6c364208307f355ad8

Aliases

arxiv: 1204.0454 · arxiv_version: 1204.0454v2 · doi: 10.48550/arxiv.1204.0454 · pith_short_12: ZEOIYARY6UMX · pith_short_16: ZEOIYARY6UMXXUWM · pith_short_8: ZEOIYARY

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/ZEOIYARY6UMXXUWMOADSXBPGHI \
  | 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: c91c8c0238f5197bd2cc70072b85e63a3ba98010f7c35e6c364208307f355ad8

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "e4ae23bbfe09db1624a73e13c857fb389fded93c0cddbcdd0468267ac48da03b",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2012-04-02T16:24:54Z",
    "title_canon_sha256": "0747b745427f99e8072dc5cfa37cf28959c5cbe354166a3512ff787ae8857e36"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1204.0454",
    "kind": "arxiv",
    "version": 2
  }
}