Pith Number

pith:6E4RSGTC

pith:2009:6E4RSGTCI2IKY2QVYUGAK2GX4V

not attested not anchored not stored refs pending

Rank gradient and torsion groups

D. Osin

arxiv:0905.1322 v5 · 2009-05-08 · 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{6E4RSGTCI2IKY2QVYUGAK2GX4V}

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	2026-05-18T02:58:03.199688Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

f139191a624690ac6a15c50c0568d7e565de8d847d602ec850567aa605393189

Aliases

arxiv: 0905.1322 · arxiv_version: 0905.1322v5 · doi: 10.48550/arxiv.0905.1322 · pith_short_12: 6E4RSGTCI2IK · pith_short_16: 6E4RSGTCI2IKY2QV · pith_short_8: 6E4RSGTC

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/6E4RSGTCI2IKY2QVYUGAK2GX4V \
  | 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: f139191a624690ac6a15c50c0568d7e565de8d847d602ec850567aa605393189

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "761302a151de42a618b5002b6216563c603025cb9ce7d03d08ffd71656faa391",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2009-05-08T19:53:43Z",
    "title_canon_sha256": "2d28fe744472a887cb6a05bae603e133bb348c4fe1611a4a4edfb7e3ab68f3a9"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0905.1322",
    "kind": "arxiv",
    "version": 5
  }
}