Pith Number

pith:W33DRXPE

pith:2008:W33DRXPED6LENSLHFNLS2WZFK2

not attested not anchored not stored refs pending

Intersections and joins of free groups

Richard P. Kent IV

arxiv:0802.0033 v2 · 2008-01-31 · math.GR · math.GT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{W33DRXPED6LENSLHFNLS2WZFK2}

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	2026-05-18T02:41:51.809378Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b6f638dde41f9646c9672b572d5b2556b487c2e1d58ca135cdfffb7e1b0674b5

Aliases

arxiv: 0802.0033 · arxiv_version: 0802.0033v2 · doi: 10.48550/arxiv.0802.0033 · pith_short_12: W33DRXPED6LE · pith_short_16: W33DRXPED6LENSLH · pith_short_8: W33DRXPE

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/W33DRXPED6LENSLHFNLS2WZFK2 \
  | 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: b6f638dde41f9646c9672b572d5b2556b487c2e1d58ca135cdfffb7e1b0674b5

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "8d7e395c348eb6aaa49f61c0dd93201216b23e281600d74ffb57e772cf6f87e5",
    "cross_cats_sorted": [
      "math.GT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2008-01-31T23:25:01Z",
    "title_canon_sha256": "be7312f911a28887a5d221423a47273f9a79fa9e8283b4e4bc49eb57750ec785"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0802.0033",
    "kind": "arxiv",
    "version": 2
  }
}