Pith Number

pith:FPKZFOCP

pith:2003:FPKZFOCPXDMY4SUJJKUILWGDCW

not attested not anchored not stored refs pending

On groups generated by two positive multi-twists: Teichmueller curves and Lehmer's number

Christopher J. Leininger

arxiv:math/0304163 v3 · 2003-04-14 · math.GT · 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{FPKZFOCPXDMY4SUJJKUILWGDCW}

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	2026-05-18T02:38:00.373713Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

2bd592b84fb8d98e4a894aa885d8c3158c1cb7503c11a44299641cc1fc1c0ce0

Aliases

arxiv: math/0304163 · arxiv_version: math/0304163v3 · doi: 10.48550/arxiv.math/0304163 · pith_short_12: FPKZFOCPXDMY · pith_short_16: FPKZFOCPXDMY4SUJ · pith_short_8: FPKZFOCP

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/FPKZFOCPXDMY4SUJJKUILWGDCW \
  | 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: 2bd592b84fb8d98e4a894aa885d8c3158c1cb7503c11a44299641cc1fc1c0ce0

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "c05a8891037564b44b88f1e10dc6495a5794b70281eeb6e3b88a92e53d24d48e",
    "cross_cats_sorted": [
      "math.GR"
    ],
    "license": "",
    "primary_cat": "math.GT",
    "submitted_at": "2003-04-14T15:03:13Z",
    "title_canon_sha256": "a0f4fb409b6ed3f9d0b7b754d00d90eb7b54bdcc68d3ebbe7e34cefdb60255ed"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0304163",
    "kind": "arxiv",
    "version": 3
  }
}