Pith Number

pith:OYWKHDR3

pith:2000:OYWKHDR3ZW4HDZU4AR4VFIJVNI

not attested not anchored not stored refs pending

An expansion of the Jones representation of genus 2 and the Torelli group

Yasushi Kasahara

arxiv:math/0012216 v1 · 2000-12-21 · math.GT · math.AT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{OYWKHDR3ZW4HDZU4AR4VFIJVNI}

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	2026-05-18T02:41:33.359392Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

762ca38e3bcdb871e69c047952a1356a15ab2c17cdb4e792fef8441e20e69231

Aliases

arxiv: math/0012216 · arxiv_version: math/0012216v1 · doi: 10.48550/arxiv.math/0012216 · pith_short_12: OYWKHDR3ZW4H · pith_short_16: OYWKHDR3ZW4HDZU4 · pith_short_8: OYWKHDR3

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/OYWKHDR3ZW4HDZU4AR4VFIJVNI \
  | 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: 762ca38e3bcdb871e69c047952a1356a15ab2c17cdb4e792fef8441e20e69231

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "4bb64de8685e332ebdc136e04bd83acba1a8809a1af5614db9b2f0268997ff81",
    "cross_cats_sorted": [
      "math.AT"
    ],
    "license": "",
    "primary_cat": "math.GT",
    "submitted_at": "2000-12-21T13:06:04Z",
    "title_canon_sha256": "f3383b56a0b8c6cd812cd230be5c4d616b8c89e34647cefe8fade92c4b295024"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0012216",
    "kind": "arxiv",
    "version": 1
  }
}