Pith Number

pith:P2MM6WZO

pith:2007:P2MM6WZOY33UEFLJBZKMCVWWAQ

not attested not anchored not stored refs pending

An infinite presentation of the Torelli group

Andrew Putman

arxiv:math/0703529 v2 · 2007-03-19 · 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{P2MM6WZOY33UEFLJBZKMCVWWAQ}

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	2026-07-05T01:08:19.535728Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

7e98cf5b2ec6f74215690e54c156d604266827907acbd598d03878e5f1eb2d0a

Aliases

arxiv: math/0703529 · arxiv_version: math/0703529v2 · doi: 10.48550/arxiv.math/0703529 · pith_short_12: P2MM6WZOY33U · pith_short_16: P2MM6WZOY33UEFLJ · pith_short_8: P2MM6WZO

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/P2MM6WZOY33UEFLJBZKMCVWWAQ \
  | 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: 7e98cf5b2ec6f74215690e54c156d604266827907acbd598d03878e5f1eb2d0a

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "1d4d9e28942746055faf4721fb8b455b683de5f071b6143c54d4689242c57988",
    "cross_cats_sorted": [
      "math.GR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GT",
    "submitted_at": "2007-03-19T05:01:11Z",
    "title_canon_sha256": "3b640d6b5ced96eb010f56520c5582d6223e0e5111abc1bd070bfa2d4a4944d3"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0703529",
    "kind": "arxiv",
    "version": 2
  }
}