Pith Number

pith:MIJEZDQC

pith:2009:MIJEZDQCVZC7A3TK3LCBOCMN55

not attested not anchored not stored refs pending

Gr\"obner-Shirshov bases for braid groups in Adyan-Thurston generators

Chanyan Zhong, Yuqun Chen

arxiv:0909.3639 v1 · 2009-09-20 · 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{MIJEZDQCVZC7A3TK3LCBOCMN55}

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	2026-05-18T03:26:32.799670Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

62124c8e02ae45f06e6adac417098def4d5f0ffecdf169ffd32e0efdbcb333ae

Aliases

arxiv: 0909.3639 · arxiv_version: 0909.3639v1 · doi: 10.48550/arxiv.0909.3639 · pith_short_12: MIJEZDQCVZC7 · pith_short_16: MIJEZDQCVZC7A3TK · pith_short_8: MIJEZDQC

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/MIJEZDQCVZC7A3TK3LCBOCMN55 \
  | 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: 62124c8e02ae45f06e6adac417098def4d5f0ffecdf169ffd32e0efdbcb333ae

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "638acb164a3ca6274cfea38dca90eda806ea3f51b24942d17fa6106ac6ed6cf6",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2009-09-20T15:51:49Z",
    "title_canon_sha256": "3c62168e2cab642eaebfd48fb36e6766eafe1f4ae89a14a40938d03889b141cb"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0909.3639",
    "kind": "arxiv",
    "version": 1
  }
}