Pith Number

pith:PRJJFF4N

pith:2010:PRJJFF4NVAXJEQZVRPOAKUEOY3

not attested not anchored not stored refs pending

The co-Hopfian property of surface braid groups

Saeko Yamagata, Yoshikata Kida

arxiv:1006.2599 v3 · 2010-06-14 · 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{PRJJFF4NVAXJEQZVRPOAKUEOY3}

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	2026-05-18T03:04:07.033190Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

7c5292978da82e9243358bdc05508ec6d82b76cbbec58cdf6e231b8b1c3e5634

Aliases

arxiv: 1006.2599 · arxiv_version: 1006.2599v3 · doi: 10.48550/arxiv.1006.2599 · pith_short_12: PRJJFF4NVAXJ · pith_short_16: PRJJFF4NVAXJEQZV · pith_short_8: PRJJFF4N

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/PRJJFF4NVAXJEQZVRPOAKUEOY3 \
  | 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: 7c5292978da82e9243358bdc05508ec6d82b76cbbec58cdf6e231b8b1c3e5634

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "9c048627f7e6ae7337e1411e3f3def7c5aabf9a7a0128d1b4d221991c60d91a0",
    "cross_cats_sorted": [
      "math.GT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2010-06-14T06:39:02Z",
    "title_canon_sha256": "9ff0e25840c62067b458f40cb20394e8f814a9b18bc5fa77c74b617389c50142"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1006.2599",
    "kind": "arxiv",
    "version": 3
  }
}