Pith Number

pith:5JHFXQOX

pith:2016:5JHFXQOXZD2ROY6DYN7PNDVMHO

not attested not anchored not stored refs pending

On stable commutator lengths of Dehn twists along separating curves

Kazuya Yoshihara, Naoyuki Monden

arxiv:1606.08643 v1 · 2016-06-28 · 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{5JHFXQOXZD2ROY6DYN7PNDVMHO}

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	2026-05-18T01:11:47.336415Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ea4e5bc1d7c8f51763c3c37ef68eac3bacb9266d1fe9d30c86c5596f15ad5d4a

Aliases

arxiv: 1606.08643 · arxiv_version: 1606.08643v1 · doi: 10.48550/arxiv.1606.08643 · pith_short_12: 5JHFXQOXZD2R · pith_short_16: 5JHFXQOXZD2ROY6D · pith_short_8: 5JHFXQOX

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/5JHFXQOXZD2ROY6DYN7PNDVMHO \
  | 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: ea4e5bc1d7c8f51763c3c37ef68eac3bacb9266d1fe9d30c86c5596f15ad5d4a

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "f8416d8e76627a56f08c3c0c5272384d7130edb574aa2d0e611e23a5c17cd277",
    "cross_cats_sorted": [
      "math.GR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GT",
    "submitted_at": "2016-06-28T10:39:50Z",
    "title_canon_sha256": "49b4f4ea5dbc5492a158b1a1f440552c115d3b7d2991de4e048dc6efbc2f71df"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1606.08643",
    "kind": "arxiv",
    "version": 1
  }
}