Pith Number

pith:O5NG7UBH

pith:2026:O5NG7UBHFIIKQWK6A2RXYQAV53

not attested not anchored not stored refs pending

Profinite rigidity of simple closed curves in surface groups

Xiaoyu Xu, Zhongzi Wang

arxiv:2607.16147 v1 · 2026-07-17 · 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{O5NG7UBHFIIKQWK6A2RXYQAV53}

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	2026-07-20T02:19:35.878455Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

775a6fd0272a10a8595e06a37c4015eee02b10ff20dfe51c5f8d8909f4492f87

Aliases

arxiv: 2607.16147 · arxiv_version: 2607.16147v1 · doi: 10.48550/arxiv.2607.16147 · pith_short_12: O5NG7UBHFIIK · pith_short_16: O5NG7UBHFIIKQWK6 · pith_short_8: O5NG7UBH

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/O5NG7UBHFIIKQWK6A2RXYQAV53 \
  | 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: 775a6fd0272a10a8595e06a37c4015eee02b10ff20dfe51c5f8d8909f4492f87

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "6cbdb9d7715b5124d228ac27e235618464f5a70ddbf1c5a8074f06969a92e3bc",
    "cross_cats_sorted": [
      "math.GR"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.GT",
    "submitted_at": "2026-07-17T17:27:08Z",
    "title_canon_sha256": "6c4983ad30a13ce4d4d38bedf778e3b904962ca30eb769713934b566ff7a93a2"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2607.16147",
    "kind": "arxiv",
    "version": 1
  }
}