Pith Number

pith:ZWPLMMSD

pith:2025:ZWPLMMSDXNGIIWTGQICPHOGCQW

not attested not anchored not stored refs pending

Noncommutative marked surfaces II: tagged triangulations, clusters, and their symmetries

Arkady Berenstein, Min Huang, Vladimir Retakh

arxiv:2507.20393 v4 · 2025-07-27 · math.RT · math.AG · math.CO · math.QA

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{ZWPLMMSDXNGIIWTGQICPHOGCQW}

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	2026-07-05T11:53:05.844717Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

cd9eb63243bb4c845a668204f3b8c285a7cd409c18a374678530b60ce6d00baa

Aliases

arxiv: 2507.20393 · arxiv_version: 2507.20393v4 · doi: 10.48550/arxiv.2507.20393 · pith_short_12: ZWPLMMSDXNGI · pith_short_16: ZWPLMMSDXNGIIWTG · pith_short_8: ZWPLMMSD

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/ZWPLMMSDXNGIIWTGQICPHOGCQW \
  | 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: cd9eb63243bb4c845a668204f3b8c285a7cd409c18a374678530b60ce6d00baa

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "2d197485f3ef1edf03274099f69d990fe33bcc94125e389f87a65ddfe1c95cab",
    "cross_cats_sorted": [
      "math.AG",
      "math.CO",
      "math.QA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.RT",
    "submitted_at": "2025-07-27T19:23:39Z",
    "title_canon_sha256": "e35f862b467278619c2778848b5dff058ec22165a66033377ff523c88033fe35"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2507.20393",
    "kind": "arxiv",
    "version": 4
  }
}