Pith Number

pith:X4NF7WQA

pith:2025:X4NF7WQAQLBZAUULJU3C2P5WKW

not attested not anchored not stored refs pending

Some characterizations of weak left braces

Shoufeng Wang

arxiv:2502.05861 v2 · 2025-02-09 · math.GR · 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{X4NF7WQAQLBZAUULJU3C2P5WKW}

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	2026-07-05T10:17:53.950242Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

bf1a5fda0082c390528b4d362d3fb6558f88f79dc1ee8d7ea3c3f9809d60b1ef

Aliases

arxiv: 2502.05861 · arxiv_version: 2502.05861v2 · doi: 10.48550/arxiv.2502.05861 · pith_short_12: X4NF7WQAQLBZ · pith_short_16: X4NF7WQAQLBZAUUL · pith_short_8: X4NF7WQA

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/X4NF7WQAQLBZAUULJU3C2P5WKW \
  | 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: bf1a5fda0082c390528b4d362d3fb6558f88f79dc1ee8d7ea3c3f9809d60b1ef

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "4d262ea2832b2ddb234f173ffd078b49e396e3a717c3d7fffccdfe1e8659a658",
    "cross_cats_sorted": [
      "math.QA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2025-02-09T11:39:28Z",
    "title_canon_sha256": "1c4e8a943280f7da8492e4596037d97a210c8e2ed5c011210d6773329077b400"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2502.05861",
    "kind": "arxiv",
    "version": 2
  }
}