Pith Number

pith:OZ5RAPJC

pith:2026:OZ5RAPJCS2UKJKVV4RTQH7NKZ7

not attested not anchored not stored refs pending

Tilting pairs and Wakamatsu tilting pairs of subcategories over cleft extensions

Guoqiang Zhao, Juxiang Sun

arxiv:2605.20720 v1 · 2026-05-20 · math.RT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{OZ5RAPJCS2UKJKVV4RTQH7NKZ7}

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	2026-05-21T01:04:50.668994Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

767b103d2296a8a4aab5e46703fdaacfd6fde06d29e2a80d569f82ef8a9987d1

Aliases

arxiv: 2605.20720 · arxiv_version: 2605.20720v1 · doi: 10.48550/arxiv.2605.20720 · pith_short_12: OZ5RAPJCS2UK · pith_short_16: OZ5RAPJCS2UKJKVV · pith_short_8: OZ5RAPJC

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/OZ5RAPJCS2UKJKVV4RTQH7NKZ7 \
  | 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: 767b103d2296a8a4aab5e46703fdaacfd6fde06d29e2a80d569f82ef8a9987d1

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "cf3f9398bc0c86973d5cbe29d0fa9539dd9e1bcbbe3eb0556784731eb757a0cb",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.RT",
    "submitted_at": "2026-05-20T05:20:33Z",
    "title_canon_sha256": "9a72d0688a65255fb85ad4cc115e0b3aeab2b128a5f8570abf3f59cec6c1de77"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.20720",
    "kind": "arxiv",
    "version": 1
  }
}