Pith Number

pith:F7XETGJK

pith:2026:F7XETGJK5QSJCNQIZWPMBPRGNO

not attested not anchored not stored refs pending

Divisibility and Real Rank Zero

Xuanlong Fu

arxiv:2605.21655 v1 · 2026-05-20 · math.OA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{F7XETGJK5QSJCNQIZWPMBPRGNO}

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	2026-05-22T01:03:27.009962Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

2fee49992aec24913608cd9ec0be266b8cd4031ffcce85fb6deeb4a6d19aead9

Aliases

arxiv: 2605.21655 · arxiv_version: 2605.21655v1 · doi: 10.48550/arxiv.2605.21655 · pith_short_12: F7XETGJK5QSJ · pith_short_16: F7XETGJK5QSJCNQI · pith_short_8: F7XETGJK

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/F7XETGJK5QSJCNQIZWPMBPRGNO \
  | 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: 2fee49992aec24913608cd9ec0be266b8cd4031ffcce85fb6deeb4a6d19aead9

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "74fb1fc422685703abf688cfcd7ad5cd1b5cdc6dcd9c30202ead8e36536e2b11",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by-nc-nd/4.0/",
    "primary_cat": "math.OA",
    "submitted_at": "2026-05-20T19:10:13Z",
    "title_canon_sha256": "7f254884a74c557c8f78b08418fedd323c4c1d8f7c0c646f5e53aa3fd84d9ca2"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.21655",
    "kind": "arxiv",
    "version": 1
  }
}