Pith Number

pith:XBBAOVQW

pith:2013:XBBAOVQW7RMVOWYKYDBNBQFK5B

not attested not anchored not stored refs pending

What makes a multi-complex exact?

Satoshi Mochizuki, Seidai Yasuda

arxiv:1305.6794 v4 · 2013-05-29 · math.AC · math.CT · math.KT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{XBBAOVQW7RMVOWYKYDBNBQFK5B}

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	2026-05-18T02:38:53.214327Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b842075616fc59575b0ac0c2d0c0aae87c3d2d9dbcbb66d07f47353e045c6d8b

Aliases

arxiv: 1305.6794 · arxiv_version: 1305.6794v4 · doi: 10.48550/arxiv.1305.6794 · pith_short_12: XBBAOVQW7RMV · pith_short_16: XBBAOVQW7RMVOWYK · pith_short_8: XBBAOVQW

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/XBBAOVQW7RMVOWYKYDBNBQFK5B \
  | 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: b842075616fc59575b0ac0c2d0c0aae87c3d2d9dbcbb66d07f47353e045c6d8b

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "9b1b0dacbd5c0a6a50e7c4c2b4607eb248ef5a52d4336867eacecd15c4619fa8",
    "cross_cats_sorted": [
      "math.CT",
      "math.KT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AC",
    "submitted_at": "2013-05-29T13:31:16Z",
    "title_canon_sha256": "6f94493b887b7e28d807513b4f8801cea82cecea778599513db5a3d1d0c07b96"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1305.6794",
    "kind": "arxiv",
    "version": 4
  }
}