Pith Number

pith:7K4NNIIZ

pith:2013:7K4NNIIZWZ4G5JJLZTTB3HCAE7

not attested not anchored not stored refs pending

Negative K-groups of abelian categories

Satoshi Mochizuki

arxiv:1306.0296 v1 · 2013-06-03 · math.KT · math.CT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{7K4NNIIZWZ4G5JJLZTTB3HCAE7}

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	2026-05-18T03:21:55.582217Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

fab8d6a119b6786ea52bcce61d9c4027da392628918f3cad1e2e309d5bce8398

Aliases

arxiv: 1306.0296 · arxiv_version: 1306.0296v1 · doi: 10.48550/arxiv.1306.0296 · pith_short_12: 7K4NNIIZWZ4G · pith_short_16: 7K4NNIIZWZ4G5JJL · pith_short_8: 7K4NNIIZ

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/7K4NNIIZWZ4G5JJLZTTB3HCAE7 \
  | 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: fab8d6a119b6786ea52bcce61d9c4027da392628918f3cad1e2e309d5bce8398

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "3e91dca8cebb8d111c8b005ad2923542fc0addb749a4dcdaeed9ea62e06efb6e",
    "cross_cats_sorted": [
      "math.CT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.KT",
    "submitted_at": "2013-06-03T05:20:24Z",
    "title_canon_sha256": "d77d29542547d57badb17d90d523a9abf07a17b849e94dc44dd9f382119b4d93"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1306.0296",
    "kind": "arxiv",
    "version": 1
  }
}