Pith Number

pith:4Y3J66FI

pith:2015:4Y3J66FI43TSKHLC4PYAW4HVES

not attested not anchored not stored refs pending

A simultaneous generalization of mutation and recollement on a triangulated category

Hiroyuki Nakaoka

arxiv:1512.02173 v2 · 2015-12-07 · 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{4Y3J66FI43TSKHLC4PYAW4HVES}

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	2026-05-18T00:36:41.536741Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e6369f78a8e6e7251d62e3f00b70f524a1ce34e2e01076bd1e6b1a607ae3e2de

Aliases

arxiv: 1512.02173 · arxiv_version: 1512.02173v2 · doi: 10.48550/arxiv.1512.02173 · pith_short_12: 4Y3J66FI43TS · pith_short_16: 4Y3J66FI43TSKHLC · pith_short_8: 4Y3J66FI

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/4Y3J66FI43TSKHLC4PYAW4HVES \
  | 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: e6369f78a8e6e7251d62e3f00b70f524a1ce34e2e01076bd1e6b1a607ae3e2de

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "1acf34e01d0340baf1162765d338c3f0f948671ff5401c36de408a4a0af7a5af",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CT",
    "submitted_at": "2015-12-07T19:13:11Z",
    "title_canon_sha256": "a3cf1748531bc4833dcd3a26b2af1adcfa1e679d0615980146086cf96e7ff9ce"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1512.02173",
    "kind": "arxiv",
    "version": 2
  }
}