Pith Number

pith:QUYKUEOY

pith:2015:QUYKUEOY5NEQJ7V5WHKVIORQIV

not attested not anchored not stored refs pending

Finiteness of the number of minimal atoms in Grothendieck categories

Ryo Kanda

arxiv:1503.02116 v3 · 2015-03-07 · math.RT · math.CT · math.RA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{QUYKUEOY5NEQJ7V5WHKVIORQIV}

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	2026-05-17T23:45:10.365502Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

8530aa11d8eb4904febdb1d5543a304555578c5ecbe9b3f6009e806cc8160847

Aliases

arxiv: 1503.02116 · arxiv_version: 1503.02116v3 · doi: 10.48550/arxiv.1503.02116 · pith_short_12: QUYKUEOY5NEQ · pith_short_16: QUYKUEOY5NEQJ7V5 · pith_short_8: QUYKUEOY

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/QUYKUEOY5NEQJ7V5WHKVIORQIV \
  | 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: 8530aa11d8eb4904febdb1d5543a304555578c5ecbe9b3f6009e806cc8160847

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "6bc56d3e8bce9c7ec76a6eaf8769f65e190e880c4bdb9d9ea32a54e5ec28ed0c",
    "cross_cats_sorted": [
      "math.CT",
      "math.RA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.RT",
    "submitted_at": "2015-03-07T01:41:09Z",
    "title_canon_sha256": "d3bb980c951d21e4380342bfb4461761b4d85d91e002b90506d648380327826f"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1503.02116",
    "kind": "arxiv",
    "version": 3
  }
}