Pith Number

pith:KKSJ6Y2K

pith:2014:KKSJ6Y2KE4U5GB6TFUFS4DIGBF

not attested not anchored not stored refs pending

Notes on commutation of limits and colimits

Marie Bjerrum, Peter Johnstone, Tom Leinster, William F. Sawin

arxiv:1409.7860 v2 · 2014-09-28 · math.CT · math.GR

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{KKSJ6Y2KE4U5GB6TFUFS4DIGBF}

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	2026-05-18T02:17:01.143534Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

52a49f634a2729d307d32d0b2e0d060956c1a911dd89841673feedd61633df1c

Aliases

arxiv: 1409.7860 · arxiv_version: 1409.7860v2 · doi: 10.48550/arxiv.1409.7860 · pith_short_12: KKSJ6Y2KE4U5 · pith_short_16: KKSJ6Y2KE4U5GB6T · pith_short_8: KKSJ6Y2K

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/KKSJ6Y2KE4U5GB6TFUFS4DIGBF \
  | 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: 52a49f634a2729d307d32d0b2e0d060956c1a911dd89841673feedd61633df1c

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "57c27d229963f456844f69f86a29ce33118d184c799ad49364cbaec8ee40c41c",
    "cross_cats_sorted": [
      "math.GR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CT",
    "submitted_at": "2014-09-28T01:23:58Z",
    "title_canon_sha256": "cd998337291eedddcb4ba0c1bd6590e590296a7ede15860c4b3090f88c8a91c2"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1409.7860",
    "kind": "arxiv",
    "version": 2
  }
}