Pith Number

pith:WOACHN5N

pith:2015:WOACHN5N2DQE4VKPFTPLWVWZIT

not attested not anchored not stored refs pending

Universal property of triangulated derivators via Keller's towers

Marco Porta

arxiv:1512.02691 v2 · 2015-12-08 · math.KT · math.AT · math.CT · math.RT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{WOACHN5N2DQE4VKPFTPLWVWZIT}

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	2026-05-18T00:46:08.339071Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b38023b7add0e04e554f2cdebb56d944ce9ab2cd098ca66aa1b61e2f65905407

Aliases

arxiv: 1512.02691 · arxiv_version: 1512.02691v2 · doi: 10.48550/arxiv.1512.02691 · pith_short_12: WOACHN5N2DQE · pith_short_16: WOACHN5N2DQE4VKP · pith_short_8: WOACHN5N

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/WOACHN5N2DQE4VKPFTPLWVWZIT \
  | 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: b38023b7add0e04e554f2cdebb56d944ce9ab2cd098ca66aa1b61e2f65905407

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "c4220ec82fb8feca4c5667cc1f9a2caf0f8e7b898bff6cffae764b09bd340c3b",
    "cross_cats_sorted": [
      "math.AT",
      "math.CT",
      "math.RT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.KT",
    "submitted_at": "2015-12-08T23:02:25Z",
    "title_canon_sha256": "852cd211c2f58a2cbf9a310a7f7b1ac8e25de39675eab36d8b7784cf659ed74b"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1512.02691",
    "kind": "arxiv",
    "version": 2
  }
}