Pith Number

pith:2NVZBCAY

pith:2012:2NVZBCAY4QEKM7ZK7HJEIRDOUC

not attested not anchored not stored refs pending

Duality and traces for indexed monoidal categories

Kate Ponto, Michael Shulman

arxiv:1211.1555 v1 · 2012-11-07 · 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{2NVZBCAY4QEKM7ZK7HJEIRDOUC}

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	2026-05-18T03:41:20.761435Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

d36b908818e408a67f2af9d244446ea0bf8f3c785c4bbdb5e56ecbe6646e5878

Aliases

arxiv: 1211.1555 · arxiv_version: 1211.1555v1 · doi: 10.48550/arxiv.1211.1555 · pith_short_12: 2NVZBCAY4QEK · pith_short_16: 2NVZBCAY4QEKM7ZK · pith_short_8: 2NVZBCAY

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/2NVZBCAY4QEKM7ZK7HJEIRDOUC \
  | 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: d36b908818e408a67f2af9d244446ea0bf8f3c785c4bbdb5e56ecbe6646e5878

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "20bc80c71281797c64eba757c2699995e69c12bcb30988ee4a4670522a9182e7",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CT",
    "submitted_at": "2012-11-07T14:15:15Z",
    "title_canon_sha256": "72f6533dd156d236b9a2d8192a3b36fad99a10feedf4dca831010f53331faf32"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1211.1555",
    "kind": "arxiv",
    "version": 1
  }
}