Pith Number

pith:6VL3QMRH

pith:2010:6VL3QMRH7RLOG4QVLRWEGQN7FU

not attested not anchored not stored refs pending

Constructing symmetric monoidal bicategories

Michael A. Shulman

arxiv:1004.0993 v1 · 2010-04-07 · 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{6VL3QMRH7RLOG4QVLRWEGQN7FU}

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.

Cited by

1 paper in Pith

Premonoidal and Kleisli double categories

Receipt and verification

First computed	2026-07-04T17:25:51.576400Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

f557b83227fc56e372155c6c4341bf2d0cccaa07465dcdb3deda44824dba3540

Aliases

arxiv: 1004.0993 · arxiv_version: 1004.0993v1 · doi: 10.48550/arxiv.1004.0993 · pith_short_12: 6VL3QMRH7RLO · pith_short_16: 6VL3QMRH7RLOG4QV · pith_short_8: 6VL3QMRH

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/6VL3QMRH7RLOG4QVLRWEGQN7FU \
  | 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: f557b83227fc56e372155c6c4341bf2d0cccaa07465dcdb3deda44824dba3540

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "b96a85067c598c014ba04e5535ff34a02b2755e3c7059da929df0277ff630d46",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CT",
    "submitted_at": "2010-04-07T02:06:25Z",
    "title_canon_sha256": "546cc4074097f6c862d2ca4bf0294448195798a59a8c5000a7f3f16dc60a4aa0"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1004.0993",
    "kind": "arxiv",
    "version": 1
  }
}