Pith Number

pith:27T44BXT

pith:2012:27T44BXTAUTFDKQYCRLKRJB5YJ

not attested not anchored not stored refs pending

Multivariable adjunctions and mates

Emily Riehl, Eugenia Cheng, Nick Gurski

arxiv:1208.4520 v2 · 2012-08-22 · math.CT · math.AT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{27T44BXTAUTFDKQYCRLKRJB5YJ}

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	2026-05-18T03:48:13.022567Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

d7e7ce06f3052651aa181456a8a43dc241ee872208bb651f8670a8edfa8ece77

Aliases

arxiv: 1208.4520 · arxiv_version: 1208.4520v2 · doi: 10.48550/arxiv.1208.4520 · pith_short_12: 27T44BXTAUTF · pith_short_16: 27T44BXTAUTFDKQY · pith_short_8: 27T44BXT

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/27T44BXTAUTFDKQYCRLKRJB5YJ \
  | 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: d7e7ce06f3052651aa181456a8a43dc241ee872208bb651f8670a8edfa8ece77

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "104d4a5940518083b307da1f0f08a86296bcf5cc153fe276adbeb5a271e5c7c5",
    "cross_cats_sorted": [
      "math.AT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CT",
    "submitted_at": "2012-08-22T15:06:39Z",
    "title_canon_sha256": "31be3b2e74a10180d75217ccf4de000c0d129e83e3e4c44ba486e6a6623570c7"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1208.4520",
    "kind": "arxiv",
    "version": 2
  }
}