Pith Number

pith:GU4VQYSY

pith:2015:GU4VQYSYS53RCZPEDFAU6GM2WA

not attested not anchored not stored refs pending

Algebraic Kan extensions along morphisms of internal algebra classifiers

Mark Weber

arxiv:1511.04911 v3 · 2015-11-16 · math.CT · math.AT · math.QA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{GU4VQYSYS53RCZPEDFAU6GM2WA}

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	2026-05-18T01:25:54.702206Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

353958625897771165e419414f199ab01f3cb11ae7df0d3e165207919ffa8ff2

Aliases

arxiv: 1511.04911 · arxiv_version: 1511.04911v3 · doi: 10.48550/arxiv.1511.04911 · pith_short_12: GU4VQYSYS53R · pith_short_16: GU4VQYSYS53RCZPE · pith_short_8: GU4VQYSY

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/GU4VQYSYS53RCZPEDFAU6GM2WA \
  | 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: 353958625897771165e419414f199ab01f3cb11ae7df0d3e165207919ffa8ff2

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "87a96ebc5ffe35194939bd749cc7cf1b3a4586adc558ae5dd280b4641db067d9",
    "cross_cats_sorted": [
      "math.AT",
      "math.QA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CT",
    "submitted_at": "2015-11-16T11:03:57Z",
    "title_canon_sha256": "f390704d8ae3f3c66e78217d88249e9aa1d67d07d0e8b9aa3f32b0ca80adcdb6"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1511.04911",
    "kind": "arxiv",
    "version": 3
  }
}