Pith Number

pith:U5A47G3N

pith:2010:U5A47G3NDRNVH2H2YRRDSACZSQ

not attested not anchored not stored refs pending

Bar complexes and extensions of classical exponential functors

Antoine Touz\'e

arxiv:1012.2724 v4 · 2010-12-13 · math.RT · 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{U5A47G3NDRNVH2H2YRRDSACZSQ}

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	2026-05-18T03:13:56.572008Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

a741cf9b6d1c5b53e8fac462390059941e453480374836a04d1f935ad42f1e9a

Aliases

arxiv: 1012.2724 · arxiv_version: 1012.2724v4 · doi: 10.48550/arxiv.1012.2724 · pith_short_12: U5A47G3NDRNV · pith_short_16: U5A47G3NDRNVH2H2 · pith_short_8: U5A47G3N

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/U5A47G3NDRNVH2H2YRRDSACZSQ \
  | 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: a741cf9b6d1c5b53e8fac462390059941e453480374836a04d1f935ad42f1e9a

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "5c672714b44b6da00a5bdffbcd48d6ac0e8485e28f1aeac068b6c982346b6f75",
    "cross_cats_sorted": [
      "math.AT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.RT",
    "submitted_at": "2010-12-13T13:32:42Z",
    "title_canon_sha256": "39abddbdc29bfa878c05d25693b10c1acc0c9a73ab18316032a10181556235a4"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1012.2724",
    "kind": "arxiv",
    "version": 4
  }
}