Pith Number

pith:3YMEJUGJ

pith:2012:3YMEJUGJXEORRN53E52IEQEO7M

not attested not anchored not stored refs pending

Lectures on bifunctors and finite generation of rational cohomology algebras

Wilberd van der Kallen

arxiv:1208.3097 v4 · 2012-08-15 · math.RT · 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{3YMEJUGJXEORRN53E52IEQEO7M}

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	2026-05-18T01:24:31.011820Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

de1844d0c9b91d18b7bb277482408efb346a2fb5c8528638db31279b8c263b04

Aliases

arxiv: 1208.3097 · arxiv_version: 1208.3097v4 · doi: 10.48550/arxiv.1208.3097 · pith_short_12: 3YMEJUGJXEOR · pith_short_16: 3YMEJUGJXEORRN53 · pith_short_8: 3YMEJUGJ

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/3YMEJUGJXEORRN53E52IEQEO7M \
  | 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: de1844d0c9b91d18b7bb277482408efb346a2fb5c8528638db31279b8c263b04

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "dc172d381f94e078df53dfe83b2a310e798c2c0e8cdbfe509bbadfbcaa0ccec2",
    "cross_cats_sorted": [
      "math.CT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.RT",
    "submitted_at": "2012-08-15T11:58:19Z",
    "title_canon_sha256": "d3c2bd8a038037f036896610de9e930a35e879485d8ab4363319d65cd4ac144a"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1208.3097",
    "kind": "arxiv",
    "version": 4
  }
}