Pith Number

pith:4F7DATLG

pith:2012:4F7DATLGVBVSNDPYPGYRTACOVE

not attested not anchored not stored refs pending

Banach algebras, Samelson products, and the Wang Differential

Claude L. Schochet

arxiv:1209.4131 v3 · 2012-09-19 · math.OA · 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{4F7DATLGVBVSNDPYPGYRTACOVE}

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	2026-05-18T02:58:22.140956Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e17e304d66a86b268df879b119804ea929097084ba4641c73b814ecbca36ec82

Aliases

arxiv: 1209.4131 · arxiv_version: 1209.4131v3 · doi: 10.48550/arxiv.1209.4131 · pith_short_12: 4F7DATLGVBVS · pith_short_16: 4F7DATLGVBVSNDPY · pith_short_8: 4F7DATLG

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/4F7DATLGVBVSNDPYPGYRTACOVE \
  | 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: e17e304d66a86b268df879b119804ea929097084ba4641c73b814ecbca36ec82

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "1f8b92c21b86dfcd9dfa4beef3ff27fa4421d69a335bea3846f8dd46d9c192d7",
    "cross_cats_sorted": [
      "math.AT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.OA",
    "submitted_at": "2012-09-19T01:40:59Z",
    "title_canon_sha256": "6a1abd801844f4433349ae8b1bcb8aa39f5b4c4fa014a11d3f4e0ad0b3f50f46"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1209.4131",
    "kind": "arxiv",
    "version": 3
  }
}