Pith Number

pith:32UYUB5C

pith:2012:32UYUB5CS5MEMPD6CPNVULJFEJ

not attested not anchored not stored refs pending

The cohomology of the braid group B_3 and of SL_2(Z) with coefficients in a geometric representation

Filippo Callegaro, Fred Cohen, Mario Salvetti

arxiv:1204.5390 v1 · 2012-04-24 · math.AT · math.GR

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{32UYUB5CS5MEMPD6CPNVULJFEJ}

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	2026-05-18T03:57:13.352501Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

dea98a07a29758463c7e13db5a2d2522463517feee9b941e87066649940bf5e5

Aliases

arxiv: 1204.5390 · arxiv_version: 1204.5390v1 · doi: 10.48550/arxiv.1204.5390 · pith_short_12: 32UYUB5CS5ME · pith_short_16: 32UYUB5CS5MEMPD6 · pith_short_8: 32UYUB5C

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/32UYUB5CS5MEMPD6CPNVULJFEJ \
  | 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: dea98a07a29758463c7e13db5a2d2522463517feee9b941e87066649940bf5e5

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "26de9d98e0bb352fd250b5d0fc6535a61db6e1a552f71bddbff67d88f526a53d",
    "cross_cats_sorted": [
      "math.GR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AT",
    "submitted_at": "2012-04-24T14:37:16Z",
    "title_canon_sha256": "e92a3af5b97044639ab80de6ae16754b1cc21716b448a07b5ed5e7cba12bdcf8"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1204.5390",
    "kind": "arxiv",
    "version": 1
  }
}