Pith Number

pith:4HY7VXZI

pith:2012:4HY7VXZIPZEQGY5BQPN3WQQOWN

not attested not anchored not stored refs pending

Cohomology of braids, principal congruence subgroups and geometric representations

Filippo Callegaro, Fred Cohen, Mario Salvetti

arxiv:1207.5652 v1 · 2012-07-24 · 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{4HY7VXZIPZEQGY5BQPN3WQQOWN}

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	2026-05-18T03:50:11.748263Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e1f1fadf287e490363a183dbbb420eb355f6ae1533d4697ce38a0d20cbbcd0e4

Aliases

arxiv: 1207.5652 · arxiv_version: 1207.5652v1 · doi: 10.48550/arxiv.1207.5652 · pith_short_12: 4HY7VXZIPZEQ · pith_short_16: 4HY7VXZIPZEQGY5B · pith_short_8: 4HY7VXZI

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/4HY7VXZIPZEQGY5BQPN3WQQOWN \
  | 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: e1f1fadf287e490363a183dbbb420eb355f6ae1533d4697ce38a0d20cbbcd0e4

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "925e132133ea60ca7f499867d3c11c2676f4bfde085d2225c1bdc78f3a385d01",
    "cross_cats_sorted": [
      "math.GR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AT",
    "submitted_at": "2012-07-24T10:39:34Z",
    "title_canon_sha256": "0d210266fd74417a57d8d632f323d15cc84e909e29ac14ab4c81944ab6523af7"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1207.5652",
    "kind": "arxiv",
    "version": 1
  }
}