Pith Number

pith:COOEJIK2

pith:2024:COOEJIK2AALIPJTVZQQTPLQJGR

not attested not anchored not stored refs pending

Generators for the level $m$ congruence subgroups of braid groups

Ishan Banerjee, Peter Huxford

arxiv:2409.09612 v1 · 2024-09-15 · math.GR · math.GT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{COOEJIK2AALIPJTVZQQTPLQJGR}

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	2026-07-05T09:07:12.047482Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

139c44a15a001687a675cc2137ae09345d73ab387df5806d4def90f590b71802

Aliases

arxiv: 2409.09612 · arxiv_version: 2409.09612v1 · doi: 10.48550/arxiv.2409.09612 · pith_short_12: COOEJIK2AALI · pith_short_16: COOEJIK2AALIPJTV · pith_short_8: COOEJIK2

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/COOEJIK2AALIPJTVZQQTPLQJGR \
  | 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: 139c44a15a001687a675cc2137ae09345d73ab387df5806d4def90f590b71802

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "589c3deb826d9724500162c5bb6cbd7b914e5b2ce2ff3f78d849807e1e427179",
    "cross_cats_sorted": [
      "math.GT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2024-09-15T04:43:29Z",
    "title_canon_sha256": "68252b3f54f865345321f7f55216b7bc2d499d5cf0f885ee8dab0bbb949f690d"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2409.09612",
    "kind": "arxiv",
    "version": 1
  }
}