Pith Number

pith:ZFB7BV3F

pith:2016:ZFB7BV3FCGEFZGFUPVTK3LDAIU

not attested not anchored not stored refs pending

Congruence subgroups of braid groups

Charalampos Stylianakis

arxiv:1609.05673 v1 · 2016-09-19 · 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{ZFB7BV3FCGEFZGFUPVTK3LDAIU}

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	2026-05-18T01:04:25.664995Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

c943f0d76511885c98b47d66adac604528e425c3bd3ea368b5b7e50374651de4

Aliases

arxiv: 1609.05673 · arxiv_version: 1609.05673v1 · doi: 10.48550/arxiv.1609.05673 · pith_short_12: ZFB7BV3FCGEF · pith_short_16: ZFB7BV3FCGEFZGFU · pith_short_8: ZFB7BV3F

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/ZFB7BV3FCGEFZGFUPVTK3LDAIU \
  | 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: c943f0d76511885c98b47d66adac604528e425c3bd3ea368b5b7e50374651de4

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "2c6abce743e0ae5b717c7452dda6a013a0e82fbee0e9137d94b90710c24056f6",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2016-09-19T11:35:48Z",
    "title_canon_sha256": "d5549e9119d061c5f93b807b3b97a82473c148f637b559de88d23bf9e6ea2ccd"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1609.05673",
    "kind": "arxiv",
    "version": 1
  }
}