Pith Number

pith:A5BAFPGO

pith:2010:A5BAFPGOP5B5Y2YL5YV6IX2CXG

not attested not anchored not stored refs pending

A combinatorial algorithm to compute presentations of mapping-class groups of orientable surfaces with one boundary component

Llu\'is Bacardit

arxiv:1101.0233 v1 · 2010-12-31 · 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{A5BAFPGOP5B5Y2YL5YV6IX2CXG}

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	2026-05-18T04:32:10.753255Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

074202bcce7f43dc6b0bee2be45f42b9a719bcae1e7b5d5e8f8637730936da2f

Aliases

arxiv: 1101.0233 · arxiv_version: 1101.0233v1 · doi: 10.48550/arxiv.1101.0233 · pith_short_12: A5BAFPGOP5B5 · pith_short_16: A5BAFPGOP5B5Y2YL · pith_short_8: A5BAFPGO

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/A5BAFPGOP5B5Y2YL5YV6IX2CXG \
  | 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: 074202bcce7f43dc6b0bee2be45f42b9a719bcae1e7b5d5e8f8637730936da2f

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "7819331b4dba290a57b92358db19ffc934d0072d05bde1a64372534971b66014",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2010-12-31T12:06:00Z",
    "title_canon_sha256": "09da479cf716965e51589a7bef66cf5232339dee64d9510180921f83fb1f989b"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1101.0233",
    "kind": "arxiv",
    "version": 1
  }
}