Pith Number

pith:TMN5IXTD

pith:2011:TMN5IXTDFYGHBYG6HLGGX56PWZ

not attested not anchored not stored refs pending

PA mapping classes with minimum dilatation and Lanneau-Thiffeault polynomials

Joan S. Birman

arxiv:1104.2873 v2 · 2011-04-14 · 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{TMN5IXTDFYGHBYG6HLGGX56PWZ}

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	2026-05-18T02:22:09.083373Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

9b1bd45e632e0c70e0de3acc6bf7cfb67a0761e2d8e3e82c69de26b1777505b1

Aliases

arxiv: 1104.2873 · arxiv_version: 1104.2873v2 · doi: 10.48550/arxiv.1104.2873 · pith_short_12: TMN5IXTDFYGH · pith_short_16: TMN5IXTDFYGHBYG6 · pith_short_8: TMN5IXTD

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/TMN5IXTDFYGHBYG6HLGGX56PWZ \
  | 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: 9b1bd45e632e0c70e0de3acc6bf7cfb67a0761e2d8e3e82c69de26b1777505b1

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "7218262956a79f562d4b78dc8eab8992fb6cb876251b3eafc6490a0915f31a55",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GT",
    "submitted_at": "2011-04-14T19:04:17Z",
    "title_canon_sha256": "ef830a02c7282808d4ac417d28d5f1264a04ce62317d283697fdc02eb6d3c948"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1104.2873",
    "kind": "arxiv",
    "version": 2
  }
}