Pith Number

pith:TTQJX52Y

pith:2009:TTQJX52YBMNC54C4ADAUZBT77P

not attested not anchored not stored refs pending

Small dilatation pseudo-Anosov mapping classes coming from the simplest hyperbolic braid

Eriko Hironaka

arxiv:0909.4517 v2 · 2009-09-24 · 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{TTQJX52YBMNC54C4ADAUZBT77P}

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	2026-05-18T02:41:51.150853Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

9ce09bf7580b1a2ef05c00c14c867ffbcfddc72e9e5d7669de19ed190b9c4799

Aliases

arxiv: 0909.4517 · arxiv_version: 0909.4517v2 · doi: 10.48550/arxiv.0909.4517 · pith_short_12: TTQJX52YBMNC · pith_short_16: TTQJX52YBMNC54C4 · pith_short_8: TTQJX52Y

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/TTQJX52YBMNC54C4ADAUZBT77P \
  | 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: 9ce09bf7580b1a2ef05c00c14c867ffbcfddc72e9e5d7669de19ed190b9c4799

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "9ed332f0c62636af023e367dc9360b7cf88d4ab1da160e58635cc05b772c04f8",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GT",
    "submitted_at": "2009-09-24T19:12:46Z",
    "title_canon_sha256": "f48739574f957ca350c4461000c45536c426493951ae0fece848047009725f3e"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0909.4517",
    "kind": "arxiv",
    "version": 2
  }
}