Pith Number

pith:VIT74UQK

pith:2022:VIT74UQKVXIVSDCC6CCVW4LNIA

not attested not anchored not stored refs pending

Fibered 3-manifolds and Veech groups

Christopher J. Leininger, Emily Shinkle, Kasra Rafi, Nicholas Rouse, Yvon Verberne

arxiv:2212.13320 v3 · 2022-12-26 · 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{VIT74UQKVXIVSDCC6CCVW4LNIA}

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	2026-07-05T11:29:45.434654Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

aa27fe520aadd1590c42f0855b716d401c9f3830d9e1f0e76a2caabf1daaaeec

Aliases

arxiv: 2212.13320 · arxiv_version: 2212.13320v3 · doi: 10.48550/arxiv.2212.13320 · pith_short_12: VIT74UQKVXIV · pith_short_16: VIT74UQKVXIVSDCC · pith_short_8: VIT74UQK

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/VIT74UQKVXIVSDCC6CCVW4LNIA \
  | 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: aa27fe520aadd1590c42f0855b716d401c9f3830d9e1f0e76a2caabf1daaaeec

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "f0b75f5385147ce2f983fac98f0bfefaa706d1de2f0cc859860164712870a917",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GT",
    "submitted_at": "2022-12-26T23:24:36Z",
    "title_canon_sha256": "cff4100a7d2182afd91e0de629addd1cf71a8dd32519cf78af98a9dcab4812a9"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2212.13320",
    "kind": "arxiv",
    "version": 3
  }
}