Pith Number

pith:E4F4MYFR

pith:2011:E4F4MYFRJOXO4EDHR76WEG37TC

not attested not anchored not stored refs pending

A ramification theorem for the ratio of canonical forms of flat surfaces in hyperbolic three-space

Yu Kawakami

arxiv:1110.3110 v3 · 2011-10-14 · math.DG · math.CV

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{E4F4MYFRJOXO4EDHR76WEG37TC}

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	2026-05-18T03:16:19.262155Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

270bc660b14baeee10678ffd621b7f9897b664b9a9da6517105b01d4194e6cad

Aliases

arxiv: 1110.3110 · arxiv_version: 1110.3110v3 · doi: 10.48550/arxiv.1110.3110 · pith_short_12: E4F4MYFRJOXO · pith_short_16: E4F4MYFRJOXO4EDH · pith_short_8: E4F4MYFR

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/E4F4MYFRJOXO4EDHR76WEG37TC \
  | 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: 270bc660b14baeee10678ffd621b7f9897b664b9a9da6517105b01d4194e6cad

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "7456b4724d8a7ad0c9ae8441dc30a797610b5362cdc32c3b186e00aa3399df1e",
    "cross_cats_sorted": [
      "math.CV"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DG",
    "submitted_at": "2011-10-14T02:09:03Z",
    "title_canon_sha256": "d4b6d612b128aec7a86af2f093bb67b27f65eecc1868080fedf53a121ac357c9"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1110.3110",
    "kind": "arxiv",
    "version": 3
  }
}