Pith Number

pith:6XXWBIVX

pith:2012:6XXWBIVXWZGWDXW2VEG5RBE4XF

not attested not anchored not stored refs pending

Essential open book foliation and fractional Dehn twist coefficient

Keiko Kawamuro, Tetsuya Ito

arxiv:1208.1559 v4 · 2012-08-08 · math.GT · math.SG

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{6XXWBIVXWZGWDXW2VEG5RBE4XF}

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	2026-05-18T01:34:30.281948Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

f5ef60a2b7b64d61dedaa90dd8849cb96ab58c4ffacd8a8b45d20c737727a77e

Aliases

arxiv: 1208.1559 · arxiv_version: 1208.1559v4 · doi: 10.48550/arxiv.1208.1559 · pith_short_12: 6XXWBIVXWZGW · pith_short_16: 6XXWBIVXWZGWDXW2 · pith_short_8: 6XXWBIVX

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/6XXWBIVXWZGWDXW2VEG5RBE4XF \
  | 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: f5ef60a2b7b64d61dedaa90dd8849cb96ab58c4ffacd8a8b45d20c737727a77e

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "d820eccd003a0e76a3bcd562e90bb2b88f347841037e38fb396b36c23e1adb7b",
    "cross_cats_sorted": [
      "math.SG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GT",
    "submitted_at": "2012-08-08T01:21:09Z",
    "title_canon_sha256": "442750dea049b4720e63c90813ebd6c8f59a3bf7847f3955f28211c41166d8c6"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1208.1559",
    "kind": "arxiv",
    "version": 4
  }
}