Pith Number

pith:MHDXSPWT

pith:2011:MHDXSPWTGBHKYGQIWIYAPK2MB3

not attested not anchored not stored refs pending

Double knot surgeries to S^4 and S^2 x S^2

Selman Akbulut

arxiv:1103.3137 v2 · 2011-03-16 · 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{MHDXSPWTGBHKYGQIWIYAPK2MB3}

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	2026-05-18T02:22:18.849628Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

61c7793ed3304eac1a08b23007ab4c0eef07ae58e6684f4dbfbac5b211eb6832

Aliases

arxiv: 1103.3137 · arxiv_version: 1103.3137v2 · doi: 10.48550/arxiv.1103.3137 · pith_short_12: MHDXSPWTGBHK · pith_short_16: MHDXSPWTGBHKYGQI · pith_short_8: MHDXSPWT

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/MHDXSPWTGBHKYGQIWIYAPK2MB3 \
  | 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: 61c7793ed3304eac1a08b23007ab4c0eef07ae58e6684f4dbfbac5b211eb6832

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "906bb46fcb13bb0862b99d07328712bf45d756afdd3552bb042a2f4a2f891528",
    "cross_cats_sorted": [
      "math.SG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GT",
    "submitted_at": "2011-03-16T10:02:30Z",
    "title_canon_sha256": "20792c4d21fc0d277735d7c2de56227eb653a3d8a4f912a101e5b547ca0219f9"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1103.3137",
    "kind": "arxiv",
    "version": 2
  }
}