Pith Number

pith:FXDPXYXI

pith:2011:FXDPXYXI6B64KGDKYOG5JT4SFF

not attested not anchored not stored refs pending

The Gromov width of 4-dimensional tori

Dusa McDuff, Felix Schlenk, Janko Latschev

arxiv:1111.6566 v2 · 2011-11-28 · 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{FXDPXYXI6B64KGDKYOG5JT4SFF}

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	2026-05-18T02:38:17.966559Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

2dc6fbe2e8f07dc5186ac38dd4cf92295758a34609d61b33e6e5d995eb296f7b

Aliases

arxiv: 1111.6566 · arxiv_version: 1111.6566v2 · doi: 10.48550/arxiv.1111.6566 · pith_short_12: FXDPXYXI6B64 · pith_short_16: FXDPXYXI6B64KGDK · pith_short_8: FXDPXYXI

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/FXDPXYXI6B64KGDKYOG5JT4SFF \
  | 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: 2dc6fbe2e8f07dc5186ac38dd4cf92295758a34609d61b33e6e5d995eb296f7b

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "71c64b09d93ccb19bef237eedbbe711db8aad98898dcc820fb266b6f44ed101b",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.SG",
    "submitted_at": "2011-11-28T19:54:15Z",
    "title_canon_sha256": "d1e43acf7aebe16416dacc9b778d9611da5f58b5bf1881eb2cd903fb7be9f061"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1111.6566",
    "kind": "arxiv",
    "version": 2
  }
}