Pith Number

pith:X4FYVZDS

pith:2010:X4FYVZDS4WLSHWP5VJDAZEVJX3

not attested not anchored not stored refs pending

Closed surface bundles of least volume

John William Aaber, Nathan M. Dunfield

arxiv:1002.3423 v5 · 2010-02-18 · math.GT · math.DG

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{X4FYVZDS4WLSHWP5VJDAZEVJX3}

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	2026-05-18T02:41:50.937137Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

bf0b8ae472e59723d9fdaa460c92a9bedb8e7e725583e4744f7d1834fc27ec54

Aliases

arxiv: 1002.3423 · arxiv_version: 1002.3423v5 · doi: 10.48550/arxiv.1002.3423 · pith_short_12: X4FYVZDS4WLS · pith_short_16: X4FYVZDS4WLSHWP5 · pith_short_8: X4FYVZDS

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/X4FYVZDS4WLSHWP5VJDAZEVJX3 \
  | 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: bf0b8ae472e59723d9fdaa460c92a9bedb8e7e725583e4744f7d1834fc27ec54

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "68d143da55dd4a33fab3b144ef401296c274875850701ba182533b32fd23a13e",
    "cross_cats_sorted": [
      "math.DG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GT",
    "submitted_at": "2010-02-18T17:36:50Z",
    "title_canon_sha256": "a7e8cb78c4d73458b293a0c006c264d7780bcf49ff3cb54944559658369918fd"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1002.3423",
    "kind": "arxiv",
    "version": 5
  }
}