Pith Number

pith:WPJ2TUND

pith:2011:WPJ2TUNDL47W5HBF64P537KDFQ

not attested not anchored not stored refs pending

Curvatures of Sobolev metrics on diffeomorphism groups

Boris Khesin, Gerard Misiolek, Jonatan Lenells, Stephen C. Preston

arxiv:1109.1816 v2 · 2011-09-08 · math.AP · 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{WPJ2TUNDL47W5HBF64P537KDFQ}

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	2026-05-18T04:13:46.694991Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b3d3a9d1a35f3f6e9c25f71fddfd432c15646da17e2af04766b270a46507d71e

Aliases

arxiv: 1109.1816 · arxiv_version: 1109.1816v2 · doi: 10.48550/arxiv.1109.1816 · pith_short_12: WPJ2TUNDL47W · pith_short_16: WPJ2TUNDL47W5HBF · pith_short_8: WPJ2TUND

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/WPJ2TUNDL47W5HBF64P537KDFQ \
  | 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: b3d3a9d1a35f3f6e9c25f71fddfd432c15646da17e2af04766b270a46507d71e

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "72015f6dd14c134831cc81056bfc9e73a4aaae26729bb5113b11759da99c50ef",
    "cross_cats_sorted": [
      "math.DG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2011-09-08T19:48:53Z",
    "title_canon_sha256": "aa5f025443eab3455b3e55ce0e7eeeb50aa55c52974b7ceb2be38d9130c54fb2"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1109.1816",
    "kind": "arxiv",
    "version": 2
  }
}