Pith Number

pith:YGPWQB2L

pith:2012:YGPWQB2L2BBQBGW6Y765ROGHKX

not attested not anchored not stored refs pending

Right-invariant Sobolev metrics of fractional order on the diffeomorphism group of the circle

Boris Kolev (I2M), Joachim Escher (IFAM)

arxiv:1202.5122 v4 · 2012-02-23 · math-ph · math.AP · math.MP

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{YGPWQB2L2BBQBGW6Y765ROGHKX}

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	2026-05-18T02:41:43.375244Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

c19f68074bd043009adec7fdd8b8c755f825f4a11e5f79eae3b10074a8a23523

Aliases

arxiv: 1202.5122 · arxiv_version: 1202.5122v4 · doi: 10.48550/arxiv.1202.5122 · pith_short_12: YGPWQB2L2BBQ · pith_short_16: YGPWQB2L2BBQBGW6 · pith_short_8: YGPWQB2L

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/YGPWQB2L2BBQBGW6Y765ROGHKX \
  | 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: c19f68074bd043009adec7fdd8b8c755f825f4a11e5f79eae3b10074a8a23523

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "7f09bbb54c2014e232e54f744cea73a38796247c0dcd49b399cfd4ddc2e01eb2",
    "cross_cats_sorted": [
      "math.AP",
      "math.MP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math-ph",
    "submitted_at": "2012-02-23T09:15:04Z",
    "title_canon_sha256": "d0b2d017ede6629297dc1de10ad34e0a9f6e782ca7e174c9b081f717df727621"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1202.5122",
    "kind": "arxiv",
    "version": 4
  }
}