Pith Number

pith:RQGPDG4M

pith:2013:RQGPDG4MZOEBBV7LNCCMZ25TDJ

not attested not anchored not stored refs pending

Sobolev spaces on graded groups

Michael Ruzhansky, Veronique Fischer

arxiv:1311.0192 v1 · 2013-11-01 · math.CA · math.SP

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{RQGPDG4MZOEBBV7LNCCMZ25TDJ}

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	2026-05-18T03:08:15.335434Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

8c0cf19b8ccb8810d7eb6884ccebb31a4f0843b9f48749ff116f63df67b9433e

Aliases

arxiv: 1311.0192 · arxiv_version: 1311.0192v1 · doi: 10.48550/arxiv.1311.0192 · pith_short_12: RQGPDG4MZOEB · pith_short_16: RQGPDG4MZOEBBV7L · pith_short_8: RQGPDG4M

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/RQGPDG4MZOEBBV7LNCCMZ25TDJ \
  | 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: 8c0cf19b8ccb8810d7eb6884ccebb31a4f0843b9f48749ff116f63df67b9433e

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "440dfe4852850916ade9dd7699c179cb5f4372c0fe04e6c046f3c394a6471e43",
    "cross_cats_sorted": [
      "math.SP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CA",
    "submitted_at": "2013-11-01T14:26:10Z",
    "title_canon_sha256": "b64bfafbfeb62426fec991b4ff5b13a5863f81c2f9c5ce88f8749da2d16276fd"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1311.0192",
    "kind": "arxiv",
    "version": 1
  }
}