Pith Number

pith:DQA63GPF

pith:2011:DQA63GPF2GH7DOOHZZX6EDJLNH

not attested not anchored not stored refs pending

A Compact Embedding Theorem for Generalized Sobolev Spaces

Richard L. Wheeden, Scott Rodney, Seng-Kee Chua

arxiv:1110.6907 v1 · 2011-10-31 · math.AP

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{DQA63GPF2GH7DOOHZZX6EDJLNH}

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	2026-05-18T04:09:53.920406Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

1c01ed99e5d18ff1b9c7ce6fe20d2b69f9476d419d7e486fd387f3190f2c46ef

Aliases

arxiv: 1110.6907 · arxiv_version: 1110.6907v1 · doi: 10.48550/arxiv.1110.6907 · pith_short_12: DQA63GPF2GH7 · pith_short_16: DQA63GPF2GH7DOOH · pith_short_8: DQA63GPF

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/DQA63GPF2GH7DOOHZZX6EDJLNH \
  | 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: 1c01ed99e5d18ff1b9c7ce6fe20d2b69f9476d419d7e486fd387f3190f2c46ef

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "cc9b8bff31e80c5c8baa86958b46945ff6dcbb8ba11fdd88538510ecc7c787af",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2011-10-31T19:08:10Z",
    "title_canon_sha256": "293d391344f4e92f48950f1b4049783b0ffaf26261608b844475322e491daefa"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1110.6907",
    "kind": "arxiv",
    "version": 1
  }
}