Pith Number

pith:FDHDVVFM

pith:2016:FDHDVVFMVPKILF4P2SA5E5TXM5

not attested not anchored not stored refs pending

Probabilistic and average linear widths of weighted Sobolev spaces on the ball equipped with a Gaussian measure

Heping Wang

arxiv:1603.04578 v1 · 2016-03-15 · math.CA · math.FA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{FDHDVVFMVPKILF4P2SA5E5TXM5}

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	2026-05-18T01:19:04.475773Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

28ce3ad4acabd485978fd481d276776767b52a8a5943733ddef0e968b28f4086

Aliases

arxiv: 1603.04578 · arxiv_version: 1603.04578v1 · doi: 10.48550/arxiv.1603.04578 · pith_short_12: FDHDVVFMVPKI · pith_short_16: FDHDVVFMVPKILF4P · pith_short_8: FDHDVVFM

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/FDHDVVFMVPKILF4P2SA5E5TXM5 \
  | 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: 28ce3ad4acabd485978fd481d276776767b52a8a5943733ddef0e968b28f4086

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "d1c4226b05689a5cb5d86fbeff5d28aaf8a16c67956f6b8f3c5d2721652d2a40",
    "cross_cats_sorted": [
      "math.FA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CA",
    "submitted_at": "2016-03-15T07:30:32Z",
    "title_canon_sha256": "80cb1eb2a45e5858c538144fe1e870940f9852e03b0398014fd99aa63021c16b"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1603.04578",
    "kind": "arxiv",
    "version": 1
  }
}