Pith Number

pith:C4MA274U

pith:2011:C4MA274UHAEWJES76FS7SBKRYB

not attested not anchored not stored refs pending

Gelfand and Kolmogorov numbers of Sobolev embeddings of weighted function spaces

Gensun Fang, Shun Zhang

arxiv:1102.0677 v2 · 2011-02-03 · math.FA · math.NA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{C4MA274UHAEWJES76FS7SBKRYB}

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	2026-05-18T03:51:48.888298Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

17180d7f94380964925ff165f90551c05ec8fe9d8e280de27f529ff9075570d0

Aliases

arxiv: 1102.0677 · arxiv_version: 1102.0677v2 · doi: 10.48550/arxiv.1102.0677 · pith_short_12: C4MA274UHAEW · pith_short_16: C4MA274UHAEWJES7 · pith_short_8: C4MA274U

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/C4MA274UHAEWJES76FS7SBKRYB \
  | 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: 17180d7f94380964925ff165f90551c05ec8fe9d8e280de27f529ff9075570d0

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "2dd3a53fa69094dd6c0165141ee0e9815a7711cd1a6a7ef46c4456a3fecacb0f",
    "cross_cats_sorted": [
      "math.NA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.FA",
    "submitted_at": "2011-02-03T13:24:31Z",
    "title_canon_sha256": "c922f606dc641590c6cf0d9976c61f8598d4c52e0c8277a66c09768dde98e4eb"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1102.0677",
    "kind": "arxiv",
    "version": 2
  }
}