Pith Number

pith:BKMGDX56

pith:2010:BKMGDX56XCQBNMVATGPC3DHDQ3

not attested not anchored not stored refs pending

Criteria for Optimal Global Integrability of Haj{\l}asz-Sobolev Functions

Yuan Zhou

arxiv:1004.5304 v1 · 2010-04-29 · math.CA · math.AP · 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{BKMGDX56XCQBNMVATGPC3DHDQ3}

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	2026-05-18T02:24:15.044641Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

0a9861dfbeb8a016b2a0999e2d8ce386cd30f039c2fab00c6d83e24cc7bfded4

Aliases

arxiv: 1004.5304 · arxiv_version: 1004.5304v1 · doi: 10.48550/arxiv.1004.5304 · pith_short_12: BKMGDX56XCQB · pith_short_16: BKMGDX56XCQBNMVA · pith_short_8: BKMGDX56

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/BKMGDX56XCQBNMVATGPC3DHDQ3 \
  | 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: 0a9861dfbeb8a016b2a0999e2d8ce386cd30f039c2fab00c6d83e24cc7bfded4

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "780ab1807f6abc35e3775711025f4258daebe1aacd63c2b8b9abfe9e8c703779",
    "cross_cats_sorted": [
      "math.AP",
      "math.FA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CA",
    "submitted_at": "2010-04-29T14:32:10Z",
    "title_canon_sha256": "6387388cdd223d7b358a81abc330407b065d5386bb049be4367bdb5f55a49bea"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1004.5304",
    "kind": "arxiv",
    "version": 1
  }
}