Pith Number

pith:AU53IJGN

pith:2019:AU53IJGNOHO2ZLVE3AOLUPOVRO

not attested not anchored not stored refs pending

Strong equivalences of approximation numbers and tractability of weighted anisotropic Sobolev embeddings

Heping Wang, JiDong Hao

arxiv:1907.00589 v1 · 2019-07-01 · math.NA · cs.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{AU53IJGNOHO2ZLVE3AOLUPOVRO}

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	2026-05-17T23:41:51.115565Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

053bb424cd71ddacaea4d81cba3dd58baa72e6f48b847dc0e7071d0aefc35c47

Aliases

arxiv: 1907.00589 · arxiv_version: 1907.00589v1 · doi: 10.48550/arxiv.1907.00589 · pith_short_12: AU53IJGNOHO2 · pith_short_16: AU53IJGNOHO2ZLVE · pith_short_8: AU53IJGN

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/AU53IJGNOHO2ZLVE3AOLUPOVRO \
  | 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: 053bb424cd71ddacaea4d81cba3dd58baa72e6f48b847dc0e7071d0aefc35c47

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "b57dbfc2e0cd0938560dcfbaf5ad66f74953fc1ef86eadacde1e530226eb1383",
    "cross_cats_sorted": [
      "cs.NA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NA",
    "submitted_at": "2019-07-01T07:52:26Z",
    "title_canon_sha256": "23e72421ec95337713773e9a4f48100ec1e8d6b4b83abb524943d1bad7700ffa"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1907.00589",
    "kind": "arxiv",
    "version": 1
  }
}