Pith Number

pith:2VPJU3KI

pith:2013:2VPJU3KIYMS77QFXSUDEDHE6KG

not attested not anchored not stored refs pending

Hajlasz Gradients Are Upper Gradients

Dachun Yang, Nageswari Shanmugalingam, Renjin Jiang, Wen Yuan

arxiv:1307.5134 v3 · 2013-07-19 · math.FA · math.CA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{2VPJU3KIYMS77QFXSUDEDHE6KG}

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	2026-05-18T02:32:31.102507Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

d55e9a6d48c325ffc0b79506419c9e5195b0902389b1ff1032f9df4755adbf1b

Aliases

arxiv: 1307.5134 · arxiv_version: 1307.5134v3 · doi: 10.48550/arxiv.1307.5134 · pith_short_12: 2VPJU3KIYMS7 · pith_short_16: 2VPJU3KIYMS77QFX · pith_short_8: 2VPJU3KI

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/2VPJU3KIYMS77QFXSUDEDHE6KG \
  | 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: d55e9a6d48c325ffc0b79506419c9e5195b0902389b1ff1032f9df4755adbf1b

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "8c5c6e1bec27ba1b2b92e72a72bab6af1e06af8c3a2640e11fdb444962192df7",
    "cross_cats_sorted": [
      "math.CA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.FA",
    "submitted_at": "2013-07-19T06:02:10Z",
    "title_canon_sha256": "a31c2cc5f65b68e87c1fd6bdfbbdd89ddc493f2e6c40f629b4708ef640fa845c"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1307.5134",
    "kind": "arxiv",
    "version": 3
  }
}