Pith Number

pith:WB7XGCM7

pith:2013:WB7XGCM7I7UXOVTEFP4YQOV2Q2

not attested not anchored not stored refs pending

Solvability of the divergence equation implies John via Poincar\'e inequality

Aapo Kauranen, Pekka Koskela, Renjin Jiang

arxiv:1307.1340 v1 · 2013-07-04 · math.CA · math.AP

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{WB7XGCM7I7UXOVTEFP4YQOV2Q2}

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	2026-05-18T03:19:14.021539Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b07f73099f47e97756642bf9883aba8681b0540444a60b2b3f36f94af1d8150e

Aliases

arxiv: 1307.1340 · arxiv_version: 1307.1340v1 · doi: 10.48550/arxiv.1307.1340 · pith_short_12: WB7XGCM7I7UX · pith_short_16: WB7XGCM7I7UXOVTE · pith_short_8: WB7XGCM7

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/WB7XGCM7I7UXOVTEFP4YQOV2Q2 \
  | 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: b07f73099f47e97756642bf9883aba8681b0540444a60b2b3f36f94af1d8150e

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "aef0c6a0d2cc271bb1093792a27a0c8e203535d8037f535c873144d1be170003",
    "cross_cats_sorted": [
      "math.AP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CA",
    "submitted_at": "2013-07-04T14:16:05Z",
    "title_canon_sha256": "f6be888bd49c3e0f35330717442a0d97b6635c548bd13f5f6f02faa9a8efabfc"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1307.1340",
    "kind": "arxiv",
    "version": 1
  }
}