Pith Number

pith:BZ2JFGXU

pith:2020:BZ2JFGXUZNOS3V522NCLUNI5OE

not attested not anchored not stored refs pending

Yau and Souplet-Zhang type gradient estimates on Riemannian manifolds with boundary under Dirichlet boundary condition

Keita Kunikawa, Yohei Sakurai

arxiv:2012.09374 v2 · 2020-12-17 · math.DG

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{BZ2JFGXUZNOS3V522NCLUNI5OE}

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	2026-07-05T03:01:34.503877Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

0e74929af4cb5d2dd7bad344ba351d71164eea5870daa2e1c77392db0fb74ddf

Aliases

arxiv: 2012.09374 · arxiv_version: 2012.09374v2 · doi: 10.48550/arxiv.2012.09374 · pith_short_12: BZ2JFGXUZNOS · pith_short_16: BZ2JFGXUZNOS3V52 · pith_short_8: BZ2JFGXU

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/BZ2JFGXUZNOS3V522NCLUNI5OE \
  | 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: 0e74929af4cb5d2dd7bad344ba351d71164eea5870daa2e1c77392db0fb74ddf

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "37358e3821e8fccffd1d13e2ab9185ba74fc5d800bd4d7b45790d04a85a6c431",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.DG",
    "submitted_at": "2020-12-17T02:59:28Z",
    "title_canon_sha256": "4132e32b4c9c1bfcffbf5e50422401fc1045bbd8607a9fb511ad66d412ac736d"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2012.09374",
    "kind": "arxiv",
    "version": 2
  }
}