Pith Number

pith:2JSBLYGF

pith:2018:2JSBLYGFUNNJ7XE63GJWXH7GZM

not attested not anchored not stored refs pending

Sharp Li-Yau type gradient estimates on hyperbolic spaces

Chengjie Yu, Feifei Zhao

arxiv:1807.05710 v2 · 2018-07-16 · 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{2JSBLYGFUNNJ7XE63GJWXH7GZM}

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	2026-05-18T00:09:41.219482Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

d26415e0c5a35a9fdc9ed9936b9fe6cb2ce55ff4b486b7ff6d80c060a5d13611

Aliases

arxiv: 1807.05710 · arxiv_version: 1807.05710v2 · doi: 10.48550/arxiv.1807.05710 · pith_short_12: 2JSBLYGFUNNJ · pith_short_16: 2JSBLYGFUNNJ7XE6 · pith_short_8: 2JSBLYGF

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/2JSBLYGFUNNJ7XE63GJWXH7GZM \
  | 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: d26415e0c5a35a9fdc9ed9936b9fe6cb2ce55ff4b486b7ff6d80c060a5d13611

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "94b5820066b864f56dd74adc765258e85f1c1c324bfe8cef4921082b80ccd341",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DG",
    "submitted_at": "2018-07-16T07:45:44Z",
    "title_canon_sha256": "12d96cb8d67ea28cfcb6b4cbef1261fb786e0b313c91cd79526e7872456be442"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1807.05710",
    "kind": "arxiv",
    "version": 2
  }
}