Pith Number

pith:ILDBP5M4

pith:2016:ILDBP5M4USWNS5PUT4GV4RLM4Q

not attested not anchored not stored refs pending

Li-Yau gradient estimate for compact manifolds with negative part of Ricci curvature in the Kato class

Christian Rose

arxiv:1608.04221 v2 · 2016-08-15 · 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{ILDBP5M4USWNS5PUT4GV4RLM4Q}

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	2026-05-18T01:03:11.641083Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

42c617f59ca4acd975f49f0d5e456ce4240e642c541bd18d9dfdda91713754bf

Aliases

arxiv: 1608.04221 · arxiv_version: 1608.04221v2 · doi: 10.48550/arxiv.1608.04221 · pith_short_12: ILDBP5M4USWN · pith_short_16: ILDBP5M4USWNS5PU · pith_short_8: ILDBP5M4

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/ILDBP5M4USWNS5PUT4GV4RLM4Q \
  | 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: 42c617f59ca4acd975f49f0d5e456ce4240e642c541bd18d9dfdda91713754bf

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "bd62d32bba5c49e88fbb2e5a36b6fe481650849983d49ff16fb487f712714feb",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DG",
    "submitted_at": "2016-08-15T09:54:57Z",
    "title_canon_sha256": "96e15ad684de109dace9f9813b15a97b9bf88ec8514609832fca476a5963b908"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1608.04221",
    "kind": "arxiv",
    "version": 2
  }
}