Pith Number

pith:XNB6B244

pith:2017:XNB6B2447MC5KNHRJOSZ7QI2EB

not attested not anchored not stored refs pending

Hamilton differential Harnack inequality and $W$-entropy for Witten Laplacian on Riemannian manifolds

Songzi Li, Xiang-Dong Li

arxiv:1707.01644 v2 · 2017-07-06 · 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{XNB6B2447MC5KNHRJOSZ7QI2EB}

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	2026-05-18T00:33:16.657818Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

bb43e0eb9cfb05d534f14ba59fc11a206ad86695fa6d513ef42c5c3b88849e90

Aliases

arxiv: 1707.01644 · arxiv_version: 1707.01644v2 · doi: 10.48550/arxiv.1707.01644 · pith_short_12: XNB6B2447MC5 · pith_short_16: XNB6B2447MC5KNHR · pith_short_8: XNB6B244

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/XNB6B2447MC5KNHRJOSZ7QI2EB \
  | 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: bb43e0eb9cfb05d534f14ba59fc11a206ad86695fa6d513ef42c5c3b88849e90

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "85b50b80dffe8d04869b5219fdacf3ac9b99f99a376da72594206b01cc390525",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DG",
    "submitted_at": "2017-07-06T05:47:14Z",
    "title_canon_sha256": "e69413568a50679410cf09f952c81c643512cc1a7da8ba732dc4c3af3f90a095"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1707.01644",
    "kind": "arxiv",
    "version": 2
  }
}