Pith Number

pith:7LJMK6EM

pith:2013:7LJMK6EMEUL7VC7PXUIXZM5ZKC

not attested not anchored not stored refs pending

$W$-entropy formula for the Witten Laplacian on manifolds with time dependent metrics and potentials

Songzi Li, Xiang-Dong Li

arxiv:1303.6019 v2 · 2013-03-25 · 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{7LJMK6EMEUL7VC7PXUIXZM5ZKC}

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	2026-05-18T01:22:25.541455Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

fad2c5788c2517fa8befbd117cb3b950b7872bdb9221a5ce69e6775f226c81aa

Aliases

arxiv: 1303.6019 · arxiv_version: 1303.6019v2 · doi: 10.48550/arxiv.1303.6019 · pith_short_12: 7LJMK6EMEUL7 · pith_short_16: 7LJMK6EMEUL7VC7P · pith_short_8: 7LJMK6EM

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/7LJMK6EMEUL7VC7PXUIXZM5ZKC \
  | 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: fad2c5788c2517fa8befbd117cb3b950b7872bdb9221a5ce69e6775f226c81aa

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "41037ce9f14184c377b7eb0a073bd6dde18c67653dbf850fac9682d4e5797313",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/3.0/",
    "primary_cat": "math.DG",
    "submitted_at": "2013-03-25T02:53:38Z",
    "title_canon_sha256": "1e78d69d5b3dba045b365375a5c0900298b405d68f94184599e0f14e5158fcc2"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1303.6019",
    "kind": "arxiv",
    "version": 2
  }
}