Pith Number

pith:V2RGWPTJ

pith:2024:V2RGWPTJNIXE3XMVJUQN3EKGOC

not attested not anchored not stored refs pending

Several isoperimetric inequalities of Dirichlet and Neumann eigenvalues of the Witten-Laplacian

Jing Mao, Ruifeng Chen

arxiv:2403.08075 v3 · 2024-03-12 · math.AP · 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{V2RGWPTJNIXE3XMVJUQN3EKGOC}

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	2026-07-05T11:19:48.463353Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

aea26b3e696a2e4ddd954d20dd914670b06cd378d88566b3d817afa56e5897f3

Aliases

arxiv: 2403.08075 · arxiv_version: 2403.08075v3 · doi: 10.48550/arxiv.2403.08075 · pith_short_12: V2RGWPTJNIXE · pith_short_16: V2RGWPTJNIXE3XMV · pith_short_8: V2RGWPTJ

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/V2RGWPTJNIXE3XMVJUQN3EKGOC \
  | 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: aea26b3e696a2e4ddd954d20dd914670b06cd378d88566b3d817afa56e5897f3

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "cfc31bf3d00de53a90eca0d66b88bac38d4302c055d6577c2eaa38d21c968c8c",
    "cross_cats_sorted": [
      "math.DG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2024-03-12T20:58:51Z",
    "title_canon_sha256": "3f134055ed258950f90f58f0af645740592bb1eeacc76ed0a13d5e3c94816349"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2403.08075",
    "kind": "arxiv",
    "version": 3
  }
}