Pith Number

pith:6GUHCNE2

pith:2026:6GUHCNE2IR4ZJJR6JHLGKP7RL7

not attested not anchored not stored refs pending

Eigenvalue comparison theorems for the Witten-Laplacian and the weighted $p$-Laplacian on complete manifolds with a modified Ricci curvature bounded from below

Jing Mao, Qiyue Ma, Ruifeng Chen

arxiv:2607.04588 v1 · 2026-07-06 · 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{6GUHCNE2IR4ZJJR6JHLGKP7RL7}

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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	2026-07-07T02:19:26.029084Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

f1a871349a447994a63e49d6653ff15ffeae9885aceae54ea0d71841889683e0

Aliases

arxiv: 2607.04588 · arxiv_version: 2607.04588v1 · doi: 10.48550/arxiv.2607.04588 · pith_short_12: 6GUHCNE2IR4Z · pith_short_16: 6GUHCNE2IR4ZJJR6 · pith_short_8: 6GUHCNE2

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/6GUHCNE2IR4ZJJR6JHLGKP7RL7 \
  | 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: f1a871349a447994a63e49d6653ff15ffeae9885aceae54ea0d71841889683e0

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "6dc26e0132d533d45c74d3997b132cc6b60805392cdb2c06b3dc0c4f214408fd",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DG",
    "submitted_at": "2026-07-06T01:25:19Z",
    "title_canon_sha256": "8894662e2f52500f9569175c93264b8a13c154af165edb954a1b116a7d36b350"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2607.04588",
    "kind": "arxiv",
    "version": 1
  }
}