Pith Number

pith:2V6C35YQ

pith:2026:2V6C35YQZ6EGFBRCK4FVXNR2UW

not attested not anchored not stored refs pending

Spectral and Geometric Stability for the Reciprocal Sum of Neumann Eigenvalues

Yulong Li, Zuoqin Wang

arxiv:2607.19008 v1 · 2026-07-21 · math.SP

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{2V6C35YQZ6EGFBRCK4FVXNR2UW}

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	2026-07-22T01:24:04.209391Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

d57c2df710cf88628622570b5bb63aa5b0db9edef50ced527c1f3e7dfcf7d40b

Aliases

arxiv: 2607.19008 · arxiv_version: 2607.19008v1 · doi: 10.48550/arxiv.2607.19008 · pith_short_12: 2V6C35YQZ6EG · pith_short_16: 2V6C35YQZ6EGFBRC · pith_short_8: 2V6C35YQ

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/2V6C35YQZ6EGFBRCK4FVXNR2UW \
  | 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: d57c2df710cf88628622570b5bb63aa5b0db9edef50ced527c1f3e7dfcf7d40b

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "7c4796364da5f009ee20f1ae62ab8cadeaf4d53baeaecdce50896640951d6aa9",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.SP",
    "submitted_at": "2026-07-21T11:48:01Z",
    "title_canon_sha256": "3a789cb19fd773b09ea991d954e9083f0dc3b2a7bad1db487d49728b9ace688f"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2607.19008",
    "kind": "arxiv",
    "version": 1
  }
}