Pith Number

pith:XBGHG3AE

pith:2025:XBGHG3AECRW3SP4L47Y5NX34KE

not attested not anchored not stored refs pending

Monotonicity of discrete spectra of Dirichlet Laplacian in 3-dimensional layers

Fedor Bakharev, Sergey Matveenko

arxiv:2508.12696 v3 · 2025-08-18 · math.SP · math.AP

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{XBGHG3AECRW3SP4L47Y5NX34KE}

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	2026-05-21T02:04:51.295072Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b84c736c04146db93f8be7f1d6df7c513920549ccc767870bf980f1ba5b42301

Aliases

arxiv: 2508.12696 · arxiv_version: 2508.12696v3 · doi: 10.48550/arxiv.2508.12696 · pith_short_12: XBGHG3AECRW3 · pith_short_16: XBGHG3AECRW3SP4L · pith_short_8: XBGHG3AE

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/XBGHG3AECRW3SP4L47Y5NX34KE \
  | 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: b84c736c04146db93f8be7f1d6df7c513920549ccc767870bf980f1ba5b42301

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "2abd4e44c7be2fc5f76d67c35dd6e36f5010c3df6af89a76cc2a1bbeaa9782f6",
    "cross_cats_sorted": [
      "math.AP"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.SP",
    "submitted_at": "2025-08-18T07:54:42Z",
    "title_canon_sha256": "141508926c73aa317c17e846e87861bd77d72dc7099c8bb5a2dd57f7905e4e99"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2508.12696",
    "kind": "arxiv",
    "version": 3
  }
}