Pith Number

pith:LMVU4DO4

pith:2011:LMVU4DO4PPFF2PK6XZPX5TYQDU

not attested not anchored not stored refs pending

A gap in the spectrum of the Neumann-Laplacian on a periodic waveguide

F.L. Bakharev, K.M. Ruotsalainen, S.A. Nazarov

arxiv:1110.5990 v1 · 2011-10-27 · 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{LMVU4DO4PPFF2PK6XZPX5TYQDU}

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	2026-05-18T03:38:33.150053Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

5b2b4e0ddc7bca5d3d5ebe5f7ecf101d0f753604a4d0486e9eba11f84b25c236

Aliases

arxiv: 1110.5990 · arxiv_version: 1110.5990v1 · doi: 10.48550/arxiv.1110.5990 · pith_short_12: LMVU4DO4PPFF · pith_short_16: LMVU4DO4PPFF2PK6 · pith_short_8: LMVU4DO4

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/LMVU4DO4PPFF2PK6XZPX5TYQDU \
  | 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: 5b2b4e0ddc7bca5d3d5ebe5f7ecf101d0f753604a4d0486e9eba11f84b25c236

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "2d058cfc21b2e57e1a63bf5a838a05f145126bbc1d719c5400ad7dc59f9c6a2a",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.SP",
    "submitted_at": "2011-10-27T06:26:51Z",
    "title_canon_sha256": "297dd88b7a59c5042e80d3ed13a9f3e49551f1aabfaf69f7db370ca21b9e415e"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1110.5990",
    "kind": "arxiv",
    "version": 1
  }
}