Pith Number

pith:FM6LK4HT

pith:2015:FM6LK4HTU3KKGK7XMTJ6EA2UEW

not attested not anchored not stored refs pending

Essential spectrum of the discrete Laplacian on a perturbed periodic graph

Akito Suzuki, Itaru Sasaki

arxiv:1509.09000 v1 · 2015-09-30 · math-ph · math.MP · 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{FM6LK4HTU3KKGK7XMTJ6EA2UEW}

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	2026-05-18T01:31:29.331097Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

2b3cb570f3a6d4a32bf764d3e203542590615108e711d40728195423135a8f15

Aliases

arxiv: 1509.09000 · arxiv_version: 1509.09000v1 · doi: 10.48550/arxiv.1509.09000 · pith_short_12: FM6LK4HTU3KK · pith_short_16: FM6LK4HTU3KKGK7X · pith_short_8: FM6LK4HT

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/FM6LK4HTU3KKGK7XMTJ6EA2UEW \
  | 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: 2b3cb570f3a6d4a32bf764d3e203542590615108e711d40728195423135a8f15

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "a517cf75a63ce02e47dfe6306b3234114061d5842a893ad0f067719d04ba2c45",
    "cross_cats_sorted": [
      "math.MP",
      "math.SP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math-ph",
    "submitted_at": "2015-09-30T02:55:00Z",
    "title_canon_sha256": "22f271d819cc1a4c9db700644bb955803e7a78f5aa32b04d5fc18db2ab9b6fce"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1509.09000",
    "kind": "arxiv",
    "version": 1
  }
}