Pith Number

pith:4XNN3ZZI

pith:2019:4XNN3ZZIFU2S3QJFWKCQSDOK2S

not attested not anchored not stored refs pending

Periodic spectrum of $n$-cubic quantun graphs

Chun-Kong Law, Tui-En Wang, Yu-Chun Luo

arxiv:1903.07332 v2 · 2019-03-18 · math.SP · math-ph · math.MP

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{4XNN3ZZIFU2S3QJFWKCQSDOK2S}

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	2026-05-17T23:49:24.479646Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e5dadde7282d352dc125b285090dcad4ab635276d500415416fe240fe78b89c8

Aliases

arxiv: 1903.07332 · arxiv_version: 1903.07332v2 · doi: 10.48550/arxiv.1903.07332 · pith_short_12: 4XNN3ZZIFU2S · pith_short_16: 4XNN3ZZIFU2S3QJF · pith_short_8: 4XNN3ZZI

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/4XNN3ZZIFU2S3QJFWKCQSDOK2S \
  | 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: e5dadde7282d352dc125b285090dcad4ab635276d500415416fe240fe78b89c8

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "6274192900feadfde7ffbfcc33720b0d3674b9982b0aa5a9cba25270d46f6f05",
    "cross_cats_sorted": [
      "math-ph",
      "math.MP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.SP",
    "submitted_at": "2019-03-18T09:47:46Z",
    "title_canon_sha256": "952a35da6a7d928092b32ce5e4eada06b6d9c9bffe22159d909d48a23832d0d9"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1903.07332",
    "kind": "arxiv",
    "version": 2
  }
}