Pith Number

pith:7BJLXNO5

pith:2018:7BJLXNO5LB3K7KAQSOLKHXCRB4

not attested not anchored not stored refs pending

Discrete Bethe--Sommerfeld Conjecture for Triangular, Square, and Hexagonal Lattices

Jake Fillman, Rui Han

arxiv:1806.01988 v1 · 2018-06-06 · 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{7BJLXNO5LB3K7KAQSOLKHXCRB4}

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	2026-05-18T00:14:03.106960Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

f852bbb5dd5876afa8109396a3dc510f328bf530476c53e205b9f2706d773373

Aliases

arxiv: 1806.01988 · arxiv_version: 1806.01988v1 · doi: 10.48550/arxiv.1806.01988 · pith_short_12: 7BJLXNO5LB3K · pith_short_16: 7BJLXNO5LB3K7KAQ · pith_short_8: 7BJLXNO5

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/7BJLXNO5LB3K7KAQSOLKHXCRB4 \
  | 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: f852bbb5dd5876afa8109396a3dc510f328bf530476c53e205b9f2706d773373

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "c2c4ae83800e4cc6152c81e0513fd9b949c0015dc49d64624fe502e086c50458",
    "cross_cats_sorted": [
      "math-ph",
      "math.MP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.SP",
    "submitted_at": "2018-06-06T02:36:35Z",
    "title_canon_sha256": "f4e7c97c81de5cdc00774ea0db70db3b17cd6bf042f693f98b86254f839a66de"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1806.01988",
    "kind": "arxiv",
    "version": 1
  }
}