Pith Number

pith:B5XOH2EJ

pith:1998:B5XOH2EJ3ARLLPPAPCOWW4PD3P

not attested not anchored not stored refs pending

Existence of the spectral gap for elliptic operators

Feng-Yu Wang

arxiv:math/9804151 v1 · 1998-04-14 · math.DG · 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{B5XOH2EJ3ARLLPPAPCOWW4PD3P}

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	2026-05-18T01:05:34.059547Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

0f6ee3e889d822b5bde0789d6b71e3dbe722e794f5089f5ab42b4a8291066616

Aliases

arxiv: math/9804151 · arxiv_version: math/9804151v1 · doi: 10.48550/arxiv.math/9804151 · pith_short_12: B5XOH2EJ3ARL · pith_short_16: B5XOH2EJ3ARLLPPA · pith_short_8: B5XOH2EJ

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/B5XOH2EJ3ARLLPPAPCOWW4PD3P \
  | 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: 0f6ee3e889d822b5bde0789d6b71e3dbe722e794f5089f5ab42b4a8291066616

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "c70b2435c4107b6745005f99cc1c54f668348865ddcfbe650f2ee27063e57ec5",
    "cross_cats_sorted": [
      "math.SP"
    ],
    "license": "",
    "primary_cat": "math.DG",
    "submitted_at": "1998-04-14T00:00:00Z",
    "title_canon_sha256": "ec60cdc7fed4bfd03ff58a9ef429cd5bb67c95d4a60795d6aedde0782eae5824"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/9804151",
    "kind": "arxiv",
    "version": 1
  }
}