Pith Number

pith:HLQFFQXK

pith:2022:HLQFFQXKKAR4VFNBE5YT2Q5ZNF

not attested not anchored not stored refs pending

Arbitrarily small spectral gaps for random hyperbolic surfaces with many cusps

Yang Shen, Yunhui Wu

arxiv:2203.15681 v4 · 2022-03-29 · math.DG · math.GT · math.PR · math.SP

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Add to your LaTeX paper

\usepackage{pith}
\pithnumber{HLQFFQXKKAR4VFNBE5YT2Q5ZNF}

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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.

Cited by

1 paper in Pith

Spectral gaps on thick part of moduli spaces

Receipt and verification

First computed	2026-07-05T11:37:58.410883Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

3ae052c2ea5023ca95a127713d43b96951751889a45c8438a8234ef533ad0795

Aliases

arxiv: 2203.15681 · arxiv_version: 2203.15681v4 · doi: 10.48550/arxiv.2203.15681 · pith_short_12: HLQFFQXKKAR4 · pith_short_16: HLQFFQXKKAR4VFNB · pith_short_8: HLQFFQXK

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/HLQFFQXKKAR4VFNBE5YT2Q5ZNF \
  | 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: 3ae052c2ea5023ca95a127713d43b96951751889a45c8438a8234ef533ad0795

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "0cdf3cd10cbfc7a6191b09c112e4dfa5f49588d9a7793c7612b5bc6e8bc8efaa",
    "cross_cats_sorted": [
      "math.GT",
      "math.PR",
      "math.SP"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.DG",
    "submitted_at": "2022-03-29T15:38:48Z",
    "title_canon_sha256": "32574c5c7ff3c487ea61be93ad293ac05beec4bd097e400bce171e920f21e59b"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2203.15681",
    "kind": "arxiv",
    "version": 4
  }
}