Pith Number

pith:2F43Q5GL

pith:2015:2F43Q5GL4PGVGEUTC4A4WDTOH6

not attested not anchored not stored refs pending

Improved fractal Weyl bounds for hyperbolic manifolds

David Borthwick, Semyon Dyatlov, Tobias Weich

arxiv:1512.00836 v2 · 2015-12-02 · math.SP · math.AP

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{2F43Q5GL4PGVGEUTC4A4WDTOH6}

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	2026-05-17T23:54:27.183355Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

d179b874cbe3cd5312931701cb0e6e3faa73aeba9a95bb057ce771fe9ad63f1e

Aliases

arxiv: 1512.00836 · arxiv_version: 1512.00836v2 · doi: 10.48550/arxiv.1512.00836 · pith_short_12: 2F43Q5GL4PGV · pith_short_16: 2F43Q5GL4PGVGEUT · pith_short_8: 2F43Q5GL

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/2F43Q5GL4PGVGEUTC4A4WDTOH6 \
  | 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: d179b874cbe3cd5312931701cb0e6e3faa73aeba9a95bb057ce771fe9ad63f1e

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "f0680f2ae47ff00999aec8eb69e5910abd4d74101a5b5bd5c34a9a9358a44a34",
    "cross_cats_sorted": [
      "math.AP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.SP",
    "submitted_at": "2015-12-02T20:38:55Z",
    "title_canon_sha256": "65129e2465ba724422df644780726b4a04deaf3a7d46e42ca63e8f56fa4e5af7"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1512.00836",
    "kind": "arxiv",
    "version": 2
  }
}