Pith Number

pith:3GSRJ7S3

pith:2013:3GSRJ7S3CMXFLBMPNH6LIJ7EDE

not attested not anchored not stored refs pending

Mean of the $L^\infty$-norm for $L^2$-normalized random waves on compact aperiodic Riemannian manifolds

Boris Hanin, Yaiza Canzani

arxiv:1310.1361 v2 · 2013-10-04 · math-ph · math.DG · math.MP · math.PR · 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{3GSRJ7S3CMXFLBMPNH6LIJ7EDE}

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	2026-05-18T02:50:03.292986Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

d9a514fe5b132e55858f69fcb427e419189941b19b67cbdfd5756b567d889fd1

Aliases

arxiv: 1310.1361 · arxiv_version: 1310.1361v2 · doi: 10.48550/arxiv.1310.1361 · pith_short_12: 3GSRJ7S3CMXF · pith_short_16: 3GSRJ7S3CMXFLBMP · pith_short_8: 3GSRJ7S3

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/3GSRJ7S3CMXFLBMPNH6LIJ7EDE \
  | 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: d9a514fe5b132e55858f69fcb427e419189941b19b67cbdfd5756b567d889fd1

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "a66c2b079a7aee1c11d455ab1feb34c87e096c66e35706b1aa3d4aecc677494e",
    "cross_cats_sorted": [
      "math.DG",
      "math.MP",
      "math.PR",
      "math.SP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math-ph",
    "submitted_at": "2013-10-04T18:32:38Z",
    "title_canon_sha256": "b3a861f3000b3ecb462a52fb40295c5fef2ed0e4553743acddbde7350421a19c"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1310.1361",
    "kind": "arxiv",
    "version": 2
  }
}