Pith Number

pith:GZC4EAES

pith:2015:GZC4EAESERWSY4APIVGTUIFNDY

not attested not anchored not stored refs pending

Quantum Ergodicity and Averaging Operators on the Sphere

Elon Lindenstrauss, Etienne Le Masson, Shimon Brooks

arxiv:1505.03887 v1 · 2015-05-14 · math.SP · math-ph · math.DS · 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{GZC4EAESERWSY4APIVGTUIFNDY}

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	2026-05-18T00:44:13.989232Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

3645c20092246d2c700f454d3a20ad1e2587f9b748f7e5efb1688dad57456f6b

Aliases

arxiv: 1505.03887 · arxiv_version: 1505.03887v1 · doi: 10.48550/arxiv.1505.03887 · pith_short_12: GZC4EAESERWS · pith_short_16: GZC4EAESERWSY4AP · pith_short_8: GZC4EAES

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/GZC4EAESERWSY4APIVGTUIFNDY \
  | 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: 3645c20092246d2c700f454d3a20ad1e2587f9b748f7e5efb1688dad57456f6b

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "f874e8ba4f33ca5335651dc7ef6fa4d04be9700bfe2a1698731f78b88b6e4dce",
    "cross_cats_sorted": [
      "math-ph",
      "math.DS",
      "math.MP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.SP",
    "submitted_at": "2015-05-14T20:49:29Z",
    "title_canon_sha256": "347371fe39be46728611010cbd785e3d1ac7674adfd5f3bac2d4076b2c46500c"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1505.03887",
    "kind": "arxiv",
    "version": 1
  }
}