Pith Number

pith:D7AZUE2Q

pith:2015:D7AZUE2QQMOOMEI6RYUZRY26FS

not attested not anchored not stored refs pending

Quantum ergodicity of Wigner induced spherical harmonics

Robert Chang

arxiv:1512.03138 v2 · 2015-12-10 · math.PR · math.AP · 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{D7AZUE2QQMOOMEI6RYUZRY26FS}

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	2026-07-05T02:56:51.851252Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

1fc19a1350831ce6111e8e2998e35e2c8cf377d04b641ea9e67a819a38f31589

Aliases

arxiv: 1512.03138 · arxiv_version: 1512.03138v2 · doi: 10.48550/arxiv.1512.03138 · pith_short_12: D7AZUE2QQMOO · pith_short_16: D7AZUE2QQMOOMEI6 · pith_short_8: D7AZUE2Q

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/D7AZUE2QQMOOMEI6RYUZRY26FS \
  | 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: 1fc19a1350831ce6111e8e2998e35e2c8cf377d04b641ea9e67a819a38f31589

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "a158e1ab339e2499a105bce9033e2ee9d1250d4110ab752ddde348304c276e2a",
    "cross_cats_sorted": [
      "math.AP",
      "math.SP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2015-12-10T04:47:41Z",
    "title_canon_sha256": "ac94c0d2235bc2c8179340ca56865aac8f2440dbeaf9126621d59864ef39fcbd"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1512.03138",
    "kind": "arxiv",
    "version": 2
  }
}