Pith Number

pith:LSWM4UAG

pith:2012:LSWM4UAGL2E3UFEBFTBLT3I4RV

not attested not anchored not stored refs pending

Quantum ergodicity for restrictions to hypersurfaces

Maciej Zworski, Semyon Dyatlov

arxiv:1204.0284 v3 · 2012-04-02 · 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{LSWM4UAGL2E3UFEBFTBLT3I4RV}

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	2026-05-18T03:40:36.457180Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

5cacce50065e89ba14812cc2b9ed1c8d5f7e61b336cb3cae74f077306d194bec

Aliases

arxiv: 1204.0284 · arxiv_version: 1204.0284v3 · doi: 10.48550/arxiv.1204.0284 · pith_short_12: LSWM4UAGL2E3 · pith_short_16: LSWM4UAGL2E3UFEB · pith_short_8: LSWM4UAG

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/LSWM4UAGL2E3UFEBFTBLT3I4RV \
  | 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: 5cacce50065e89ba14812cc2b9ed1c8d5f7e61b336cb3cae74f077306d194bec

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "816dfc5f8e97c15b6753f6203b890e96cd0ada103a300c89f31c5b430183b658",
    "cross_cats_sorted": [
      "math.SP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2012-04-02T00:45:00Z",
    "title_canon_sha256": "b3213346be1d14c273ea25bd74398638e1ecee39542d7e02a99d6133bd5206fe"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1204.0284",
    "kind": "arxiv",
    "version": 3
  }
}