Pith Number

pith:OZTUTTSN

pith:2011:OZTUTTSNCCAILTFC4WPFAU4FU6

not attested not anchored not stored refs pending

Phase transitions for random states and a semi-circle law for the partial transpose

Deping Ye, Guillaume Aubrun, Stanislaw J. Szarek

arxiv:1112.4582 v2 · 2011-12-20 · quant-ph · math.FA · math.PR

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{OZTUTTSNCCAILTFC4WPFAU4FU6}

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	2026-05-18T03:58:26.172290Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

766749ce4d108085cca2e59e505385a7a9a1a5cea3a5d3fe9d6fd2d8c63ae328

Aliases

arxiv: 1112.4582 · arxiv_version: 1112.4582v2 · doi: 10.48550/arxiv.1112.4582 · pith_short_12: OZTUTTSNCCAI · pith_short_16: OZTUTTSNCCAILTFC · pith_short_8: OZTUTTSN

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/OZTUTTSNCCAILTFC4WPFAU4FU6 \
  | 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: 766749ce4d108085cca2e59e505385a7a9a1a5cea3a5d3fe9d6fd2d8c63ae328

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "fd77e0a2a941bb114867a45d1485c83445c4754c7a63747322c5740cad2940ff",
    "cross_cats_sorted": [
      "math.FA",
      "math.PR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "quant-ph",
    "submitted_at": "2011-12-20T06:40:14Z",
    "title_canon_sha256": "dca814a4f4e7c5f174a99f85a534ab32bf0addd7acac8d3dcc799895a2f587bf"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1112.4582",
    "kind": "arxiv",
    "version": 2
  }
}