Pith Number

pith:4L7766HG

pith:2015:4L7766HG7QGU33G27B2OZBXRMM

not attested not anchored not stored refs pending

Optimal Estimation of Low Rank Density Matrices

Dong Xia, Vladimir Koltchinskii

arxiv:1507.05131 v4 · 2015-07-17 · stat.ML

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{4L7766HG7QGU33G27B2OZBXRMM}

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	2026-05-18T01:17:00.602123Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e2ffff78e6fc0d4decdaf874ec86f16325c4cda5bdc2f656a2294f5befd9b50b

Aliases

arxiv: 1507.05131 · arxiv_version: 1507.05131v4 · doi: 10.48550/arxiv.1507.05131 · pith_short_12: 4L7766HG7QGU · pith_short_16: 4L7766HG7QGU33G2 · pith_short_8: 4L7766HG

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/4L7766HG7QGU33G27B2OZBXRMM \
  | 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: e2ffff78e6fc0d4decdaf874ec86f16325c4cda5bdc2f656a2294f5befd9b50b

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "cb5058da923bc3dc0ce982f81a79280e3c903744aea5cd3b7dbe5a4f1a312d9c",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "stat.ML",
    "submitted_at": "2015-07-17T23:05:40Z",
    "title_canon_sha256": "9d0bfd584fa699c719f06ed9a4a8e7a2536fd557082d80aa766b5cab8f9e1dd8"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1507.05131",
    "kind": "arxiv",
    "version": 4
  }
}