Pith Number

pith:PR4ONNGF

pith:2016:PR4ONNGFOE5JJB572UM5XLUBJF

not attested not anchored not stored refs pending

A Unified Convergence Analysis of the Multiplicative Update Algorithm for Regularized Nonnegative Matrix Factorization

Renbo Zhao, Vincent Y. F. Tan

arxiv:1609.00951 v3 · 2016-09-04 · math.OC · cs.IT · math.IT · 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{PR4ONNGFOE5JJB572UM5XLUBJF}

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	2026-05-18T00:42:51.594194Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

7c78e6b4c5713a9487bfd519dbae81495d3d5dd9becd020a64b220014b62bccb

Aliases

arxiv: 1609.00951 · arxiv_version: 1609.00951v3 · doi: 10.48550/arxiv.1609.00951 · pith_short_12: PR4ONNGFOE5J · pith_short_16: PR4ONNGFOE5JJB57 · pith_short_8: PR4ONNGF

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/PR4ONNGFOE5JJB572UM5XLUBJF \
  | 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: 7c78e6b4c5713a9487bfd519dbae81495d3d5dd9becd020a64b220014b62bccb

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "0b9d46d8b0e8a8644ba31d9387ef7c0d5f26ce1691630b8144806a8bd22c17da",
    "cross_cats_sorted": [
      "cs.IT",
      "math.IT",
      "stat.ML"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.OC",
    "submitted_at": "2016-09-04T15:47:43Z",
    "title_canon_sha256": "ecb88a34971a7d75d5a2a0b378ad058f394517231621ef59ad288ef3bf5dbe9e"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1609.00951",
    "kind": "arxiv",
    "version": 3
  }
}