Pith Number

pith:NHQU5JYY

pith:2026:NHQU5JYYY4PNC23K3T4IHIKL6S

not attested not anchored not stored refs pending

Lagrange multipliers in Maximum likelihood estimations and Least squares problems with Constraints

Takeshi Fukasawa

arxiv:2606.07984 v1 · 2026-06-06 · econ.EM · cs.NA · math.NA · stat.CO

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{NHQU5JYYY4PNC23K3T4IHIKL6S}

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	2026-06-09T01:04:57.156327Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

69e14ea718c71ed16b6adcf883a14bf4b60109d2b5a53c0c439f1949e8b0c1fb

Aliases

arxiv: 2606.07984 · arxiv_version: 2606.07984v1 · doi: 10.48550/arxiv.2606.07984 · pith_short_12: NHQU5JYYY4PN · pith_short_16: NHQU5JYYY4PNC23K · pith_short_8: NHQU5JYY

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/NHQU5JYYY4PNC23K3T4IHIKL6S \
  | 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: 69e14ea718c71ed16b6adcf883a14bf4b60109d2b5a53c0c439f1949e8b0c1fb

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "bf4367465ca1c10c8f0a0637af687d8d0894765b6214bce1fdf3f2b686a6db15",
    "cross_cats_sorted": [
      "cs.NA",
      "math.NA",
      "stat.CO"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "econ.EM",
    "submitted_at": "2026-06-06T05:22:03Z",
    "title_canon_sha256": "3c7f7b415dcd64070701f931f018c0a94e96fb3d15018e59e34b276db0bf4670"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2606.07984",
    "kind": "arxiv",
    "version": 1
  }
}