Pith Number

pith:MWULNRZM

pith:2007:MWULNRZMLIEQDFVNAUMBML264E

not attested not anchored not stored refs pending

Sparse and stable Markowitz portfolios

Christine De Mol, Domenico Giannone, Ignace Loris, Ingrid Daubechies, Joshua Brodie

arxiv:0708.0046 v3 · 2007-07-31 · q-fin.PM · math.FA · stat.AP

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{MWULNRZMLIEQDFVNAUMBML264E}

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	2026-05-18T03:37:42.194470Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

65a8b6c72c5a090196ad0518162f5ee113122df169438e95001a5488b3402762

Aliases

arxiv: 0708.0046 · arxiv_version: 0708.0046v3 · doi: 10.48550/arxiv.0708.0046 · pith_short_12: MWULNRZMLIEQ · pith_short_16: MWULNRZMLIEQDFVN · pith_short_8: MWULNRZM

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/MWULNRZMLIEQDFVNAUMBML264E \
  | 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: 65a8b6c72c5a090196ad0518162f5ee113122df169438e95001a5488b3402762

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "c45bb770bfe69c78fee9712866059ad50c21ce242054b9759292aa7836c94590",
    "cross_cats_sorted": [
      "math.FA",
      "stat.AP"
    ],
    "license": "",
    "primary_cat": "q-fin.PM",
    "submitted_at": "2007-07-31T22:59:46Z",
    "title_canon_sha256": "fe92b828662c9f72c58bfb073d33c341faedbdf1d6fc255011bae1b2254e0098"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0708.0046",
    "kind": "arxiv",
    "version": 3
  }
}