Pith Number

pith:5NWH3GUI

pith:2026:5NWH3GUI5JGTDLG4CZSHKIQJE4

not attested not anchored not stored refs pending

Functional Bilevel Optimization for Predictive Fairness

Ieva Petrulionyte, Julien Mairal, Michael Arbel

arxiv:2607.05098 v1 · 2026-07-06 · cs.LG · 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{5NWH3GUI5JGTDLG4CZSHKIQJE4}

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	2026-07-07T03:19:15.949229Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

eb6c7d9a88ea4d31acdc1664752209270caac6db50a3638f0697a7ef650309c6

Aliases

arxiv: 2607.05098 · arxiv_version: 2607.05098v1 · doi: 10.48550/arxiv.2607.05098 · pith_short_12: 5NWH3GUI5JGT · pith_short_16: 5NWH3GUI5JGTDLG4 · pith_short_8: 5NWH3GUI

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/5NWH3GUI5JGTDLG4CZSHKIQJE4 \
  | 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: eb6c7d9a88ea4d31acdc1664752209270caac6db50a3638f0697a7ef650309c6

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "4442c86a4ffdfdd7ac9b3523b077fa62dcab1a2c6b36256b5c3f9b26ca8b5a9c",
    "cross_cats_sorted": [
      "stat.ML"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "cs.LG",
    "submitted_at": "2026-07-06T13:56:16Z",
    "title_canon_sha256": "e3525729033730be783180f7d8c68801404a3c68f04c7b60a3c473d73fcb04c4"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2607.05098",
    "kind": "arxiv",
    "version": 1
  }
}