Pith Number

pith:XF2EDCLS

pith:2025:XF2EDCLSY2SJOMQQBJPSAUQLRD

not attested not anchored not stored refs pending

Beyond Value Functions: Single-Loop Bilevel Optimization under Flatness Conditions

Lisha Chen, Liuyuan Jiang, Quan Xiao, Tianyi Chen

arxiv:2507.20400 v1 · 2025-07-27 · math.OC

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{XF2EDCLSY2SJOMQQBJPSAUQLRD}

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	2026-07-05T11:44:18.668303Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b974418972c6a49732100a5f20520b88cb3a4882131e256c7766c7ae4d3f1982

Aliases

arxiv: 2507.20400 · arxiv_version: 2507.20400v1 · doi: 10.48550/arxiv.2507.20400 · pith_short_12: XF2EDCLSY2SJ · pith_short_16: XF2EDCLSY2SJOMQQ · pith_short_8: XF2EDCLS

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/XF2EDCLSY2SJOMQQBJPSAUQLRD \
  | 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: b974418972c6a49732100a5f20520b88cb3a4882131e256c7766c7ae4d3f1982

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "68b904501c895ca889cd0fc40724fa5448a31ba0f679a9117d5feac654f58a2f",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.OC",
    "submitted_at": "2025-07-27T19:49:15Z",
    "title_canon_sha256": "705ca40cd5367150d0035448f24dcfe3646af6999184f503018b2c9580c89bf1"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2507.20400",
    "kind": "arxiv",
    "version": 1
  }
}