Pith Number

pith:Z5SCDLI2

pith:2025:Z5SCDLI2DIHWQCYIBPK2ER4KNE

not attested not anchored not stored refs pending

Projected Gradient Descent for Constrained Decision-Dependent Optimization

Changxin Liu, Karl H. Johansson, Michael M. Zavlanos, Thomas Parisini, Zifan Wang

arxiv:2508.08856 v1 · 2025-08-12 · 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{Z5SCDLI2DIHWQCYIBPK2ER4KNE}

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	2026-07-05T11:52:35.415130Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

cf6421ad1a1a0f680b080bd5a2478a6914e543e375190a808b9c489fcc59419e

Aliases

arxiv: 2508.08856 · arxiv_version: 2508.08856v1 · doi: 10.48550/arxiv.2508.08856 · pith_short_12: Z5SCDLI2DIHW · pith_short_16: Z5SCDLI2DIHWQCYI · pith_short_8: Z5SCDLI2

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/Z5SCDLI2DIHWQCYIBPK2ER4KNE \
  | 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: cf6421ad1a1a0f680b080bd5a2478a6914e543e375190a808b9c489fcc59419e

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "efed71756fb595bb76b1a3b1a7e57e51bc002c6e60098679e690a970c147365b",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.OC",
    "submitted_at": "2025-08-12T11:30:32Z",
    "title_canon_sha256": "65a93503eb5eddb202ce3b0693f7fc1172a7082bdeafc68fc8dd8148040b5471"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2508.08856",
    "kind": "arxiv",
    "version": 1
  }
}