Pith Number

pith:I6NMSF2B

pith:2026:I6NMSF2B5B2C4ZWABQRKY7AEES

not attested not anchored not stored refs pending

A Single-Loop Minorized Dual Decomposition Method for Nonsmooth Multi-Stage Stochastic Programming

Dan Luo, Hailin Sun, Lei Yang, Yang You

arxiv:2606.20383 v1 · 2026-06-18 · 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{I6NMSF2B5B2C4ZWABQRKY7AEES}

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	2026-06-19T16:13:11.108493Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

479ac91741e8742e66c00c22ac7c0424b8c89562f16135f1a2eeb0a1a0be9b4d

Aliases

arxiv: 2606.20383 · arxiv_version: 2606.20383v1 · doi: 10.48550/arxiv.2606.20383 · pith_short_12: I6NMSF2B5B2C · pith_short_16: I6NMSF2B5B2C4ZWA · pith_short_8: I6NMSF2B

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/I6NMSF2B5B2C4ZWABQRKY7AEES \
  | 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: 479ac91741e8742e66c00c22ac7c0424b8c89562f16135f1a2eeb0a1a0be9b4d

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "e47eff1461281c420aadc92998964e23b796a41d83d7f601b230512ef56f0df7",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.OC",
    "submitted_at": "2026-06-18T15:41:19Z",
    "title_canon_sha256": "5713808b5954b04234d7dde275ed3674ab95ce7434b2d1fc467abfadb1387ce6"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2606.20383",
    "kind": "arxiv",
    "version": 1
  }
}