Pith Number

pith:GQPDW3DS

pith:2010:GQPDW3DS7EH5CX5YXEIFFLYNNM

not attested not anchored not stored refs pending

Maximum Principle for Forward-Backward Doubly Stochastic Control Systems and Applications

Liangquan Zhang, Yufeng Shi

arxiv:1005.4129 v1 · 2010-05-22 · 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{GQPDW3DS7EH5CX5YXEIFFLYNNM}

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	2026-05-18T03:55:00.648645Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

341e3b6c72f90fd15fb8b91052af0d6b12f56a2f44ca71ce2bb51162ffec03e5

Aliases

arxiv: 1005.4129 · arxiv_version: 1005.4129v1 · doi: 10.48550/arxiv.1005.4129 · pith_short_12: GQPDW3DS7EH5 · pith_short_16: GQPDW3DS7EH5CX5Y · pith_short_8: GQPDW3DS

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/GQPDW3DS7EH5CX5YXEIFFLYNNM \
  | 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: 341e3b6c72f90fd15fb8b91052af0d6b12f56a2f44ca71ce2bb51162ffec03e5

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "87424b5cbc94ba6a3dd6b1da9e2c8ba2bbeedb6f39dc5964d1a124b57fb66809",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.OC",
    "submitted_at": "2010-05-22T14:21:59Z",
    "title_canon_sha256": "8356bb5922cab490e06f9a1b6be16e1de19cbe991afad28398086fe5f317b20e"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1005.4129",
    "kind": "arxiv",
    "version": 1
  }
}