Pith Number

pith:D6F72QXH

pith:2010:D6F72QXHSJYH4FQZCIJ76BWS73

not attested not anchored not stored refs pending

Second-Order Necessary/Sufficient Conditions for Optimal Control Problems in the Absence of Linear Structure

Hongwei Lou

arxiv:1008.1020 v1 · 2010-08-05 · 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{D6F72QXHSJYH4FQZCIJ76BWS73}

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	2026-05-18T04:42:34.770695Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

1f8bfd42e792707e16191213ff06d2feca237d3eb858e4f5eb25f473ff477549

Aliases

arxiv: 1008.1020 · arxiv_version: 1008.1020v1 · doi: 10.48550/arxiv.1008.1020 · pith_short_12: D6F72QXHSJYH · pith_short_16: D6F72QXHSJYH4FQZ · pith_short_8: D6F72QXH

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/D6F72QXHSJYH4FQZCIJ76BWS73 \
  | 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: 1f8bfd42e792707e16191213ff06d2feca237d3eb858e4f5eb25f473ff477549

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "a25971d1412618a416b700933153e361eaf4e395038cf658deec546c452f0cd1",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.OC",
    "submitted_at": "2010-08-05T16:46:41Z",
    "title_canon_sha256": "b23e7c53cc874154fd8760677d96c099c78920744aedd22611ebc50312b11003"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1008.1020",
    "kind": "arxiv",
    "version": 1
  }
}