Pith Number

pith:AQITXVVX

pith:2015:AQITXVVXJ7GBSBBNBAG2SOBHPO

not attested not anchored not stored refs pending

Pointwise second-order necessary conditions for stochastic optimal controls, Part II: The general case

Haisen Zhang, Xu Zhang

arxiv:1509.07995 v2 · 2015-09-26 · 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{AQITXVVXJ7GBSBBNBAG2SOBHPO}

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	2026-05-18T01:29:53.617670Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

04113bd6b74fcc19042d080da938277b9a2468e6fe15444b13711b34fcf45983

Aliases

arxiv: 1509.07995 · arxiv_version: 1509.07995v2 · doi: 10.48550/arxiv.1509.07995 · pith_short_12: AQITXVVXJ7GB · pith_short_16: AQITXVVXJ7GBSBBN · pith_short_8: AQITXVVX

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/AQITXVVXJ7GBSBBNBAG2SOBHPO \
  | 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: 04113bd6b74fcc19042d080da938277b9a2468e6fe15444b13711b34fcf45983

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "9756e99376aa59204929b5b300187e8bc1457d893059036d3b5a7c6cf83e8822",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.OC",
    "submitted_at": "2015-09-26T15:21:51Z",
    "title_canon_sha256": "a2481f244e7eff4b1a2fe3f9115b296e103330bcde1740cdf28d1a062a414d4c"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1509.07995",
    "kind": "arxiv",
    "version": 2
  }
}