Pith Number

pith:HMJ4YGSD

pith:2012:HMJ4YGSDUMUBQONLQ3VIIOU3KY

not attested not anchored not stored refs pending

Singular solutions in optimal control: second order conditions and a shooting algorithm

M. Soledad Aronna

arxiv:1210.7425 v2 · 2012-10-28 · math.OC · math.NA

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{HMJ4YGSDUMUBQONLQ3VIIOU3KY}

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	2026-05-17T23:56:30.592855Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

3b13cc1a43a3281839ab86ea843a9b563cab7f4f97ae4ef7ab8f95a55c63be5a

Aliases

arxiv: 1210.7425 · arxiv_version: 1210.7425v2 · doi: 10.48550/arxiv.1210.7425 · pith_short_12: HMJ4YGSDUMUB · pith_short_16: HMJ4YGSDUMUBQONL · pith_short_8: HMJ4YGSD

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/HMJ4YGSDUMUBQONLQ3VIIOU3KY \
  | 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: 3b13cc1a43a3281839ab86ea843a9b563cab7f4f97ae4ef7ab8f95a55c63be5a

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "02e5ea8c211eef49cce287974e83e47eee587cfe8ece74914608f21e86825bbb",
    "cross_cats_sorted": [
      "math.NA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.OC",
    "submitted_at": "2012-10-28T08:48:59Z",
    "title_canon_sha256": "2a4a65db4972ae54d60f9847377bf716d12af715bd75e2ff2310c457fae34bb1"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1210.7425",
    "kind": "arxiv",
    "version": 2
  }
}