Pith Number

pith:WUX77AMO

pith:2016:WUX77AMOR2GDECBVW5XFZZ5PDL

not attested not anchored not stored refs pending

Convergence rate for a Gauss collocation method applied to constrained optimal control

Anil V. Rao, Jun Liu, Subhashree Mohapatra, William W. Hager, Xiang-Sheng Wang

arxiv:1607.02798 v4 · 2016-07-11 · 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{WUX77AMOR2GDECBVW5XFZZ5PDL}

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	2026-05-18T00:05:46.430872Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b52fff818e8e8c320835b76e5ce7af1ae6d3c00157d81945c46fb28b6951dafc

Aliases

arxiv: 1607.02798 · arxiv_version: 1607.02798v4 · doi: 10.48550/arxiv.1607.02798 · pith_short_12: WUX77AMOR2GD · pith_short_16: WUX77AMOR2GDECBV · pith_short_8: WUX77AMO

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/WUX77AMOR2GDECBVW5XFZZ5PDL \
  | 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: b52fff818e8e8c320835b76e5ce7af1ae6d3c00157d81945c46fb28b6951dafc

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "ba5a4967391d740d2de28df7606294a2688d365418e129e2a5012476388d962f",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NA",
    "submitted_at": "2016-07-11T00:09:30Z",
    "title_canon_sha256": "1fed0f09aff1c96d66f32e1b6aa99637fce5214e519d244db4e800959177cbb3"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1607.02798",
    "kind": "arxiv",
    "version": 4
  }
}