Pith Number

pith:LJ7ODEOB

pith:2015:LJ7ODEOBVMK33SBRYUUBQETSNJ

not attested not anchored not stored refs pending

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

Anil V. Rao, Hongyan Hou, William W. Hager

arxiv:1507.08263 v3 · 2015-07-29 · 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{LJ7ODEOBVMK33SBRYUUBQETSNJ}

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	2026-05-18T01:11:18.154422Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

5a7ee191c1ab15bdc831c5281812726a67fee3dc6dda557d7b3b79e7e9267bd8

Aliases

arxiv: 1507.08263 · arxiv_version: 1507.08263v3 · doi: 10.48550/arxiv.1507.08263 · pith_short_12: LJ7ODEOBVMK3 · pith_short_16: LJ7ODEOBVMK33SBR · pith_short_8: LJ7ODEOB

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/LJ7ODEOBVMK33SBRYUUBQETSNJ \
  | 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: 5a7ee191c1ab15bdc831c5281812726a67fee3dc6dda557d7b3b79e7e9267bd8

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "fa7b18c5d7d4049584c519f523d1309346c2ffa986ddb1bbfba0d02482d0959e",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.OC",
    "submitted_at": "2015-07-29T19:05:23Z",
    "title_canon_sha256": "20950b42c099700bae03acb6f0ca6f9e6c5a16e1352ee97fa99df12d67602f16"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1507.08263",
    "kind": "arxiv",
    "version": 3
  }
}