Pith Number

pith:KEW4VX5I

pith:2012:KEW4VX5IEQ3U3NZ4PIV42YI2BD

not attested not anchored not stored refs pending

A Singular Differential Equation Stemming from an Optimal Control Problem in Financial Economics

Ale\v{s} \v{C}ern\'y, Michael Winkler, Pavol Brunovsk\'y

arxiv:1209.5027 v3 · 2012-09-22 · math.OC · math.CA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{KEW4VX5IEQ3U3NZ4PIV42YI2BD}

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	2026-05-18T00:39:48.519364Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

512dcadfa824374db73c7a2bcd611a08f4c562486655b5cf7294cf41c3eb5af0

Aliases

arxiv: 1209.5027 · arxiv_version: 1209.5027v3 · doi: 10.48550/arxiv.1209.5027 · pith_short_12: KEW4VX5IEQ3U · pith_short_16: KEW4VX5IEQ3U3NZ4 · pith_short_8: KEW4VX5I

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/KEW4VX5IEQ3U3NZ4PIV42YI2BD \
  | 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: 512dcadfa824374db73c7a2bcd611a08f4c562486655b5cf7294cf41c3eb5af0

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "b85d9614f400f1d97890f2d1060542902d1469693f797083705304ff1d4dab77",
    "cross_cats_sorted": [
      "math.CA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.OC",
    "submitted_at": "2012-09-22T22:47:54Z",
    "title_canon_sha256": "3e9063a8cddd0d216f037d4618fdab5c0d54755a135da1964996b70bb75475ef"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1209.5027",
    "kind": "arxiv",
    "version": 3
  }
}