Pith Number

pith:WHCH7WCH

pith:2016:WHCH7WCHPB4E7S4VJKRVXDWNQU

not attested not anchored not stored refs pending

Hybrid Optimal Control Problems for a Class of Semilinear Parabolic Equations

Karl Kunisch, Laurent Pfeiffer, S\'ebastien Court

arxiv:1611.09745 v1 · 2016-11-29 · 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{WHCH7WCHPB4E7S4VJKRVXDWNQU}

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	2026-05-18T00:56:13.124932Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b1c47fd84778784fcb954aa35b8ecd853080b278559376500b26035bbfbfd8a3

Aliases

arxiv: 1611.09745 · arxiv_version: 1611.09745v1 · doi: 10.48550/arxiv.1611.09745 · pith_short_12: WHCH7WCHPB4E · pith_short_16: WHCH7WCHPB4E7S4V · pith_short_8: WHCH7WCH

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/WHCH7WCHPB4E7S4VJKRVXDWNQU \
  | 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: b1c47fd84778784fcb954aa35b8ecd853080b278559376500b26035bbfbfd8a3

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "fb1476b9d8c4acfbbb2ee307cf3cf8d97f48a443c5064fcda7668b98346cab23",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.OC",
    "submitted_at": "2016-11-29T17:38:32Z",
    "title_canon_sha256": "15a6fd86566a8a9e6fe65d65576b43da7e3c7d334b68abd43d743daf8d3cf90c"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1611.09745",
    "kind": "arxiv",
    "version": 1
  }
}