Pith Number

pith:QXTME2OS

pith:2011:QXTME2OSVU2MPFTOQJBLADCENL

not attested not anchored not stored refs pending

Equivalence of three different kinds of optimal control problems for heat equations and its applications

Gengsheng Wang, Yashan Xu

arxiv:1110.3885 v2 · 2011-10-18 · math.OC

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Add to your LaTeX paper

\usepackage{pith}
\pithnumber{QXTME2OSVU2MPFTOQJBLADCENL}

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	2026-05-18T04:10:36.883725Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

85e6c269d2ad34c7966e8242b00c446afe38ed14f6e47757cedede79f28e0371

Aliases

arxiv: 1110.3885 · arxiv_version: 1110.3885v2 · doi: 10.48550/arxiv.1110.3885 · pith_short_12: QXTME2OSVU2M · pith_short_16: QXTME2OSVU2MPFTO · pith_short_8: QXTME2OS

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/QXTME2OSVU2MPFTOQJBLADCENL \
  | 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: 85e6c269d2ad34c7966e8242b00c446afe38ed14f6e47757cedede79f28e0371

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "c8956ca9ba0aaa9e719696a46f78f761ad28aba610419e51292f867c92ac72ac",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/3.0/",
    "primary_cat": "math.OC",
    "submitted_at": "2011-10-18T06:37:06Z",
    "title_canon_sha256": "397201a880bfa635fe9ce6f47f48ead2164b7dfb6d9dbce957e3fa061ef2412a"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1110.3885",
    "kind": "arxiv",
    "version": 2
  }
}