Pith Number

pith:V6TV7WNK

pith:2012:V6TV7WNKHW5Y6XMLVL47M632ML

not attested not anchored not stored refs pending

Optimal control of an Allen-Cahn equation with singular potentials and dynamic boundary condition

J\"urgen Sprekels, Pierluigi Colli

arxiv:1212.2359 v2 · 2012-12-11 · math.AP

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{V6TV7WNKHW5Y6XMLVL47M632ML}

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	2026-05-18T02:39:25.791723Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

afa75fd9aa3dbb8f5d8baaf9f67b7a62ff1f19098fc495568a1de7ddda177714

Aliases

arxiv: 1212.2359 · arxiv_version: 1212.2359v2 · doi: 10.48550/arxiv.1212.2359 · pith_short_12: V6TV7WNKHW5Y · pith_short_16: V6TV7WNKHW5Y6XML · pith_short_8: V6TV7WNK

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/V6TV7WNKHW5Y6XMLVL47M632ML \
  | 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: afa75fd9aa3dbb8f5d8baaf9f67b7a62ff1f19098fc495568a1de7ddda177714

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "360bf8907fdf2788519110580102222bf1b9f77aab647cf6f498530a8f2674a7",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2012-12-11T09:59:53Z",
    "title_canon_sha256": "eab782ee8edefbe4d2b5f02f832befddbd1f41e0301295b798290fdc5e1f201b"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1212.2359",
    "kind": "arxiv",
    "version": 2
  }
}