Pith Number

pith:QJMW3EA2

pith:2018:QJMW3EA2WWU2QOP2F4D274T2QQ

not attested not anchored not stored refs pending

External optimal control of nonlocal PDEs

Harbir Antil, Mahamadi Warma, Ratna Khatri

arxiv:1811.04515 v2 · 2018-11-12 · math.OC · cs.NA · math.AP · math.NA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{QJMW3EA2WWU2QOP2F4D274T2QQ}

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	2026-06-04T20:13:40.609842Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

82596d901ab5a9a839fa2f07aff27a843e1c02ef416e5149ba6ad1b3af424781

Aliases

arxiv: 1811.04515 · arxiv_version: 1811.04515v2 · doi: 10.48550/arxiv.1811.04515 · pith_short_12: QJMW3EA2WWU2 · pith_short_16: QJMW3EA2WWU2QOP2 · pith_short_8: QJMW3EA2

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/QJMW3EA2WWU2QOP2F4D274T2QQ \
  | 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: 82596d901ab5a9a839fa2f07aff27a843e1c02ef416e5149ba6ad1b3af424781

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "ad664a8a5492faa183cc9483938cf8364aea7afeb225edff6c0bea8dd6511c06",
    "cross_cats_sorted": [
      "cs.NA",
      "math.AP",
      "math.NA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.OC",
    "submitted_at": "2018-11-12T00:21:18Z",
    "title_canon_sha256": "f982cd7e18f8fa9af8d76958f33f8cc4aa268780833633679bed534195e928ca"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1811.04515",
    "kind": "arxiv",
    "version": 2
  }
}