Pith Number

pith:3XRO7DQP

pith:2016:3XRO7DQP26O4RMNBORZ4Y2B7D4

not attested not anchored not stored refs pending

Optimal control of treatment time in a diffuse interface model of tumor growth

Elisabetta Rocca, Harald Garcke, Kei-Fong Lam

arxiv:1608.00488 v1 · 2016-08-01 · math.OC · math.AP · q-bio.TO

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{3XRO7DQP26O4RMNBORZ4Y2B7D4}

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	2026-05-18T01:10:11.701803Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

dde2ef8e0fd79dc8b1a17473cc683f1f324db260bdcbddaae694355668416c60

Aliases

arxiv: 1608.00488 · arxiv_version: 1608.00488v1 · doi: 10.48550/arxiv.1608.00488 · pith_short_12: 3XRO7DQP26O4 · pith_short_16: 3XRO7DQP26O4RMNB · pith_short_8: 3XRO7DQP

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/3XRO7DQP26O4RMNBORZ4Y2B7D4 \
  | 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: dde2ef8e0fd79dc8b1a17473cc683f1f324db260bdcbddaae694355668416c60

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "0f63db0a487d73450b73106b0d312431684f3dea87b90c884e5df17356cc35be",
    "cross_cats_sorted": [
      "math.AP",
      "q-bio.TO"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.OC",
    "submitted_at": "2016-08-01T16:37:11Z",
    "title_canon_sha256": "e88c64054b8f914483f8755c450ba0508e67afae84990287d3e4ff8711d22e00"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1608.00488",
    "kind": "arxiv",
    "version": 1
  }
}