Pith Number

pith:YA4JLBLU

pith:2018:YA4JLBLULTHZ2HEBWQBZC4CRDC

not attested not anchored not stored refs pending

Optimal medication for tumors modeled by a Cahn-Hilliard-Brinkman equation

Matthias Ebenbeck, Patrik Knopf

arxiv:1811.07783 v3 · 2018-11-19 · math.OC · 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{YA4JLBLULTHZ2HEBWQBZC4CRDC}

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.

Cited by

1 paper in Pith

A distributed control problem for a fractional tumor growth model

Receipt and verification

First computed	2026-07-05T03:21:03.727016Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

c0389585745ccf9d1c81b40391705118ba043305f7b2eb1e6d7b7bb2174c3dec

Aliases

arxiv: 1811.07783 · arxiv_version: 1811.07783v3 · doi: 10.48550/arxiv.1811.07783 · pith_short_12: YA4JLBLULTHZ · pith_short_16: YA4JLBLULTHZ2HEB · pith_short_8: YA4JLBLU

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/YA4JLBLULTHZ2HEBWQBZC4CRDC \
  | 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: c0389585745ccf9d1c81b40391705118ba043305f7b2eb1e6d7b7bb2174c3dec

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "4de5a9f28c201455a8d05e20e9c67a1b5ab8f9593adae1974bbb55c3c2697e0d",
    "cross_cats_sorted": [
      "math.AP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.OC",
    "submitted_at": "2018-11-19T16:31:34Z",
    "title_canon_sha256": "5d072cb375bf49da3420db79f875576d8ea063473e0f94f883c54afb8b8b6280"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1811.07783",
    "kind": "arxiv",
    "version": 3
  }
}