Pith Number

pith:NM73FGJ4

pith:2021:NM73FGJ4AM5PAENGNYEUPKI74U

not attested not anchored not stored refs pending

Long-time dynamics of the Cahn--Hilliard equation with kinetic rate dependent dynamic boundary conditions

Harald Garcke, Patrik Knopf, Sema Yayla

arxiv:2103.15612 v4 · 2021-03-29 · math.AP · math-ph · math.DS · math.MP

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{NM73FGJ4AM5PAENGNYEUPKI74U}

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	2026-07-05T07:04:08.584378Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

6b3fb2993c033af011a66e0947a91fe52f266413e4db834ee8343852264244e1

Aliases

arxiv: 2103.15612 · arxiv_version: 2103.15612v4 · doi: 10.48550/arxiv.2103.15612 · pith_short_12: NM73FGJ4AM5P · pith_short_16: NM73FGJ4AM5PAENG · pith_short_8: NM73FGJ4

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/NM73FGJ4AM5PAENGNYEUPKI74U \
  | 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: 6b3fb2993c033af011a66e0947a91fe52f266413e4db834ee8343852264244e1

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "eaf9185d9c86cef2389df8057fc6187c8f03225311644321d226018dbd73db3a",
    "cross_cats_sorted": [
      "math-ph",
      "math.DS",
      "math.MP"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2021-03-29T13:47:01Z",
    "title_canon_sha256": "c400f44616d75e13146fdd1a63c279ede02f0e7eb6eee17fcd5fe19c5e150b54"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2103.15612",
    "kind": "arxiv",
    "version": 4
  }
}