Pith Number

pith:VM7U2MRM

pith:2022:VM7U2MRM3C6VSY22NO6VSD4KUF

not attested not anchored not stored refs pending

The Hodge-Laplacian on the \v{C}ech-de Rham complex governs coupled problems

Daniel F{\o}rland Holmen, Jan Martin Nordbotten, Jon Eivind Vatne, Wietse Marijn Boon

arxiv:2211.04556 v2 · 2022-11-08 · 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{VM7U2MRM3C6VSY22NO6VSD4KUF}

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	2026-07-05T06:39:50.307330Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ab3f4d322cd8bd59635a6bbd590f8aa143411a0986fb1a56d14116d0b2a76193

Aliases

arxiv: 2211.04556 · arxiv_version: 2211.04556v2 · doi: 10.48550/arxiv.2211.04556 · pith_short_12: VM7U2MRM3C6V · pith_short_16: VM7U2MRM3C6VSY22 · pith_short_8: VM7U2MRM

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/VM7U2MRM3C6VSY22NO6VSD4KUF \
  | 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: ab3f4d322cd8bd59635a6bbd590f8aa143411a0986fb1a56d14116d0b2a76193

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "fc28012256f2405daaf50e6650af85755ce313f02b30cee253ba1cc62c0121a5",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2022-11-08T20:57:10Z",
    "title_canon_sha256": "7165b1c620246ce3dd65f780d288c4ad8b3584608bf0aeeb3d388de1d01fbcb9"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2211.04556",
    "kind": "arxiv",
    "version": 2
  }
}