Pith Number

pith:6T76GIID

pith:2016:6T76GIID46OK5IQSG5FOFW77KO

not attested not anchored not stored refs pending

On Closed and Exact Grad-grad- and div-Div-Complexes, Corresponding Compact Embeddings for Tensor Rotations, and a Related Decomposition Result for Biharmonic Problems in 3D

Dirk Pauly, Walter Zulehner

arxiv:1609.05873 v4 · 2016-09-19 · math.AP · math-ph · math.FA · math.MP · 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{6T76GIID46OK5IQSG5FOFW77KO}

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	2026-05-18T00:45:30.365956Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

f4ffe32103e79caea212374ae2dbff53b2f25e4dd1f82de3fc3bf3b3da1ccea3

Aliases

arxiv: 1609.05873 · arxiv_version: 1609.05873v4 · doi: 10.48550/arxiv.1609.05873 · pith_short_12: 6T76GIID46OK · pith_short_16: 6T76GIID46OK5IQS · pith_short_8: 6T76GIID

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/6T76GIID46OK5IQSG5FOFW77KO \
  | 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: f4ffe32103e79caea212374ae2dbff53b2f25e4dd1f82de3fc3bf3b3da1ccea3

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "fc57246896196a0dd47b5ab198ed7152b5e8caf086ddd9c243aa4c2cbd39ac05",
    "cross_cats_sorted": [
      "math-ph",
      "math.FA",
      "math.MP",
      "math.NA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2016-09-19T19:13:37Z",
    "title_canon_sha256": "403ec1c13d2017ef1014ffb5ee293841a40f382b5d9c0797ff4de218845dc492"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1609.05873",
    "kind": "arxiv",
    "version": 4
  }
}