Pith Number

pith:HTH76A5W

pith:2010:HTH76A5WMAILMCN2BADE5UZJ6J

not attested not anchored not stored refs pending

The Hodge-de Rham Decomposition Theorem And Some Applications Pertaining to Partial Differential Equations

Paul Bracken

arxiv:1001.2348 v1 · 2010-01-14 · math.DG · math.MG

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{HTH76A5WMAILMCN2BADE5UZJ6J}

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	2026-05-18T02:50:01.156119Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

3ccfff03b66010b609ba08064ed329f253a18d6cb10221a76cf5bd81e2786bd1

Aliases

arxiv: 1001.2348 · arxiv_version: 1001.2348v1 · doi: 10.48550/arxiv.1001.2348 · pith_short_12: HTH76A5WMAIL · pith_short_16: HTH76A5WMAILMCN2 · pith_short_8: HTH76A5W

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/HTH76A5WMAILMCN2BADE5UZJ6J \
  | 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: 3ccfff03b66010b609ba08064ed329f253a18d6cb10221a76cf5bd81e2786bd1

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "56ba7707b032dcc954b6000a6df3bda14c51bda9dd8eef758af6e11672dda382",
    "cross_cats_sorted": [
      "math.MG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DG",
    "submitted_at": "2010-01-14T01:36:20Z",
    "title_canon_sha256": "d6d6aa4c47c177ea5510541af23e4d1beb8c81e561a462b7f3867955d2ee81f4"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1001.2348",
    "kind": "arxiv",
    "version": 1
  }
}