Pith Number

pith:76KKNP5Y

pith:2024:76KKNP5Y5ILHLEZIYU2RPMMA5P

not attested not anchored not stored refs pending

Solutions of the divergence equation in Hardy and lipschitz spaces

Mar\'ia Eugenia Cejas, Ricardo G. Dur\'an

arxiv:2412.21048 v1 · 2024-12-30 · math.AP · math.FA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{76KKNP5Y5ILHLEZIYU2RPMMA5P}

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	2026-07-05T09:55:26.596467Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ff94a6bfb8ea16759328c53517b180ebe92438c0ef9988686dc85d2a044e6047

Aliases

arxiv: 2412.21048 · arxiv_version: 2412.21048v1 · doi: 10.48550/arxiv.2412.21048 · pith_short_12: 76KKNP5Y5ILH · pith_short_16: 76KKNP5Y5ILHLEZI · pith_short_8: 76KKNP5Y

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/76KKNP5Y5ILHLEZIYU2RPMMA5P \
  | 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: ff94a6bfb8ea16759328c53517b180ebe92438c0ef9988686dc85d2a044e6047

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "673c9672116e573c4ab4830baa0458c8af5494c8c3b2b6d78cbaa67d96f153c6",
    "cross_cats_sorted": [
      "math.FA"
    ],
    "license": "http://creativecommons.org/licenses/by-nc-nd/4.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2024-12-30T16:07:55Z",
    "title_canon_sha256": "cfff1bed45519246b61095f864976e223f6b4950be5d8d7981cfd8682a897b10"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2412.21048",
    "kind": "arxiv",
    "version": 1
  }
}