Pith Number

pith:55Z3KCBW

pith:2013:55Z3KCBWGFQUWUAJXVLXHJS6BQ

not attested not anchored not stored refs pending

Existence and regularity of multivalued solutions to elliptic equations and systems

Brian Krummel

arxiv:1309.6233 v1 · 2013-09-24 · math.DG · 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{55Z3KCBWGFQUWUAJXVLXHJS6BQ}

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	2026-05-18T03:12:23.422014Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ef73b5083631614b5009bd5773a65e0c25337d8a04abdf3bc0476604c2a26ad3

Aliases

arxiv: 1309.6233 · arxiv_version: 1309.6233v1 · doi: 10.48550/arxiv.1309.6233 · pith_short_12: 55Z3KCBWGFQU · pith_short_16: 55Z3KCBWGFQUWUAJ · pith_short_8: 55Z3KCBW

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/55Z3KCBWGFQUWUAJXVLXHJS6BQ \
  | 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: ef73b5083631614b5009bd5773a65e0c25337d8a04abdf3bc0476604c2a26ad3

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "fcb108825ac36173ed1a19f16ae0b0b83ad2ae2ac0a08b5cd99098b3cbf58a2e",
    "cross_cats_sorted": [
      "math.AP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DG",
    "submitted_at": "2013-09-24T16:05:19Z",
    "title_canon_sha256": "ee92c81cf1c0f31d48d514750ce240faea445e6df7c26e4b7385c65d1e0d4c56"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1309.6233",
    "kind": "arxiv",
    "version": 1
  }
}