Pith Number

pith:VCQX2VXU

pith:2012:VCQX2VXUWGLUGQPSPN5CCDIA5K

not attested not anchored not stored refs pending

Optimal Hardy Weight for Second-Order Elliptic Operator: An Answer to a Problem of Agmon

B. Devyver, M. Fraas, Y. Pinchover

arxiv:1208.2342 v5 · 2012-08-11 · math.AP · math-ph · math.MP · math.SP

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{VCQX2VXUWGLUGQPSPN5CCDIA5K}

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	2026-05-18T01:00:40.931522Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

a8a17d56f4b1974341f27b7a210d00eaa0a3d471d72f7d08fca5f8ae1663483e

Aliases

arxiv: 1208.2342 · arxiv_version: 1208.2342v5 · doi: 10.48550/arxiv.1208.2342 · pith_short_12: VCQX2VXUWGLU · pith_short_16: VCQX2VXUWGLUGQPS · pith_short_8: VCQX2VXU

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/VCQX2VXUWGLUGQPSPN5CCDIA5K \
  | 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: a8a17d56f4b1974341f27b7a210d00eaa0a3d471d72f7d08fca5f8ae1663483e

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "e1c599f25da86213b1362a5cafb0e73adb1a5ca0addddb6b71a4382d60293a15",
    "cross_cats_sorted": [
      "math-ph",
      "math.MP",
      "math.SP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2012-08-11T12:37:31Z",
    "title_canon_sha256": "40bcf35ed3458d8c44c4f53250bf4924d40ec7fda68926d6724f5fd69178d9ae"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1208.2342",
    "kind": "arxiv",
    "version": 5
  }
}