Pith Number

pith:PVFFZXJU

pith:2014:PVFFZXJUVLGCFYQ7JHSTM6BUSZ

not attested not anchored not stored refs pending

Optimal results for the fractional heat equation involving the Hardy potential

Ana Primo, Boumediene Abdellaoui, Ireneo Peral, Mar\'ia Medina

arxiv:1412.8159 v3 · 2014-12-28 · 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{PVFFZXJUVLGCFYQ7JHSTM6BUSZ}

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	2026-05-18T01:30:25.457781Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

7d4a5cdd34aacc22e21f49e5367834966fb53e98cfc3c49ce5b396a5eb8148e4

Aliases

arxiv: 1412.8159 · arxiv_version: 1412.8159v3 · doi: 10.48550/arxiv.1412.8159 · pith_short_12: PVFFZXJUVLGC · pith_short_16: PVFFZXJUVLGCFYQ7 · pith_short_8: PVFFZXJU

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/PVFFZXJUVLGCFYQ7JHSTM6BUSZ \
  | 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: 7d4a5cdd34aacc22e21f49e5367834966fb53e98cfc3c49ce5b396a5eb8148e4

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "050aa3d2cbb7ae411ecfa6e4d2d8afc22362b467bb4811c7c881db739b33c8bc",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2014-12-28T12:43:46Z",
    "title_canon_sha256": "47f44d70222cb49a56aa5ec0875df93372f0b5941f380922c2f443f6b4723dfd"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1412.8159",
    "kind": "arxiv",
    "version": 3
  }
}