Pith Number

pith:HKKKPKO2

pith:2018:HKKKPKO23OQA43EV4IV5EMDF2T

not attested not anchored not stored refs pending

A Hardy-type inequality and some spectral characterizations for the Dirac-Coulomb operator

Biagio Cassano, Fabio Pizzichillo, Luis Vega

arxiv:1810.01309 v1 · 2018-10-02 · 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{HKKKPKO23OQA43EV4IV5EMDF2T}

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	2026-05-18T00:04:18.285101Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

3a94a7a9dadba00e6c95e22bd23065d4d558572d9f238f741fa3ca654c16551a

Aliases

arxiv: 1810.01309 · arxiv_version: 1810.01309v1 · doi: 10.48550/arxiv.1810.01309 · pith_short_12: HKKKPKO23OQA · pith_short_16: HKKKPKO23OQA43EV · pith_short_8: HKKKPKO2

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/HKKKPKO23OQA43EV4IV5EMDF2T \
  | 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: 3a94a7a9dadba00e6c95e22bd23065d4d558572d9f238f741fa3ca654c16551a

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "f4b65205fbcf9ea7c70cb2be6e59eaaab08d6bba75be3e8ea352633913c1b439",
    "cross_cats_sorted": [
      "math-ph",
      "math.MP",
      "math.SP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2018-10-02T14:51:32Z",
    "title_canon_sha256": "a43879de5f951a7871174bcebdcb3149f5cfee2468312e638b73c901e7caf6d2"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1810.01309",
    "kind": "arxiv",
    "version": 1
  }
}