Pith Number

pith:6P6G36QB

pith:2016:6P6G36QBZM44VL3IKFIR7STEBT

not attested not anchored not stored refs pending

Canceling effects in higher-order Hardy-Sobolev inequalities

Andrea Cianchi, Norisuke Ioku

arxiv:1607.07122 v2 · 2016-07-25 · 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{6P6G36QBZM44VL3IKFIR7STEBT}

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	2026-05-18T01:09:54.478741Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

f3fc6dfa01cb39caaf6851511fca640cdbafd7c236de0da62ade40dd335c3f43

Aliases

arxiv: 1607.07122 · arxiv_version: 1607.07122v2 · doi: 10.48550/arxiv.1607.07122 · pith_short_12: 6P6G36QBZM44 · pith_short_16: 6P6G36QBZM44VL3I · pith_short_8: 6P6G36QB

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/6P6G36QBZM44VL3IKFIR7STEBT \
  | 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: f3fc6dfa01cb39caaf6851511fca640cdbafd7c236de0da62ade40dd335c3f43

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "5ae395ddde442756a16294885b82fccfb5330cd937a65f50921bff05f43016b9",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.FA",
    "submitted_at": "2016-07-25T01:08:44Z",
    "title_canon_sha256": "3c80d96ab3f45f7666ad320e04b1212e785f47731a1aac5168a4b5af19a8baaa"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1607.07122",
    "kind": "arxiv",
    "version": 2
  }
}