Pith Number

pith:47SUJSC3

pith:2025:47SUJSC3B5KOG34J2MGG7YB2FO

not attested not anchored not stored refs pending

Optimal Sobolev inequalities of high order with $L^2$-remainder

Fr\'ed\'eric Robert, Lorenzo Carletti

arxiv:2506.17028 v1 · 2025-06-20 · 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{47SUJSC3B5KOG34J2MGG7YB2FO}

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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.

Cited by

1 paper in Pith

A priori bounds for energy-bounded solutions of critical polyharmonic equations

Receipt and verification

First computed	2026-07-05T11:24:55.021785Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e7e544c85b0f54e36f89d30c6fe03a2b8791521076a854bf5d8528c38a5bb4e9

Aliases

arxiv: 2506.17028 · arxiv_version: 2506.17028v1 · doi: 10.48550/arxiv.2506.17028 · pith_short_12: 47SUJSC3B5KO · pith_short_16: 47SUJSC3B5KOG34J · pith_short_8: 47SUJSC3

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/47SUJSC3B5KOG34J2MGG7YB2FO \
  | 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: e7e544c85b0f54e36f89d30c6fe03a2b8791521076a854bf5d8528c38a5bb4e9

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "71f53897fca3a92066f989b4ae6792e58c12a704d553ca72cb0ff0c651ac0799",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2025-06-20T14:25:02Z",
    "title_canon_sha256": "ac81fe9e174341c8e91c30c672e441c8c900a94cff819932d690b8cba2e826c3"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2506.17028",
    "kind": "arxiv",
    "version": 1
  }
}