Pith Number

pith:57XUYTPJ

pith:2025:57XUYTPJLKPN6C5BWTSM4EK6OP

not attested not anchored not stored refs pending

Stability of spinorial Sobolev inequalities on $\mathbb{S}^n$

Guofang Wang, Mingwei Zhang

arxiv:2508.09047 v2 · 2025-08-12 · math.DG · math-ph · math.AP · math.MP

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{57XUYTPJLKPN6C5BWTSM4EK6OP}

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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

Stability for the Affine Sobolev Inequality and its Critical Points for $p\ge 2$

Receipt and verification

First computed	2026-07-05T11:56:22.470512Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

efef4c4de95a9edf0ba1b4e4ce115e73dd42e00f0c5447beaebe27f502cb6e06

Aliases

arxiv: 2508.09047 · arxiv_version: 2508.09047v2 · doi: 10.48550/arxiv.2508.09047 · pith_short_12: 57XUYTPJLKPN · pith_short_16: 57XUYTPJLKPN6C5B · pith_short_8: 57XUYTPJ

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/57XUYTPJLKPN6C5BWTSM4EK6OP \
  | 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: efef4c4de95a9edf0ba1b4e4ce115e73dd42e00f0c5447beaebe27f502cb6e06

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "4db47e1355dde28663de1c7de63a6d30a0a548c8132218b4c1f00b0344acc598",
    "cross_cats_sorted": [
      "math-ph",
      "math.AP",
      "math.MP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DG",
    "submitted_at": "2025-08-12T16:09:08Z",
    "title_canon_sha256": "1f820c010ca96ca1d547b3ef96fe0c650e8d531f318939460dd1800ffdc03d35"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2508.09047",
    "kind": "arxiv",
    "version": 2
  }
}