Pith Number

pith:7AOPL66J

pith:2025:7AOPL66JNLE7EZRYR3Q6NTMJ6K

not attested not anchored not stored refs pending

Stability inequalities with explicit constants for a family of reverse Sobolev inequalities on the sphere

Tobias K\"onig

arxiv:2504.19939 v2 · 2025-04-28 · 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{7AOPL66JNLE7EZRYR3Q6NTMJ6K}

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	2026-07-05T11:00:06.897299Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

f81cf5fbc96ac9f266388ee1e6cd89f2a3e4cc716e7483661e4a4a0dc0677924

Aliases

arxiv: 2504.19939 · arxiv_version: 2504.19939v2 · doi: 10.48550/arxiv.2504.19939 · pith_short_12: 7AOPL66JNLE7 · pith_short_16: 7AOPL66JNLE7EZRY · pith_short_8: 7AOPL66J

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/7AOPL66JNLE7EZRYR3Q6NTMJ6K \
  | 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: f81cf5fbc96ac9f266388ee1e6cd89f2a3e4cc716e7483661e4a4a0dc0677924

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "8d4ae3657e5f84d538d94d8f6e25f6d46a9c6a306ab5f9b1b04e00a51c728b17",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2025-04-28T16:09:42Z",
    "title_canon_sha256": "f1e97fdd63538e11078a3d171f6b57fd2733807e5f100e873f5c49da9b0f2930"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2504.19939",
    "kind": "arxiv",
    "version": 2
  }
}