Pith Number

pith:3IFLZ6H4

pith:2026:3IFLZ6H4KRXQMP2ORIOSW5HP6C

not attested not anchored not stored refs pending

Sharp Quantitative Stability for the Affine \(p\)-Sobolev Inequality, Part I: The Case \(2\le p<n\)

Gui-Dong Li, Jianjun Zhang, Song Fan

arxiv:2606.09555 v1 · 2026-06-08 · 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{3IFLZ6H4KRXQMP2ORIOSW5HP6C}

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	2026-06-09T02:08:54.762951Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

da0abcf8fc546f063f4e8a1d2b74eff0924e8e17ce6ab35d4bc6b33043e339b9

Aliases

arxiv: 2606.09555 · arxiv_version: 2606.09555v1 · doi: 10.48550/arxiv.2606.09555 · pith_short_12: 3IFLZ6H4KRXQ · pith_short_16: 3IFLZ6H4KRXQMP2O · pith_short_8: 3IFLZ6H4

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/3IFLZ6H4KRXQMP2ORIOSW5HP6C \
  | 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: da0abcf8fc546f063f4e8a1d2b74eff0924e8e17ce6ab35d4bc6b33043e339b9

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "61df95cba160a94ae569a8428151ab89e641a2450e7a75b4a4ef54b2c103a12b",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2026-06-08T14:31:06Z",
    "title_canon_sha256": "9d02e7ba48f67dbb6e4238787e2a30b514973988689993aa41c9fe8d29608437"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2606.09555",
    "kind": "arxiv",
    "version": 1
  }
}