Pith Number

pith:2L62ZS6K

pith:2026:2L62ZS6K7TKYVNT3N4SXXBCEMV

not attested not anchored not stored refs pending

Stability for Critical Points of the Hardy--Littlewood--Sobolev Inequality and a Dual Stability Framework

Guozhen Lu, Hanli Tang, Lu Chen

arxiv:2605.19288 v1 · 2026-05-19 · math.AP · math.CA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{2L62ZS6K7TKYVNT3N4SXXBCEMV}

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	2026-05-20T01:05:37.759919Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

d2fdaccbcafcd58ab67b6f257b844465599586825639c79aa74aa7f77f3c2649

Aliases

arxiv: 2605.19288 · arxiv_version: 2605.19288v1 · doi: 10.48550/arxiv.2605.19288 · pith_short_12: 2L62ZS6K7TKY · pith_short_16: 2L62ZS6K7TKYVNT3 · pith_short_8: 2L62ZS6K

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/2L62ZS6K7TKYVNT3N4SXXBCEMV \
  | 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: d2fdaccbcafcd58ab67b6f257b844465599586825639c79aa74aa7f77f3c2649

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "f811c626d12ef0201e142eea04c779a85160423394fd35b9c948804a2e03edd6",
    "cross_cats_sorted": [
      "math.CA"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2026-05-19T03:06:43Z",
    "title_canon_sha256": "2af8c7c74c42a07dfefefb6f1e38b7795663d440c08b38b9f175b29dcadb45bb"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.19288",
    "kind": "arxiv",
    "version": 1
  }
}