Pith Number

pith:TZRVQW42

pith:2026:TZRVQW42Z24RCR6ORMDASPW27B

not attested not anchored not stored refs pending

A Density-Distance Version of the Carlen--Frank--Lieb Stability Theorem

Gangsong Leng

arxiv:2606.03749 v1 · 2026-06-02 · math.AP · math.FA · math.MG

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{TZRVQW42Z24RCR6ORMDASPW27B}

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	2026-06-03T01:06:06.424112Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

9e63585b9aceb91147ce8b06093edaf85ad69de68e14bcfd4bb6de56ef3eb6e8

Aliases

arxiv: 2606.03749 · arxiv_version: 2606.03749v1 · doi: 10.48550/arxiv.2606.03749 · pith_short_12: TZRVQW42Z24R · pith_short_16: TZRVQW42Z24RCR6O · pith_short_8: TZRVQW42

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/TZRVQW42Z24RCR6ORMDASPW27B \
  | 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: 9e63585b9aceb91147ce8b06093edaf85ad69de68e14bcfd4bb6de56ef3eb6e8

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "b7662c623e61e656aab66ff4d0c01d524b7f069b1989217eb2a45bef85556fa0",
    "cross_cats_sorted": [
      "math.FA",
      "math.MG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2026-06-02T15:01:54Z",
    "title_canon_sha256": "089228c2fdd7571a43696dc423f1461514ce3a2a9efed793625cb620be3c8475"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2606.03749",
    "kind": "arxiv",
    "version": 1
  }
}