Pith Number

pith:YW6APDPZ

pith:2026:YW6APDPZUW2JDKW5PK3VJASYO6

not attested not anchored not stored refs pending

From generalized Poincar\'e to Poincar\'e-Sobolev inequalities via self-improving methods

Alejandro Claros, Carlos P\'erez, Linfei Zheng

arxiv:2606.08556 v1 · 2026-06-07 · 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{YW6APDPZUW2JDKW5PK3VJASYO6}

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	2026-06-09T01:05:40.066940Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

c5bc078df9a5b491aadd7ab7548258779550c10ddb5f44c36b686301c64b039e

Aliases

arxiv: 2606.08556 · arxiv_version: 2606.08556v1 · doi: 10.48550/arxiv.2606.08556 · pith_short_12: YW6APDPZUW2J · pith_short_16: YW6APDPZUW2JDKW5 · pith_short_8: YW6APDPZ

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/YW6APDPZUW2JDKW5PK3VJASYO6 \
  | 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: c5bc078df9a5b491aadd7ab7548258779550c10ddb5f44c36b686301c64b039e

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "6cd5471fa496fb08326fe1934641ed259b29feb19c373c41318ab60c6000ecf0",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.CA",
    "submitted_at": "2026-06-07T10:28:02Z",
    "title_canon_sha256": "75efd22858c1e111d0ff09b999cfbfdcfebd6265bb5d6c6b32a6e07514c3bff2"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2606.08556",
    "kind": "arxiv",
    "version": 1
  }
}