Pith Number

pith:U5X4RA7P

pith:2026:U5X4RA7POEETNSSWZTT5A45GSF

not attested not anchored not stored refs pending

Sharp Gradient Stability for the Sobolev Trace Inequality

Xi-Nan Ma, Yang Zhou, Yitian Zhang

arxiv:2607.17588 v1 · 2026-07-20 · 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{U5X4RA7POEETNSSWZTT5A45GSF}

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	2026-07-21T01:21:53.879010Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

a76fc883ef710936ca56cce7d073a6914ea04a3bd6ddfaff0219a2504487cd47

Aliases

arxiv: 2607.17588 · arxiv_version: 2607.17588v1 · doi: 10.48550/arxiv.2607.17588 · pith_short_12: U5X4RA7POEET · pith_short_16: U5X4RA7POEETNSSW · pith_short_8: U5X4RA7P

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/U5X4RA7POEETNSSWZTT5A45GSF \
  | 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: a76fc883ef710936ca56cce7d073a6914ea04a3bd6ddfaff0219a2504487cd47

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "e38053d0d5b09e0a04db7ccb30a47cfbbff2ae93f2c490bda9c8aff442e217a6",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2026-07-20T06:09:47Z",
    "title_canon_sha256": "3bf85e9da4238d8955ed73cf0e874a3dacb685de11d2a7167be4f7e12f1f00bd"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2607.17588",
    "kind": "arxiv",
    "version": 1
  }
}