Pith Number

pith:2D7V5WAJ

pith:2025:2D7V5WAJECJG2CODCOYNUG75TZ

not attested not anchored not stored refs pending

Quantitative stability of critical points for the nonlocal-Sobolev inequality in Heisenberg group

Jialin Wang, Jijie Xu, Shuijin Zhang

arxiv:2508.08614 v1 · 2025-08-12 · math.AP

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\usepackage{pith}
\pithnumber{2D7V5WAJECJG2CODCOYNUG75TZ}

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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.

Cited by

1 paper in Pith

Optimal Stability Bounds, Minimizers, and Critical Points for a Critical Nonlocal Sobolev Inequality on the Heisenberg Group

Receipt and verification

First computed	2026-07-05T11:52:31.233261Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

d0ff5ed80920926d09c313b0da1bfd9e470111b76c9b39e7f58f2ad8838e32b1

Aliases

arxiv: 2508.08614 · arxiv_version: 2508.08614v1 · doi: 10.48550/arxiv.2508.08614 · pith_short_12: 2D7V5WAJECJG · pith_short_16: 2D7V5WAJECJG2COD · pith_short_8: 2D7V5WAJ

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/2D7V5WAJECJG2CODCOYNUG75TZ \
  | 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: d0ff5ed80920926d09c313b0da1bfd9e470111b76c9b39e7f58f2ad8838e32b1

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "b8ce4e8b8c0390b4a058c14a4e9bd6dad94cc03da14b7801cec87979c4cd09c6",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by-nc-nd/4.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2025-08-12T03:54:23Z",
    "title_canon_sha256": "2e3bcb5b212cf216341631730d3c8a1046394d484a632694087e83a9d59b8bf5"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2508.08614",
    "kind": "arxiv",
    "version": 1
  }
}