Pith Number

pith:GALOXJBC

pith:2025:GALOXJBCLOIP4S7S255KZECFIX

not attested not anchored not stored refs pending

Asymptotically sharp stability of Sobolev inequalities on the Heisenberg group with dimension-dependent constants

Bohan Wang, Guozhen Lu, Hanli Tang, Lu Chen

arxiv:2507.12725 v2 · 2025-07-17 · 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{GALOXJBCLOIP4S7S255KZECFIX}

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	2026-07-05T11:40:01.733816Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

3016eba4225b90fe4bf2d77aac904545ccc8efa8f46f8489579020a632e934aa

Aliases

arxiv: 2507.12725 · arxiv_version: 2507.12725v2 · doi: 10.48550/arxiv.2507.12725 · pith_short_12: GALOXJBCLOIP · pith_short_16: GALOXJBCLOIP4S7S · pith_short_8: GALOXJBC

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/GALOXJBCLOIP4S7S255KZECFIX \
  | 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: 3016eba4225b90fe4bf2d77aac904545ccc8efa8f46f8489579020a632e934aa

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "332091e18b695fea28b6b977828faf966f084254ee6e35e85c35090ddfe1ad32",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2025-07-17T02:03:05Z",
    "title_canon_sha256": "fae8444229e10284faf4bba8f090c59da589c487563850aa78bc1fed01c20b13"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2507.12725",
    "kind": "arxiv",
    "version": 2
  }
}