Pith Number

pith:XABY2CWZ

pith:2026:XABY2CWZ532UKB7PBCXQTZ5CB2

not attested not anchored not stored refs pending

Quantitative stability in distribution for the Sobolev inequality under curvature dimension condition

Ivan Yuri Violo, Max Fathi

arxiv:2607.05304 v1 · 2026-07-06 · math.AP · math.DG · 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{XABY2CWZ532UKB7PBCXQTZ5CB2}

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	2026-07-07T03:19:22.906771Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b8038d0ad9eef54507ef08af09e7a20ebe3dbf31e158cb424cd605a913294f32

Aliases

arxiv: 2607.05304 · arxiv_version: 2607.05304v1 · doi: 10.48550/arxiv.2607.05304 · pith_short_12: XABY2CWZ532U · pith_short_16: XABY2CWZ532UKB7P · pith_short_8: XABY2CWZ

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/XABY2CWZ532UKB7PBCXQTZ5CB2 \
  | 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: b8038d0ad9eef54507ef08af09e7a20ebe3dbf31e158cb424cd605a913294f32

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "445845b9f090f0f85c1c7d6b182c2442f5a8485d56d2b73ed5105afa777a4cdc",
    "cross_cats_sorted": [
      "math.DG",
      "math.MG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2026-07-06T16:45:39Z",
    "title_canon_sha256": "aaa12dbd5b8c9c8d35b85b3d9032816c396df516da515a0fbe1e66cf8ff5b10c"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2607.05304",
    "kind": "arxiv",
    "version": 1
  }
}