Pith Number

pith:XPDI5J2R

pith:2025:XPDI5J2RCIH5OUDBD3KRAS3UIB

not attested not anchored not stored refs pending

Quantum limits of the Martinet sub-Laplacian

V\'ictor Arnaiz

arxiv:2505.19326 v2 · 2025-05-25 · math.AP · math-ph · math.MP · math.SP

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{XPDI5J2RCIH5OUDBD3KRAS3UIB}

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	2026-07-05T11:19:07.446679Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

bbc68ea751120fd750611ed5104b7440403fd3de69eefce3d124bfdb0c1af0a7

Aliases

arxiv: 2505.19326 · arxiv_version: 2505.19326v2 · doi: 10.48550/arxiv.2505.19326 · pith_short_12: XPDI5J2RCIH5 · pith_short_16: XPDI5J2RCIH5OUDB · pith_short_8: XPDI5J2R

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/XPDI5J2RCIH5OUDBD3KRAS3UIB \
  | 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: bbc68ea751120fd750611ed5104b7440403fd3de69eefce3d124bfdb0c1af0a7

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "e73f05498f11d4838e98ccc0a018b5a7d2c3ed2f08d9fcb401b2b14e50aa420a",
    "cross_cats_sorted": [
      "math-ph",
      "math.MP",
      "math.SP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2025-05-25T21:24:16Z",
    "title_canon_sha256": "a0694309267adfaec2a66a0c227546c8a1ed4741c7789fe60a0547ba888a539e"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2505.19326",
    "kind": "arxiv",
    "version": 2
  }
}