Pith Number

pith:MDVSAZKR

pith:2015:MDVSAZKR4XV3ZI56EBOGZMFP75

not attested not anchored not stored refs pending

Spectral multipliers on $2$-step groups: topological versus homogeneous dimension

Alessio Martini, Detlef M\"uller

arxiv:1508.01687 v2 · 2015-08-07 · math.AP · math.FA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{MDVSAZKR4XV3ZI56EBOGZMFP75}

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	2026-05-18T01:01:34.656479Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

60eb206551e5ebbca3be205c6cb0afff48b28aed0e6f7918c7585c820f0ef679

Aliases

arxiv: 1508.01687 · arxiv_version: 1508.01687v2 · doi: 10.48550/arxiv.1508.01687 · pith_short_12: MDVSAZKR4XV3 · pith_short_16: MDVSAZKR4XV3ZI56 · pith_short_8: MDVSAZKR

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/MDVSAZKR4XV3ZI56EBOGZMFP75 \
  | 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: 60eb206551e5ebbca3be205c6cb0afff48b28aed0e6f7918c7585c820f0ef679

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "0cb8306088328364bb7fd8573b88f16cdf26d116a50085858f5e0d1b784b534f",
    "cross_cats_sorted": [
      "math.FA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2015-08-07T13:37:09Z",
    "title_canon_sha256": "65604d28bd4052d4d8dd7599bbb483ca0ac5a5df6bf5dd13bf51b2b2b2bfa2df"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1508.01687",
    "kind": "arxiv",
    "version": 2
  }
}