Pith Number

pith:SSYXUOPW

pith:2013:SSYXUOPWYIPTC6R7XWK3M2CDMG

not attested not anchored not stored refs pending

Spectral multiplier theorems of Euclidean type on new classes of 2-step stratified groups

Alessio Martini, Detlef M\"uller

arxiv:1306.0387 v2 · 2013-06-03 · 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{SSYXUOPWYIPTC6R7XWK3M2CDMG}

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	2026-05-18T02:29:39.297701Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

94b17a39f6c21f317a3fbd95b6684361b93d50b8335d36962604479803d92e41

Aliases

arxiv: 1306.0387 · arxiv_version: 1306.0387v2 · doi: 10.48550/arxiv.1306.0387 · pith_short_12: SSYXUOPWYIPT · pith_short_16: SSYXUOPWYIPTC6R7 · pith_short_8: SSYXUOPW

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/SSYXUOPWYIPTC6R7XWK3M2CDMG \
  | 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: 94b17a39f6c21f317a3fbd95b6684361b93d50b8335d36962604479803d92e41

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "0a473980bbf30872e717f5522dcf1700bda3b7aa80de4fe0abc3da339386a7d2",
    "cross_cats_sorted": [
      "math.FA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2013-06-03T12:52:48Z",
    "title_canon_sha256": "351834ff33cf73b778c73fc62cda19623fd8886183d596a10a8c807060a944d6"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1306.0387",
    "kind": "arxiv",
    "version": 2
  }
}