Pith Number

pith:ZG5B2MGW

pith:2018:ZG5B2MGWAFR5IY7O7HRFJW36FA

not attested not anchored not stored refs pending

Vacuum distribution, norm and spectral properties for sums of monotone position operators

Vitonofrio Crismale, Yun Gang Lu

arxiv:1812.08688 v1 · 2018-12-20 · math.OA · math.PR

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{ZG5B2MGWAFR5IY7O7HRFJW36FA}

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	2026-05-17T23:57:49.368573Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

c9ba1d30d60163d463eef9e254db7e280eb73505fb52ae814293e86aaea2c309

Aliases

arxiv: 1812.08688 · arxiv_version: 1812.08688v1 · doi: 10.48550/arxiv.1812.08688 · pith_short_12: ZG5B2MGWAFR5 · pith_short_16: ZG5B2MGWAFR5IY7O · pith_short_8: ZG5B2MGW

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/ZG5B2MGWAFR5IY7O7HRFJW36FA \
  | 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: c9ba1d30d60163d463eef9e254db7e280eb73505fb52ae814293e86aaea2c309

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "919fc5659cfe923217f5d9b47d57b417189054caac4b4d011062a6b1a6a19d46",
    "cross_cats_sorted": [
      "math.PR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.OA",
    "submitted_at": "2018-12-20T16:42:47Z",
    "title_canon_sha256": "0684da14cab3575a7c6d8ef9b525e0708d22d8fb7fc326aa3585cc0fe8f10f11"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1812.08688",
    "kind": "arxiv",
    "version": 1
  }
}