Pith Number

pith:3N3G2M5T

pith:2012:3N3G2M5TOLH7GEVAOPLABKC7W6

not attested not anchored not stored refs pending

Non-commutative stochastic distributions and applications to linear systems theory

Daniel Alpay, Guy Salomon

arxiv:1209.4580 v2 · 2012-09-20 · math.FA · 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{3N3G2M5TOLH7GEVAOPLABKC7W6}

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	2026-05-18T03:32:47.462386Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

db766d33b372cff312a073d600a85fb7975a47aae96b7ce6e939efae1c85860d

Aliases

arxiv: 1209.4580 · arxiv_version: 1209.4580v2 · doi: 10.48550/arxiv.1209.4580 · pith_short_12: 3N3G2M5TOLH7 · pith_short_16: 3N3G2M5TOLH7GEVA · pith_short_8: 3N3G2M5T

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/3N3G2M5TOLH7GEVAOPLABKC7W6 \
  | 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: db766d33b372cff312a073d600a85fb7975a47aae96b7ce6e939efae1c85860d

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "2334c0eea2b58414dcf5be25b610d858ae218949b6e5116c38592ed6cb1fca97",
    "cross_cats_sorted": [
      "math.PR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.FA",
    "submitted_at": "2012-09-20T16:43:56Z",
    "title_canon_sha256": "07500bfb2dcb151c4a7340cfd9920e4177a4a79c06a5232b23355a534b4c4355"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1209.4580",
    "kind": "arxiv",
    "version": 2
  }
}