Pith Number

pith:PCOM7EBC

pith:2015:PCOM7EBCV3YYBADFBMWLWMPQQX

not attested not anchored not stored refs pending

A stochastic density matrix approach to approximation of probability distributions and its application to nonlinear systems

Igor G. Vladimirov

arxiv:1506.04775 v2 · 2015-06-15 · math.PR · cs.SY · math.AP · math.NA · math.ST · stat.TH

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{PCOM7EBCV3YYBADFBMWLWMPQQX}

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	2026-05-18T00:58:10.681986Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

789ccf9022aef18080650b2cbb31f085d1bb485c55c588db58001b7c05a8ed4c

Aliases

arxiv: 1506.04775 · arxiv_version: 1506.04775v2 · doi: 10.48550/arxiv.1506.04775 · pith_short_12: PCOM7EBCV3YY · pith_short_16: PCOM7EBCV3YYBADF · pith_short_8: PCOM7EBC

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/PCOM7EBCV3YYBADFBMWLWMPQQX \
  | 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: 789ccf9022aef18080650b2cbb31f085d1bb485c55c588db58001b7c05a8ed4c

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "fd842e195c92ee6f29477031f064e5c49b897222b7b26d8412eb02e959bb5df9",
    "cross_cats_sorted": [
      "cs.SY",
      "math.AP",
      "math.NA",
      "math.ST",
      "stat.TH"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2015-06-15T21:16:36Z",
    "title_canon_sha256": "959c5350f60c08d913361af5cb22ccac435ba69e01604301600642fe58cec1ee"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1506.04775",
    "kind": "arxiv",
    "version": 2
  }
}