Pith Number

pith:66YIGUCF

pith:2026:66YIGUCF5U4TWECJRTWFPDPHHH

not attested not anchored not stored refs pending

Pontryagin Maximum Principle in Free Probability Theory

Georg Schl\"uchtermann, Michael Wibmer

arxiv:2606.21778 v1 · 2026-06-19 · 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{66YIGUCF5U4TWECJRTWFPDPHHH}

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	2026-06-23T01:13:22.316434Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

f7b0835045ed393b10498cec578de739ce57b1ddd1d9647e15dde714c9e035ae

Aliases

arxiv: 2606.21778 · arxiv_version: 2606.21778v1 · doi: 10.48550/arxiv.2606.21778 · pith_short_12: 66YIGUCF5U4T · pith_short_16: 66YIGUCF5U4TWECJ · pith_short_8: 66YIGUCF

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/66YIGUCF5U4TWECJRTWFPDPHHH \
  | 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: f7b0835045ed393b10498cec578de739ce57b1ddd1d9647e15dde714c9e035ae

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "9932846561f33aae1352486fa84a61dd78600e2468a0d42c4623f2767dd13335",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2026-06-19T21:55:03Z",
    "title_canon_sha256": "46f2eb2f228e5332f33143275ec93ba8fb126ecdae9fe28ed8abac04d6ec0b5c"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2606.21778",
    "kind": "arxiv",
    "version": 1
  }
}