Pith Number

pith:VWZCB5RC

pith:2026:VWZCB5RCHFG54DSRFKSXLAY4FW

not attested not anchored not stored refs pending

Periodicity, type $II_1$ factors and free Poisson laws in interacting Fock spaces

\'Eric Ricard, Vitonofrio Crismale, Yun Gang Lu

arxiv:2606.18162 v1 · 2026-06-16 · 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{VWZCB5RCHFG54DSRFKSXLAY4FW}

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	2026-06-19T16:10:49.835830Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

adb220f622394dde0e512aa575831c2d96e4347b7de7474de0f28da9f0db7842

Aliases

arxiv: 2606.18162 · arxiv_version: 2606.18162v1 · doi: 10.48550/arxiv.2606.18162 · pith_short_12: VWZCB5RCHFG5 · pith_short_16: VWZCB5RCHFG54DSR · pith_short_8: VWZCB5RC

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/VWZCB5RCHFG54DSRFKSXLAY4FW \
  | 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: adb220f622394dde0e512aa575831c2d96e4347b7de7474de0f28da9f0db7842

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "8a7e5c3191f7c1bdca9b1a29a0f97dba0fe98faf0dc864c04ad1ffc672b19451",
    "cross_cats_sorted": [
      "math.PR"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.OA",
    "submitted_at": "2026-06-16T17:00:43Z",
    "title_canon_sha256": "54c22566264637932d702fa699db48d220d1606403b51c7d462070f630a028e4"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2606.18162",
    "kind": "arxiv",
    "version": 1
  }
}