Pith Number

pith:PSVK4SKL

pith:2021:PSVK4SKLRL7ZCCCBQWF6AM56G4

not attested not anchored not stored refs pending

A characterization of rationality for operators in free semicircular elements

Akihiro Miyagawa

arxiv:2109.08841 v2 · 2021-09-18 · math.OA · math.FA · math.RA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{PSVK4SKLRL7ZCCCBQWF6AM56G4}

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	2026-07-05T05:22:04.491678Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

7caaae494b8aff910841858be033be372f3f1a5bbf27844f6c15d4c3a8dc1071

Aliases

arxiv: 2109.08841 · arxiv_version: 2109.08841v2 · doi: 10.48550/arxiv.2109.08841 · pith_short_12: PSVK4SKLRL7Z · pith_short_16: PSVK4SKLRL7ZCCCB · pith_short_8: PSVK4SKL

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/PSVK4SKLRL7ZCCCBQWF6AM56G4 \
  | 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: 7caaae494b8aff910841858be033be372f3f1a5bbf27844f6c15d4c3a8dc1071

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "62f7f2f5af653c65120371b97a4be2a508d1bcef025348e1ddc95e094b1e22b5",
    "cross_cats_sorted": [
      "math.FA",
      "math.RA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.OA",
    "submitted_at": "2021-09-18T05:51:14Z",
    "title_canon_sha256": "7ecfdf0b78ade4cfbdf59a53fd32948b36a19b66a9b9e130a0d4b9d62e79a868"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2109.08841",
    "kind": "arxiv",
    "version": 2
  }
}