Pith Number

pith:FKZ2WWQB

pith:2018:FKZ2WWQBJXQI5H7KXAKQRZU3HC

not attested not anchored not stored refs pending

On the relative bicentralizer flows and the relative flow of weights of inclusions of factors of type III$_1$

Toshihiko Masuda

arxiv:1812.02877 v1 · 2018-12-07 · math.OA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{FKZ2WWQBJXQI5H7KXAKQRZU3HC}

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	2026-05-17T23:58:51.561450Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

2ab3ab5a014de08e9feab81508e69b38b08279136e9ce6170c734e978209c784

Aliases

arxiv: 1812.02877 · arxiv_version: 1812.02877v1 · doi: 10.48550/arxiv.1812.02877 · pith_short_12: FKZ2WWQBJXQI · pith_short_16: FKZ2WWQBJXQI5H7K · pith_short_8: FKZ2WWQB

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/FKZ2WWQBJXQI5H7KXAKQRZU3HC \
  | 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: 2ab3ab5a014de08e9feab81508e69b38b08279136e9ce6170c734e978209c784

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "1bb30e774cc044252fedac43403604432ead8946adaadde4ccd7db688bcfabdb",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.OA",
    "submitted_at": "2018-12-07T02:15:02Z",
    "title_canon_sha256": "12a86a3e863766be585aed9477592ff3e86d2fbc8a86595ba437d75a1159ad60"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1812.02877",
    "kind": "arxiv",
    "version": 1
  }
}