Pith Number

pith:TGGZQ4Z6

pith:2001:TGGZQ4Z6RLP4YKF3FKGWQATUZF

not attested not anchored not stored refs pending

Strongly Singular Masas in Type $II_1$ Factors

Allan Sinclair, Roger Smith

arxiv:math/0107075 v1 · 2001-07-10 · 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{TGGZQ4Z6RLP4YKF3FKGWQATUZF}

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	2026-05-18T01:05:37.670764Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

998d98733e8adfcc28bb2a8d680274c96ed6cac4ee12fd3e60c5aacb6881ddad

Aliases

arxiv: math/0107075 · arxiv_version: math/0107075v1 · doi: 10.48550/arxiv.math/0107075 · pith_short_12: TGGZQ4Z6RLP4 · pith_short_16: TGGZQ4Z6RLP4YKF3 · pith_short_8: TGGZQ4Z6

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/TGGZQ4Z6RLP4YKF3FKGWQATUZF \
  | 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: 998d98733e8adfcc28bb2a8d680274c96ed6cac4ee12fd3e60c5aacb6881ddad

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "db59809fe579f1ac8e5e5a6dedb4ca95abf3045c97e1f6f75ed278464b7b838a",
    "cross_cats_sorted": [],
    "license": "",
    "primary_cat": "math.OA",
    "submitted_at": "2001-07-10T20:39:56Z",
    "title_canon_sha256": "51aed808d2d5a523a28c2ee097c72f35b6615f20b5222934c0335d2781a53fa1"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0107075",
    "kind": "arxiv",
    "version": 1
  }
}