Pith Number

pith:DIZ33I4Y

pith:2020:DIZ33I4YVU3GRPH6GUYLC4SEY4

not attested not anchored not stored refs pending

Strong sums of projections in type ${\rm II}$ factors

Junsheng Fang, Xinyan Cao, Zhaolin Yao

arxiv:2010.10099 v1 · 2020-10-20 · 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{DIZ33I4YVU3GRPH6GUYLC4SEY4}

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	2026-07-05T01:44:27.239622Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

1a33bda398ad3668bcfe3530b17244c73aeeb90ab074febe77061db89ddb4166

Aliases

arxiv: 2010.10099 · arxiv_version: 2010.10099v1 · doi: 10.48550/arxiv.2010.10099 · pith_short_12: DIZ33I4YVU3G · pith_short_16: DIZ33I4YVU3GRPH6 · pith_short_8: DIZ33I4Y

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/DIZ33I4YVU3GRPH6GUYLC4SEY4 \
  | 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: 1a33bda398ad3668bcfe3530b17244c73aeeb90ab074febe77061db89ddb4166

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "860592cb2b8f42fe7f4e99969b1a3c74b072cc2725271310b9f3307a74796fcd",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.OA",
    "submitted_at": "2020-10-20T07:48:43Z",
    "title_canon_sha256": "e135aa79fde9fcc4348c7fa6b868bf64083c45d0bff0373952dd0da288a2d792"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2010.10099",
    "kind": "arxiv",
    "version": 1
  }
}