Pith Number

pith:FT66XEG4

pith:2019:FT66XEG4G6MMTZTOWPGS5ROVO2

not attested not anchored not stored refs pending

Relative entropy for von Neumann subalgebras

Li Gao, Marius Junge, Nicholas LaRacuente

arxiv:1909.01906 v3 · 2019-09-04 · 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{FT66XEG4G6MMTZTOWPGS5ROVO2}

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	2026-07-05T01:51:37.004088Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

2cfdeb90dc3798c9e66eb3cd2ec5d576aabe622344a853d7ec3ff4937e453e94

Aliases

arxiv: 1909.01906 · arxiv_version: 1909.01906v3 · doi: 10.48550/arxiv.1909.01906 · pith_short_12: FT66XEG4G6MM · pith_short_16: FT66XEG4G6MMTZTO · pith_short_8: FT66XEG4

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/FT66XEG4G6MMTZTOWPGS5ROVO2 \
  | 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: 2cfdeb90dc3798c9e66eb3cd2ec5d576aabe622344a853d7ec3ff4937e453e94

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "453cc7c5f2f7c0329202e6fee3284891f1b290ae5000dcdd9bd7ee748901db42",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.OA",
    "submitted_at": "2019-09-04T15:58:59Z",
    "title_canon_sha256": "c0b9af998b63c7d0ce65ac65cf6a8ad8d6c22a143bcc6df51ab1cb4ae594d73f"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1909.01906",
    "kind": "arxiv",
    "version": 3
  }
}