Pith Number

pith:Y7GJFDXQ

pith:2017:Y7GJFDXQKPFI24LXPAO4C6DWD2

not attested not anchored not stored refs pending

Harmonic analysis and BMO-spaces of free Araki-Woods factors

Martijn Caspers

arxiv:1708.09578 v4 · 2017-08-31 · math.OA · math.FA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{Y7GJFDXQKPFI24LXPAO4C6DWD2}

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	2026-05-18T00:23:45.431704Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

c7cc928ef053ca8d7177781dc178761eac4a4651e05d9fcd74b6d8db3d16d6a4

Aliases

arxiv: 1708.09578 · arxiv_version: 1708.09578v4 · doi: 10.48550/arxiv.1708.09578 · pith_short_12: Y7GJFDXQKPFI · pith_short_16: Y7GJFDXQKPFI24LX · pith_short_8: Y7GJFDXQ

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/Y7GJFDXQKPFI24LXPAO4C6DWD2 \
  | 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: c7cc928ef053ca8d7177781dc178761eac4a4651e05d9fcd74b6d8db3d16d6a4

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "b0726c0cb62423bac96e900bd7476249da8491f9703e340d896217eeef4b4a79",
    "cross_cats_sorted": [
      "math.FA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.OA",
    "submitted_at": "2017-08-31T06:19:40Z",
    "title_canon_sha256": "98dac72a9eafef4b4680016fbc76a9a0f392713054a7283dc29b56911faee606"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1708.09578",
    "kind": "arxiv",
    "version": 4
  }
}