Pith Number

pith:J4CDGI3R

pith:2016:J4CDGI3RTFGYCENTFRPL5VYC5L

not attested not anchored not stored refs pending

Cauchy transforms arising from homomorphic conditional expectations parametrize free Pick functions but those arising from conditional expectations do not

J. E. Pascoe, Ryan Tully-Doyle

arxiv:1607.06737 v1 · 2016-07-22 · math.FA · 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{J4CDGI3RTFGYCENTFRPL5VYC5L}

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	2026-05-18T01:10:39.210450Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

4f04332371994d8111b32c5ebed702eac0ecd0d89f78e296ee3933e047b5803b

Aliases

arxiv: 1607.06737 · arxiv_version: 1607.06737v1 · doi: 10.48550/arxiv.1607.06737 · pith_short_12: J4CDGI3RTFGY · pith_short_16: J4CDGI3RTFGYCENT · pith_short_8: J4CDGI3R

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/J4CDGI3RTFGYCENTFRPL5VYC5L \
  | 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: 4f04332371994d8111b32c5ebed702eac0ecd0d89f78e296ee3933e047b5803b

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "10b5939cf0de1c079b8b07a09d76d8694a9e609bb0b87e8085f3b813150c0d60",
    "cross_cats_sorted": [
      "math.OA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.FA",
    "submitted_at": "2016-07-22T16:45:49Z",
    "title_canon_sha256": "36ff03cdbdf5fdcc3dda1f95fcb19829d70c5f26a10ccad61e1da54cd697b47c"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1607.06737",
    "kind": "arxiv",
    "version": 1
  }
}