Pith Number

pith:CTO4BKKP

pith:2026:CTO4BKKPT5FI4GOUGBMEQ5YPGZ

not attested not anchored not stored refs pending

The Balance Property: The Constrained Case, with a View on Risk Sharing

Mario V. W\"uthrich

arxiv:2606.07276 v1 · 2026-06-05 · math.ST · q-fin.RM · stat.TH

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{CTO4BKKPT5FI4GOUGBMEQ5YPGZ}

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	2026-06-08T01:05:17.049163Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

14ddc0a94f9f4a8e19d4305848770f36602ded957cb40a0d55e67e14c785d214

Aliases

arxiv: 2606.07276 · arxiv_version: 2606.07276v1 · doi: 10.48550/arxiv.2606.07276 · pith_short_12: CTO4BKKPT5FI · pith_short_16: CTO4BKKPT5FI4GOU · pith_short_8: CTO4BKKP

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/CTO4BKKPT5FI4GOUGBMEQ5YPGZ \
  | 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: 14ddc0a94f9f4a8e19d4305848770f36602ded957cb40a0d55e67e14c785d214

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "f6502a9d9c35943a646ab9879dfdd01e496ef55a1028934a01d56955cd03f783",
    "cross_cats_sorted": [
      "q-fin.RM",
      "stat.TH"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.ST",
    "submitted_at": "2026-06-05T13:53:03Z",
    "title_canon_sha256": "bbb53ef7dbf58f537a03c575c9f1a833fb2d52495fe1e4b48c00e878c4bb2aa3"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2606.07276",
    "kind": "arxiv",
    "version": 1
  }
}