Pith Number

pith:7ZYJIOTP

pith:2026:7ZYJIOTPKIY56GNPLRRYCZ255V

not attested not anchored not stored refs pending

Sinkhorn-Knopp balancing with generalised martingale-type constraints

Abigail Langbridge, Martin Corless, Robert Shorten

arxiv:2606.26739 v1 · 2026-06-25 · math.OC

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{7ZYJIOTPKIY56GNPLRRYCZ255V}

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	2026-06-26T01:15:58.449521Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

fe70943a6f5231df19af5c6381675ded6ea94415ff20bd8c70f49240a4411155

Aliases

arxiv: 2606.26739 · arxiv_version: 2606.26739v1 · doi: 10.48550/arxiv.2606.26739 · pith_short_12: 7ZYJIOTPKIY5 · pith_short_16: 7ZYJIOTPKIY56GNP · pith_short_8: 7ZYJIOTP

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/7ZYJIOTPKIY56GNPLRRYCZ255V \
  | 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: fe70943a6f5231df19af5c6381675ded6ea94415ff20bd8c70f49240a4411155

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "f197a12a5451cf1e727b11431070c29fbaa68fe748f86c4d6c777f00100d4200",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.OC",
    "submitted_at": "2026-06-25T08:23:06Z",
    "title_canon_sha256": "0c938efa70867f88f86958486a97cc4671678311d08d013774709494fd4d23dc"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2606.26739",
    "kind": "arxiv",
    "version": 1
  }
}