Pith Number

pith:MPRVGHZT

pith:2026:MPRVGHZTC3ODQI6HXQCIAAP7EU

not attested not anchored not stored refs pending

Blackwell Approachability and Gradient Equilibrium are Equivalent

Brian W. Lee, Michael I. Jordan, Nika Haghtalab, Ryan J. Tibshirani

arxiv:2606.27315 v1 · 2026-06-25 · cs.LG

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{MPRVGHZTC3ODQI6HXQCIAAP7EU}

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	2026-06-26T01:16:18.478739Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

63e3531f3316dc3823c7bc048001ff253225050b7e4fb15b45d87158add8bc69

Aliases

arxiv: 2606.27315 · arxiv_version: 2606.27315v1 · doi: 10.48550/arxiv.2606.27315 · pith_short_12: MPRVGHZTC3OD · pith_short_16: MPRVGHZTC3ODQI6H · pith_short_8: MPRVGHZT

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/MPRVGHZTC3ODQI6HXQCIAAP7EU \
  | 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: 63e3531f3316dc3823c7bc048001ff253225050b7e4fb15b45d87158add8bc69

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "1a97c3a9406052352980e9fa2404832413762eadc109b60e43e8a9ceb5caf159",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "cs.LG",
    "submitted_at": "2026-06-25T17:29:48Z",
    "title_canon_sha256": "5a05960939ed99f34d99802e594962a78ab91f3b4dd1420a86ef1d91f0c1dec4"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2606.27315",
    "kind": "arxiv",
    "version": 1
  }
}