Pith Number

pith:QNFHQCTF

pith:2026:QNFHQCTFDKLZ6GJ6OQKVJIYNCW

not attested not anchored not stored refs pending

Implicit Midpoint Gradient Descent: Fast and Learning rate free convergence for Zero-Sum Games

Gaoqi Xue, James P. Bailey

arxiv:2607.09950 v1 · 2026-07-10 · cs.GT · 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{QNFHQCTFDKLZ6GJ6OQKVJIYNCW}

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	2026-07-14T00:18:44.432620Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

834a780a651a979f193e741554a30d15970f386dd4f635254ba0a45e8638b37d

Aliases

arxiv: 2607.09950 · arxiv_version: 2607.09950v1 · doi: 10.48550/arxiv.2607.09950 · pith_short_12: QNFHQCTFDKLZ · pith_short_16: QNFHQCTFDKLZ6GJ6 · pith_short_8: QNFHQCTF

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/QNFHQCTFDKLZ6GJ6OQKVJIYNCW \
  | 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: 834a780a651a979f193e741554a30d15970f386dd4f635254ba0a45e8638b37d

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "416c8b7badcc4fe31e880c62d2ed276ae6a983efecf7f00ecefe783e36e6793c",
    "cross_cats_sorted": [
      "math.OC"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "cs.GT",
    "submitted_at": "2026-07-10T20:04:08Z",
    "title_canon_sha256": "0e9cb1e5869481cc971f33115ff7ac755d9b9ba867071e03111d5a6bf7b2a4d1"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2607.09950",
    "kind": "arxiv",
    "version": 1
  }
}