Pith Number

pith:36QXMUAW

pith:2024:36QXMUAW3THSQIKSPORMMTXAOB

not attested not anchored not stored refs pending

Topological Generalization Bounds for Discrete-Time Stochastic Optimization Algorithms

Benjamin Dupuis, Rayna Andreeva, Rik Sarkar, Tolga Birdal, Umut \c{S}im\c{s}ekli

arxiv:2407.08723 v2 · 2024-07-11 · cs.LG · math.AT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{36QXMUAW3THSQIKSPORMMTXAOB}

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	2026-07-05T09:49:07.698513Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

dfa1765016dccf2821527ba2c64ee07057d3436db3009fd47aa4ef2a5bdc3d3e

Aliases

arxiv: 2407.08723 · arxiv_version: 2407.08723v2 · doi: 10.48550/arxiv.2407.08723 · pith_short_12: 36QXMUAW3THS · pith_short_16: 36QXMUAW3THSQIKS · pith_short_8: 36QXMUAW

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/36QXMUAW3THSQIKSPORMMTXAOB \
  | 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: dfa1765016dccf2821527ba2c64ee07057d3436db3009fd47aa4ef2a5bdc3d3e

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "acd5c92679b31b229f2e855a7fc4925991897f1369ec4ca1f24996e6783d7ba4",
    "cross_cats_sorted": [
      "math.AT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "cs.LG",
    "submitted_at": "2024-07-11T17:56:03Z",
    "title_canon_sha256": "cc38ad39e658a3a631e04ec4ebd647ffafbfaa5f1d23912b4a4340e6d94202fc"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2407.08723",
    "kind": "arxiv",
    "version": 2
  }
}