Pith Number

pith:O33LZKML

pith:2024:O33LZKML22O43FBTHW5MW3SDI2

not attested not anchored not stored refs pending

Toward a Unified Theory of Gradient Descent under Generalized Smoothness

Alexander Tyurin

arxiv:2412.11773 v2 · 2024-12-16 · 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{O33LZKML22O43FBTHW5MW3SDI2}

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	2026-07-05T11:28:12.931106Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

76f6bca98bd69dcd94333dbacb6e4346bae904e81eaea3103b8c65fe6bae6313

Aliases

arxiv: 2412.11773 · arxiv_version: 2412.11773v2 · doi: 10.48550/arxiv.2412.11773 · pith_short_12: O33LZKML22O4 · pith_short_16: O33LZKML22O43FBT · pith_short_8: O33LZKML

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/O33LZKML22O43FBTHW5MW3SDI2 \
  | 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: 76f6bca98bd69dcd94333dbacb6e4346bae904e81eaea3103b8c65fe6bae6313

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "d6f2bf780c89bf5fa398d650e419a33eda91859338c513790bddd326827dbf6f",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.OC",
    "submitted_at": "2024-12-16T13:46:02Z",
    "title_canon_sha256": "a1e4e03c21ea0d65cc010b92c27f22b84353cf0e7f18c6c007ab5564c7bb1e55"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2412.11773",
    "kind": "arxiv",
    "version": 2
  }
}