Pith Number

pith:GBXMSZ43

pith:2026:GBXMSZ43FCMC3ULTTVIO75CDOW

not attested not anchored not stored refs pending

Geometric--Nongeometric Optimizer Calculus: A Modular Language for Reachable Gradient Methods

Zavier Li

arxiv:2607.07206 v1 · 2026-07-08 · cs.LG · 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{GBXMSZ43FCMC3ULTTVIO75CDOW}

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	2026-07-09T01:20:17.803085Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

306ec9679b28982dd1739d50eff44375a43504591f06f85b5d03433f4a7041e4

Aliases

arxiv: 2607.07206 · arxiv_version: 2607.07206v1 · doi: 10.48550/arxiv.2607.07206 · pith_short_12: GBXMSZ43FCMC · pith_short_16: GBXMSZ43FCMC3ULT · pith_short_8: GBXMSZ43

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/GBXMSZ43FCMC3ULTTVIO75CDOW \
  | 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: 306ec9679b28982dd1739d50eff44375a43504591f06f85b5d03433f4a7041e4

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "eba5e0b6b3eeee990df83a13f69c9d95793204d97df745b50c6f756b2b89ef79",
    "cross_cats_sorted": [
      "math.OC"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "cs.LG",
    "submitted_at": "2026-07-08T09:40:44Z",
    "title_canon_sha256": "9805cac08a2674ac01a3193d0f363736dea3c5e36c06ef5bb9c04aa86ace137a"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2607.07206",
    "kind": "arxiv",
    "version": 1
  }
}