Pith Number

pith:72AKGRGX

pith:2026:72AKGRGXLGYSCZMAHLFWUB43WQ

not attested not anchored not stored refs pending

Fourier-Diagonalized Natural Gradients and Sobolev Mirror Descent

Jeongbin Jo

arxiv:2607.01634 v1 · 2026-07-02 · math.NA · cs.NA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{72AKGRGXLGYSCZMAHLFWUB43WQ}

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	2026-07-03T01:17:04.009021Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

fe80a344d759b12165803acb6a079bb40a06798320ed920cef31a1b36325df14

Aliases

arxiv: 2607.01634 · arxiv_version: 2607.01634v1 · doi: 10.48550/arxiv.2607.01634 · pith_short_12: 72AKGRGXLGYS · pith_short_16: 72AKGRGXLGYSCZMA · pith_short_8: 72AKGRGX

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/72AKGRGXLGYSCZMAHLFWUB43WQ \
  | 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: fe80a344d759b12165803acb6a079bb40a06798320ed920cef31a1b36325df14

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "6627fdb9aa9015e4a64bbe2048d6cdcaa5a11b64e501942a8ff3824341a76343",
    "cross_cats_sorted": [
      "cs.NA"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.NA",
    "submitted_at": "2026-07-02T03:05:45Z",
    "title_canon_sha256": "e2401071fa29529dd8fb9c3dde8012bc5888e23e980ff46287c6979cb1c40994"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2607.01634",
    "kind": "arxiv",
    "version": 1
  }
}