Pith Number

pith:LGZVJ2Q5

pith:2026:LGZVJ2Q5O45HS4GXINFDJFLIAU

not attested not anchored not stored refs pending

A Link between Shock-wave Theory and Symmetry-reduced Stochastic Gradient Descent for Artificial Neural Networks

Taiki Miyagawa

arxiv:2606.18303 v1 · 2026-06-16 · cs.LG · cs.AI

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{LGZVJ2Q5O45HS4GXINFDJFLIAU}

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	2026-06-19T16:10:57.414303Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

59b354ea1d773a7970d7434a349568053b5a5941dbbd5c7be66ff4ed2595bd78

Aliases

arxiv: 2606.18303 · arxiv_version: 2606.18303v1 · doi: 10.48550/arxiv.2606.18303 · pith_short_12: LGZVJ2Q5O45H · pith_short_16: LGZVJ2Q5O45HS4GX · pith_short_8: LGZVJ2Q5

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/LGZVJ2Q5O45HS4GXINFDJFLIAU \
  | 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: 59b354ea1d773a7970d7434a349568053b5a5941dbbd5c7be66ff4ed2595bd78

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "2efbf925ad2270e106121c0a1d840d2003a948fbb0e8d09ad986a7a3dc7804e8",
    "cross_cats_sorted": [
      "cs.AI"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "cs.LG",
    "submitted_at": "2026-06-16T06:20:52Z",
    "title_canon_sha256": "22dc49445373d19c79bb80dae043495b04b9610dc38647218a0ab9dc12f3ca1a"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2606.18303",
    "kind": "arxiv",
    "version": 1
  }
}