Pith Number

pith:QCIR7JUY

pith:2026:QCIR7JUYC7UC6A4MOD4B2RTS34

not attested not anchored not stored refs pending

Landscape analysis for shallow neural networks: Complete classification of critical points for cubic activation and affine target functions

Diyora Salimova, Ilkhom Mukhammadiev, Shokhrukh Ibragimov

arxiv:2607.15173 v1 · 2026-07-16 · 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{QCIR7JUYC7UC6A4MOD4B2RTS34}

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	2026-07-17T01:22:12.878788Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

80911fa69817e82f038c70f81d4672df093b98d24270b7dfc2d4a1ee52e7cb96

Aliases

arxiv: 2607.15173 · arxiv_version: 2607.15173v1 · doi: 10.48550/arxiv.2607.15173 · pith_short_12: QCIR7JUYC7UC · pith_short_16: QCIR7JUYC7UC6A4M · pith_short_8: QCIR7JUY

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/QCIR7JUYC7UC6A4MOD4B2RTS34 \
  | 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: 80911fa69817e82f038c70f81d4672df093b98d24270b7dfc2d4a1ee52e7cb96

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "91a6ad3d02d3a095a3f512dd37cdc5ed046a653898c941b8404d54650b30b4a4",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.OC",
    "submitted_at": "2026-07-16T16:22:16Z",
    "title_canon_sha256": "3460baca3e0450eefe38476f65e41f2923298cf862aef033f67fff6092051019"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2607.15173",
    "kind": "arxiv",
    "version": 1
  }
}