Pith Number

pith:RSJG2TCY

pith:2025:RSJG2TCYEF5TBDPFGWK6TRZXKZ

not attested not anchored not stored refs pending

Toric geometry of ReLU neural networks

Yaoying Fu

arxiv:2509.05894 v1 · 2025-09-07 · math.AG · cs.LG · stat.ML

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{RSJG2TCYEF5TBDPFGWK6TRZXKZ}

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.

Cited by

1 paper in Pith

On the fibers and semi-algebraicity of ReLU neuromanifolds

Receipt and verification

First computed	2026-07-05T12:07:40.849780Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

8c926d4c58217b308de53595e9c7375657979a6f2151f5971f2d409eb10ae07b

Aliases

arxiv: 2509.05894 · arxiv_version: 2509.05894v1 · doi: 10.48550/arxiv.2509.05894 · pith_short_12: RSJG2TCYEF5T · pith_short_16: RSJG2TCYEF5TBDPF · pith_short_8: RSJG2TCY

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/RSJG2TCYEF5TBDPFGWK6TRZXKZ \
  | 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: 8c926d4c58217b308de53595e9c7375657979a6f2151f5971f2d409eb10ae07b

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "8a97e446f8eb8f0f137fbf89399d266d541206edfdc5e6851c28ea0fb2ae25f4",
    "cross_cats_sorted": [
      "cs.LG",
      "stat.ML"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AG",
    "submitted_at": "2025-09-07T02:08:23Z",
    "title_canon_sha256": "afa288b6bcb79a885278ed544eb1c611b67a3f026c7c2d0ec0859022dcfb2911"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2509.05894",
    "kind": "arxiv",
    "version": 1
  }
}