Pith Number

pith:ZGM5JPI2

pith:2019:ZGM5JPI2CSG4PHJQ3MEJO6MWUL

not attested not anchored not stored refs pending

Pure and Spurious Critical Points: a Geometric Study of Linear Networks

Joan Bruna, Kathl\'en Kohn, Matthew Trager

arxiv:1910.01671 v2 · 2019-10-03 · cs.LG · math.AG · 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{ZGM5JPI2CSG4PHJQ3MEJO6MWUL}

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	2026-07-05T00:52:27.478965Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

c999d4bd1a148dc79d30db08977996a2fd819630d53a6301c8c80cc76f0e951f

Aliases

arxiv: 1910.01671 · arxiv_version: 1910.01671v2 · doi: 10.48550/arxiv.1910.01671 · pith_short_12: ZGM5JPI2CSG4 · pith_short_16: ZGM5JPI2CSG4PHJQ · pith_short_8: ZGM5JPI2

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/ZGM5JPI2CSG4PHJQ3MEJO6MWUL \
  | 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: c999d4bd1a148dc79d30db08977996a2fd819630d53a6301c8c80cc76f0e951f

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "0bde633c669432bf4a29b4d650dfe008f34f855fa4594c66e29586c54a1a6c8a",
    "cross_cats_sorted": [
      "math.AG",
      "stat.ML"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "cs.LG",
    "submitted_at": "2019-10-03T18:22:30Z",
    "title_canon_sha256": "f803ab99b86b7630266c9e406503ab59af0e6840809bebe63c2b76fad4fc7376"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1910.01671",
    "kind": "arxiv",
    "version": 2
  }
}