Pith Number

pith:UNPKT54Z

pith:2016:UNPKT54ZIWKATVZ5ACLXWMU3SH

not attested not anchored not stored refs pending

Topology and Geometry of Half-Rectified Network Optimization

C. Daniel Freeman, Joan Bruna

arxiv:1611.01540 v4 · 2016-11-04 · stat.ML · cs.LG

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{UNPKT54ZIWKATVZ5ACLXWMU3SH}

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

3 papers in Pith

Weight-space symmetry in deep networks gives rise to permutation saddles, connected by equal-loss valleys across the loss landscape

The Platonic Representation Hypothesis

Select-then-differentiate: Solving Bilevel Optimization with Manifold Lower-level Solution Sets

Receipt and verification

First computed	2026-05-18T00:43:13.947359Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

a35ea9f799459409d73d00977b329b91fca61c2d0a25d00cd26579d670273dd1

Aliases

arxiv: 1611.01540 · arxiv_version: 1611.01540v4 · doi: 10.48550/arxiv.1611.01540 · pith_short_12: UNPKT54ZIWKA · pith_short_16: UNPKT54ZIWKATVZ5 · pith_short_8: UNPKT54Z

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/UNPKT54ZIWKATVZ5ACLXWMU3SH \
  | 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: a35ea9f799459409d73d00977b329b91fca61c2d0a25d00cd26579d670273dd1

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "a12f69396dfaa5b26d85a98847e57a5359e6daa760af06952f33e5b6144798dc",
    "cross_cats_sorted": [
      "cs.LG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "stat.ML",
    "submitted_at": "2016-11-04T21:17:42Z",
    "title_canon_sha256": "60eab8a665c5259267c2960f6732820f80c45e8a5469203d34a462411dd1467c"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1611.01540",
    "kind": "arxiv",
    "version": 4
  }
}