Pith Number

pith:JDFWXM5B

pith:2026:JDFWXM5BJLFFNLFN5SQJT5LAOQ

not attested not anchored not stored refs pending

Low-dimensional topology of deep neural networks

Junyu Ren, Lek-Heng Lim

arxiv:2606.31856 v1 · 2026-06-30 · cs.LG · math.GT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{JDFWXM5BJLFFNLFN5SQJT5LAOQ}

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	2026-07-01T01:18:17.677372Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

48cb6bb3a14aca56acadeca099f56074044e52752a0334090bf192463009ac89

Aliases

arxiv: 2606.31856 · arxiv_version: 2606.31856v1 · doi: 10.48550/arxiv.2606.31856 · pith_short_12: JDFWXM5BJLFF · pith_short_16: JDFWXM5BJLFFNLFN · pith_short_8: JDFWXM5B

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/JDFWXM5BJLFFNLFN5SQJT5LAOQ \
  | 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: 48cb6bb3a14aca56acadeca099f56074044e52752a0334090bf192463009ac89

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "96b65983cd5ba5ee8b81d0d298305c41f110fbe9681e39ca12ee7991b8936752",
    "cross_cats_sorted": [
      "math.GT"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "cs.LG",
    "submitted_at": "2026-06-30T15:53:11Z",
    "title_canon_sha256": "8fc4b03c05e6da40421c4a05bffc075d68f4594a94807c4cabb3c420a2673ef6"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2606.31856",
    "kind": "arxiv",
    "version": 1
  }
}