Pith Number

pith:2L65VLF4

pith:2018:2L65VLF4GY6WT6TSS3NJXOP5IJ

not attested not anchored not stored refs pending

Limits on representing Boolean functions by linear combinations of simple functions: thresholds, ReLUs, and low-degree polynomials

R. Ryan Williams

arxiv:1802.09121 v1 · 2018-02-26 · cs.CC · cs.DM · cs.NE

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{2L65VLF4GY6WT6TSS3NJXOP5IJ}

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	2026-05-18T00:22:34.711052Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

d2fddaacbc363d69fa7296da9bb9fd426bdc10e955f0b3ffecb29188b7aaa556

Aliases

arxiv: 1802.09121 · arxiv_version: 1802.09121v1 · doi: 10.48550/arxiv.1802.09121 · pith_short_12: 2L65VLF4GY6W · pith_short_16: 2L65VLF4GY6WT6TS · pith_short_8: 2L65VLF4

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/2L65VLF4GY6WT6TSS3NJXOP5IJ \
  | 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: d2fddaacbc363d69fa7296da9bb9fd426bdc10e955f0b3ffecb29188b7aaa556

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "14b9a877ff9cd159d7770c00be58456470c408365a00b380443d0f54166bdc17",
    "cross_cats_sorted": [
      "cs.DM",
      "cs.NE"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "cs.CC",
    "submitted_at": "2018-02-26T01:30:21Z",
    "title_canon_sha256": "249b11f556bb1967d27cfe38a039cbb168776a9ee84cddc992a6a28217cf24ef"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1802.09121",
    "kind": "arxiv",
    "version": 1
  }
}