Pith Number

pith:TKNTN5XB

pith:2018:TKNTN5XBVJFPPMGBANANLVMAOX

not attested not anchored not stored refs pending

A Near-Optimal Depth-Hierarchy Theorem for Small-Depth Multilinear Circuits

Christian Engels, Nutan Limaye, Srikanth Srinivasan, Suryajith Chillara

arxiv:1804.02520 v1 · 2018-04-07 · cs.CC

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{TKNTN5XBVJFPPMGBANANLVMAOX}

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	2026-05-18T00:18:59.243822Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

9a9b36f6e1aa4af7b0c10340d5d58075f6d6c196c45646374067def56d9b91f6

Aliases

arxiv: 1804.02520 · arxiv_version: 1804.02520v1 · doi: 10.48550/arxiv.1804.02520 · pith_short_12: TKNTN5XBVJFP · pith_short_16: TKNTN5XBVJFPPMGB · pith_short_8: TKNTN5XB

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/TKNTN5XBVJFPPMGBANANLVMAOX \
  | 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: 9a9b36f6e1aa4af7b0c10340d5d58075f6d6c196c45646374067def56d9b91f6

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "ce98d6008d12259b5981954787f4674833d1ba94f9564e4b1d388d7eab8c5d35",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by-sa/4.0/",
    "primary_cat": "cs.CC",
    "submitted_at": "2018-04-07T07:27:44Z",
    "title_canon_sha256": "cafaf8581d1cdada9f96ff61801882936dc5075b51000ef4d4dfa1234e84aadf"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1804.02520",
    "kind": "arxiv",
    "version": 1
  }
}