Pith Number

pith:JBJWRPKR

pith:2020:JBJWRPKR64KEGFJY6PAWN4EBXG

not attested not anchored not stored refs pending

Approximation Bounds for Random Neural Networks and Reservoir Systems

Juan-Pablo Ortega, Lukas Gonon, Lyudmila Grigoryeva

arxiv:2002.05933 v2 · 2020-02-14 · math.PR · cs.NE · cs.SY · eess.SY

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{JBJWRPKR64KEGFJY6PAWN4EBXG}

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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

Embedding and Approximation Theorems for Echo State Networks

Receipt and verification

First computed	2026-07-05T02:15:22.548702Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

485368bd51f714431538f3c166f081b9bd9fff202319d06c5e0800aa3ef8b5ce

Aliases

arxiv: 2002.05933 · arxiv_version: 2002.05933v2 · doi: 10.48550/arxiv.2002.05933 · pith_short_12: JBJWRPKR64KE · pith_short_16: JBJWRPKR64KEGFJY · pith_short_8: JBJWRPKR

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/JBJWRPKR64KEGFJY6PAWN4EBXG \
  | 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: 485368bd51f714431538f3c166f081b9bd9fff202319d06c5e0800aa3ef8b5ce

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "e9e76c65d2ea9307f5adef36f11ada5b3a056d5f12480543ce27d27790e3f832",
    "cross_cats_sorted": [
      "cs.NE",
      "cs.SY",
      "eess.SY"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2020-02-14T09:43:28Z",
    "title_canon_sha256": "2ec536cb0f7b7752883e1f792bce61a6673a098a8827b36c5a0b99317c3c89c9"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2002.05933",
    "kind": "arxiv",
    "version": 2
  }
}