Pith Number

pith:EM3OGYHU

pith:2026:EM3OGYHU57MSRKJVG7LBHOGUTB

not attested not anchored not stored refs pending

Neural network approximation in discrete dual norms with adaptive test spaces

Ignacio Brevis, Kristoffer G. van der Zee, Sergio Rojas, Tanakorn Udomworarat

arxiv:2606.20972 v1 · 2026-06-18 · math.NA · cs.NA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{EM3OGYHU57MSRKJVG7LBHOGUTB}

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	2026-06-23T01:12:23.734969Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

2336e360f4efd928a93537d613b8d4985634ed10926eaa161b279c58d3ef792b

Aliases

arxiv: 2606.20972 · arxiv_version: 2606.20972v1 · doi: 10.48550/arxiv.2606.20972 · pith_short_12: EM3OGYHU57MS · pith_short_16: EM3OGYHU57MSRKJV · pith_short_8: EM3OGYHU

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/EM3OGYHU57MSRKJVG7LBHOGUTB \
  | 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: 2336e360f4efd928a93537d613b8d4985634ed10926eaa161b279c58d3ef792b

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "eaa34b0d4c47c2a4f9fd562f7dd8bd89873c923c73db55603038193ccdf5125a",
    "cross_cats_sorted": [
      "cs.NA"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.NA",
    "submitted_at": "2026-06-18T22:30:57Z",
    "title_canon_sha256": "7c10d77da0673133c0da50b7a3a1b0d59c6bb87b611f2be0438ab4af61f76c0c"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2606.20972",
    "kind": "arxiv",
    "version": 1
  }
}