Pith Number

pith:R3SACWIO

pith:2021:R3SACWIOVPLCXREJHBNKRY2FCL

not attested not anchored not stored refs pending

Neural Networks in Fr\'echet spaces

Fred Espen Benth, Luca Galimberti, Nils Detering

arxiv:2109.13512 v4 · 2021-09-28 · math.FA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{R3SACWIOVPLCXREJHBNKRY2FCL}

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	2026-07-05T04:23:37.883140Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

8ee401590eabd62bc489385aa8e34512c079779d7c42b1262cef65d44808ac68

Aliases

arxiv: 2109.13512 · arxiv_version: 2109.13512v4 · doi: 10.48550/arxiv.2109.13512 · pith_short_12: R3SACWIOVPLC · pith_short_16: R3SACWIOVPLCXREJ · pith_short_8: R3SACWIO

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/R3SACWIOVPLCXREJHBNKRY2FCL \
  | 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: 8ee401590eabd62bc489385aa8e34512c079779d7c42b1262cef65d44808ac68

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "24a97c365e585ef4f65eb8a928868450d260d8f5998d3ead0bb08e076a38e67c",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.FA",
    "submitted_at": "2021-09-28T06:26:25Z",
    "title_canon_sha256": "d1165cf7307735bb50ac729d1f6cce5f378f359734d48295f34e934f8f5520a4"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2109.13512",
    "kind": "arxiv",
    "version": 4
  }
}