Pith Number

pith:VAS5YOWA

pith:2021:VAS5YOWAXVNAXW7XIUITAYDZIP

not attested not anchored not stored refs pending

Categorical Foundations of Gradient-Based Learning

Bruno Gavranovi\'c, Fabio Zanasi, G.S.H. Cruttwell, Neil Ghani, Paul Wilson

arxiv:2103.01931 v2 · 2021-03-02 · cs.LG · math.CT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{VAS5YOWAXVNAXW7XIUITAYDZIP}

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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

Polycategorical Constructions for Unitary Supermaps of Arbitrary Dimension

Receipt and verification

First computed	2026-07-05T02:57:16.811202Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

a825dc3ac0bd5a0bdbf7451130607943f536ca4120271f9c655a894573d46ff9

Aliases

arxiv: 2103.01931 · arxiv_version: 2103.01931v2 · doi: 10.48550/arxiv.2103.01931 · pith_short_12: VAS5YOWAXVNA · pith_short_16: VAS5YOWAXVNAXW7X · pith_short_8: VAS5YOWA

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/VAS5YOWAXVNAXW7XIUITAYDZIP \
  | 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: a825dc3ac0bd5a0bdbf7451130607943f536ca4120271f9c655a894573d46ff9

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "8b57afbda9a9a5aabf32132d75debac4ed48564d0a0fd0e18a7070d4c1bd2d0b",
    "cross_cats_sorted": [
      "math.CT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "cs.LG",
    "submitted_at": "2021-03-02T18:43:10Z",
    "title_canon_sha256": "37ba30f58e2a7c17edf14ccf554d621020c4d6eb8898e06bcc62cb0648f770a5"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2103.01931",
    "kind": "arxiv",
    "version": 2
  }
}