Pith Number

pith:3U67TQ5H

pith:2026:3U67TQ5HOZM7AU5NUMO2XATASN

not attested not anchored not stored refs pending

New Complexity-Theoretic Frontiers of Tractability for Neural Network Training

Cornelius Brand, Mathis Rocton, Robert Ganian

arxiv:2607.20811 v1 · 2026-07-23 · cs.LG · cs.DS

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{3U67TQ5HOZM7AU5NUMO2XATASN}

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	2026-07-24T00:23:35.948466Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

dd3df9c3a77659f053ada31dab82609351dfc2c392d480484a5e6cdaa3f29a83

Aliases

arxiv: 2607.20811 · arxiv_version: 2607.20811v1 · doi: 10.48550/arxiv.2607.20811 · pith_short_12: 3U67TQ5HOZM7 · pith_short_16: 3U67TQ5HOZM7AU5N · pith_short_8: 3U67TQ5H

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/3U67TQ5HOZM7AU5NUMO2XATASN \
  | 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: dd3df9c3a77659f053ada31dab82609351dfc2c392d480484a5e6cdaa3f29a83

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "847ee2390ed9f76d2cc9753303fd107770c7a3345b6f6afe78e635e56f35ee39",
    "cross_cats_sorted": [
      "cs.DS"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "cs.LG",
    "submitted_at": "2026-07-23T00:44:44Z",
    "title_canon_sha256": "e5ecf2c8685f89d2332085ff2fc56dd8894a2d8f34c9a3fb5d0ffbd2593f41a7"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2607.20811",
    "kind": "arxiv",
    "version": 1
  }
}