Pith Number

pith:UKZKARNS

pith:2026:UKZKARNSLVRU3FMQW5HIT7CBTS

not attested not anchored not stored refs pending

Spectral Reach: Understanding Neural Scaling as Progress into the Spectral Tail

Christian Holm, Jonas Scheunemann, Konstantin Nikolaou, Samuel Tovey, Sven Krippendorf

arxiv:2605.31244 v1 · 2026-05-29 · cs.LG · physics.comp-ph

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{UKZKARNSLVRU3FMQW5HIT7CBTS}

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	2026-06-01T01:04:06.223746Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

a2b2a045b25d634d9590b74e89fc419c8528284cdeefed3fe5b2b669183727ee

Aliases

arxiv: 2605.31244 · arxiv_version: 2605.31244v1 · doi: 10.48550/arxiv.2605.31244 · pith_short_12: UKZKARNSLVRU · pith_short_16: UKZKARNSLVRU3FMQ · pith_short_8: UKZKARNS

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/UKZKARNSLVRU3FMQW5HIT7CBTS \
  | 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: a2b2a045b25d634d9590b74e89fc419c8528284cdeefed3fe5b2b669183727ee

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "663af8881d0139df2cefcb6db5eb833c9be3efdd7f6aa22b603ea24e7de944bb",
    "cross_cats_sorted": [
      "physics.comp-ph"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "cs.LG",
    "submitted_at": "2026-05-29T12:43:51Z",
    "title_canon_sha256": "6c2f453ec323d76089aa890bdd9a7f4dfb6f4e5cdebaf9ed7d4c5a54f7801f6b"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.31244",
    "kind": "arxiv",
    "version": 1
  }
}