Pith Number

pith:4VSAJOTJ

pith:2026:4VSAJOTJLTFCVY4ALZE2XEDGAH

not attested not anchored not stored refs pending

The Stability of Singular Distribution: A Spectral Perspective on the Two-Phase Dynamics of Language Model Pre-training

Chenxi Jia, Hongtao Zhang, Wei Chen, Wenjie Zhou, Xueqi Cheng

arxiv:2605.26489 v1 · 2026-05-26 · cs.LG

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{4VSAJOTJLTFCVY4ALZE2XEDGAH}

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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.

Receipt and verification

First computed	2026-05-27T01:05:20.933230Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e56404ba695cca2ae3805e49ab906601e32910633e577c82f8e0bf3ff1e94f74

Aliases

arxiv: 2605.26489 · arxiv_version: 2605.26489v1 · doi: 10.48550/arxiv.2605.26489 · pith_short_12: 4VSAJOTJLTFC · pith_short_16: 4VSAJOTJLTFCVY4A · pith_short_8: 4VSAJOTJ

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/4VSAJOTJLTFCVY4ALZE2XEDGAH \
  | 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: e56404ba695cca2ae3805e49ab906601e32910633e577c82f8e0bf3ff1e94f74

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "049b0c8211e61b175ad68eccf3d00ab3e69c298449a4a8ea98019e5249dcb6de",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "cs.LG",
    "submitted_at": "2026-05-26T03:03:24Z",
    "title_canon_sha256": "c25a235daca071f3102b881489218d5597b24c8618979621c102a411b98b295f"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.26489",
    "kind": "arxiv",
    "version": 1
  }
}