Pith Number

pith:M3A43VCO

pith:2026:M3A43VCORYU22JL4GEJZ75UZLE

not attested not anchored not stored refs pending

Spectral phase transitions and trainability in neural network learning dynamics

Biagio Lucini, Chanju Park, Dario Bocchi, Francesco D'Amico, Gert Aarts

arxiv:2606.28486 v1 · 2026-06-26 · cond-mat.dis-nn · 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{M3A43VCORYU22JL4GEJZ75UZLE}

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	2026-06-30T00:15:15.623541Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

66c1cdd44e8e29ad257c31139ff699592c1bb15aba44cffe41394ce3c04e813a

Aliases

arxiv: 2606.28486 · arxiv_version: 2606.28486v1 · doi: 10.48550/arxiv.2606.28486 · pith_short_12: M3A43VCORYU2 · pith_short_16: M3A43VCORYU22JL4 · pith_short_8: M3A43VCO

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/M3A43VCORYU22JL4GEJZ75UZLE \
  | 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: 66c1cdd44e8e29ad257c31139ff699592c1bb15aba44cffe41394ce3c04e813a

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "ffaf85ee2ef7055653aa206643b42a05becb053617fd0bd800a5875d98f73f89",
    "cross_cats_sorted": [
      "cs.LG"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "cond-mat.dis-nn",
    "submitted_at": "2026-06-26T18:00:01Z",
    "title_canon_sha256": "d673525e17c91dbb489d13f8e80299c28778a658ee637a51e294b0e6945da3f3"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2606.28486",
    "kind": "arxiv",
    "version": 1
  }
}