Pith Number

pith:FQQW7YLV

pith:2026:FQQW7YLV5CJTASAX3G5Q3IM2RY

not attested not anchored not stored refs pending

Spectral phase transitions in Gaussian multi-index models

Florent Krzakala, Pierre Mergny, Vanessa Piccolo

arxiv:2608.12183 v1 · 2026-08-12 · math.ST · math.PR · stat.TH

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{FQQW7YLV5CJTASAX3G5Q3IM2RY}

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	2026-08-13T01:30:19.485381Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

2c216fe175e893304817d9bb0da19a8e246d073f939527fc54a6c1486a700acb

Aliases

arxiv: 2608.12183 · arxiv_version: 2608.12183v1 · doi: 10.48550/arxiv.2608.12183 · pith_short_12: FQQW7YLV5CJT · pith_short_16: FQQW7YLV5CJTASAX · pith_short_8: FQQW7YLV

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/FQQW7YLV5CJTASAX3G5Q3IM2RY \
  | 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: 2c216fe175e893304817d9bb0da19a8e246d073f939527fc54a6c1486a700acb

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "e2a865941cc2430ce1ef464c93ce0bdd8541bc02255843be09447fc92802215e",
    "cross_cats_sorted": [
      "math.PR",
      "stat.TH"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.ST",
    "submitted_at": "2026-08-12T15:35:34Z",
    "title_canon_sha256": "b536ec65b16ae7c9d2d72a0c51663feebc30ff54469d6fd021107cc502cedcd7"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2608.12183",
    "kind": "arxiv",
    "version": 1
  }
}