Pith Number

pith:VIITZ6PK

pith:2024:VIITZ6PKNXZ2QUFJQGALFESZCD

not attested not anchored not stored refs pending

A Hopf-like formula for mean-field spin glass models

Victor Issa (ENS de Lyon)

arxiv:2410.08754 v1 · 2024-10-11 · math.PR

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{VIITZ6PKNXZ2QUFJQGALFESZCD}

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.

Cited by

1 paper in Pith

The Free Energy of an Enriched Continuous Random Energy Model in the Weak Correlation Regime

Receipt and verification

First computed	2026-07-05T09:19:17.123106Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

aa113cf9ea6df3a850a98180b2925910ea653b78bed6dff274f6099734ee8b6c

Aliases

arxiv: 2410.08754 · arxiv_version: 2410.08754v1 · doi: 10.48550/arxiv.2410.08754 · pith_short_12: VIITZ6PKNXZ2 · pith_short_16: VIITZ6PKNXZ2QUFJ · pith_short_8: VIITZ6PK

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/VIITZ6PKNXZ2QUFJQGALFESZCD \
  | 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: aa113cf9ea6df3a850a98180b2925910ea653b78bed6dff274f6099734ee8b6c

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "666f48a1487d1de1a34aee6c3d14b0b1f6323e57e32b438bb1386c2f19a07c49",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2024-10-11T12:12:48Z",
    "title_canon_sha256": "bccc14208b3cf92cfc57c996ede96ebd006243300e8028de0ec5280b14b06720"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2410.08754",
    "kind": "arxiv",
    "version": 1
  }
}