Pith Number

pith:4VX2KPE7

pith:2026:4VX2KPE7QOQVONTNTL2AXFDHQG

not attested not anchored not stored refs pending

The Order of Free Energy Fluctuations in the Critical Sherrington-Kirkpatrick Model Revisited

Adrien Schertzer

arxiv:2606.21360 v1 · 2026-06-19 · 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{4VX2KPE7QOQVONTNTL2AXFDHQG}

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	2026-06-23T01:13:07.694422Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e56fa53c9f83a157366d9af40b9467819570cb14732181f90e29558125b7eb51

Aliases

arxiv: 2606.21360 · arxiv_version: 2606.21360v1 · doi: 10.48550/arxiv.2606.21360 · pith_short_12: 4VX2KPE7QOQV · pith_short_16: 4VX2KPE7QOQVONTN · pith_short_8: 4VX2KPE7

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/4VX2KPE7QOQVONTNTL2AXFDHQG \
  | 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: e56fa53c9f83a157366d9af40b9467819570cb14732181f90e29558125b7eb51

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "25c7cb75f86b0791c3c7532566ab046808eed4d7db27d5bb10102f98afa3627d",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2026-06-19T12:04:08Z",
    "title_canon_sha256": "500615ebf7ee2e874b939aec3b321f056bc92e1af5acc685a2d95f9e94267070"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2606.21360",
    "kind": "arxiv",
    "version": 1
  }
}