Pith Number

pith:CHHSWP5H

pith:2006:CHHSWP5HPPBFJB4J22GYIF47EY

not attested not anchored not stored refs pending

The replica symmetric region in the Sherrington-Kirkpatrick mean field spin glass model. The Almeida-Thouless line

Francesco Guerra

arxiv:cond-mat/0604674 v1 · 2006-04-28 · cond-mat.dis-nn

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{CHHSWP5HPPBFJB4J22GYIF47EY}

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

Guerra interpolation for inverse freezing

Receipt and verification

First computed	2026-07-04T14:54:21.253011Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

11cf2b3fa77bc2548789d68d84179f262ac5c32c9b9e507afc7912d7a687e883

Aliases

arxiv: cond-mat/0604674 · arxiv_version: cond-mat/0604674v1 · doi: 10.48550/arxiv.cond-mat/0604674 · pith_short_12: CHHSWP5HPPBF · pith_short_16: CHHSWP5HPPBFJB4J · pith_short_8: CHHSWP5H

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/CHHSWP5HPPBFJB4J22GYIF47EY \
  | 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: 11cf2b3fa77bc2548789d68d84179f262ac5c32c9b9e507afc7912d7a687e883

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "3c8f1a354682a452cd0981306876b3943fdf580b9e8c480f2ef76a9defad5a2d",
    "cross_cats_sorted": [],
    "license": "",
    "primary_cat": "cond-mat.dis-nn",
    "submitted_at": "2006-04-28T17:59:51Z",
    "title_canon_sha256": "e66b0b25d542e5dea58c804f162cd9e5ad3b46cad0895f0b16eaf0529ddcbfb8"
  },
  "schema_version": "1.0",
  "source": {
    "id": "cond-mat/0604674",
    "kind": "arxiv",
    "version": 1
  }
}