Pith Number

pith:T2NQRR47

pith:2018:T2NQRR47ZTCQ3DTCWAJTEFLUYC

not attested not anchored not stored refs pending

A Morita type proof of the replica-symmetric formula for SK

Erwin Bolthausen

arxiv:1809.07972 v1 · 2018-09-21 · 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{T2NQRR47ZTCQ3DTCWAJTEFLUYC}

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	2026-05-18T00:05:10.725888Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

9e9b08c79fccc50d8e62b013321574c085772a9e544f53f566e6c2fb2adfcf7b

Aliases

arxiv: 1809.07972 · arxiv_version: 1809.07972v1 · doi: 10.48550/arxiv.1809.07972 · pith_short_12: T2NQRR47ZTCQ · pith_short_16: T2NQRR47ZTCQ3DTC · pith_short_8: T2NQRR47

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/T2NQRR47ZTCQ3DTCWAJTEFLUYC \
  | 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: 9e9b08c79fccc50d8e62b013321574c085772a9e544f53f566e6c2fb2adfcf7b

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "8363165cdd57dacf6af0bec2ee027deee5f61f9ab12275848dccaa7cbb9e5bbb",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2018-09-21T08:04:26Z",
    "title_canon_sha256": "bf3ba16b828aad6fa724f85f070918d34f42341e4b2c2c1770fec027652adfad"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1809.07972",
    "kind": "arxiv",
    "version": 1
  }
}