Pith Number

pith:BNPGBKCC

pith:2025:BNPGBKCCV2SOP3TDMFHXM3UI72

not attested not anchored not stored refs pending

On the Discontinuous Breaking of Replica Symmetry and Shattering in Mean-Field Spin Glasses

Ahmed El Alaoui, Antonio Auffinger, Mark Sellke

arxiv:2506.02238 v1 · 2025-06-02 · math.PR · cond-mat.dis-nn · math-ph · math.MP

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{BNPGBKCCV2SOP3TDMFHXM3UI72}

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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

Lower bound on the mixing time of $p$-spin glasses

Receipt and verification

First computed	2026-07-05T11:14:35.107326Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

0b5e60a842aea4e7ee63614f766e88fe95f8c39897492c4b0d302421a329b7e3

Aliases

arxiv: 2506.02238 · arxiv_version: 2506.02238v1 · doi: 10.48550/arxiv.2506.02238 · pith_short_12: BNPGBKCCV2SO · pith_short_16: BNPGBKCCV2SOP3TD · pith_short_8: BNPGBKCC

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/BNPGBKCCV2SOP3TDMFHXM3UI72 \
  | 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: 0b5e60a842aea4e7ee63614f766e88fe95f8c39897492c4b0d302421a329b7e3

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "65b51461c730b87260cde9f70f9362dba63af50fb491dc59387ba3250e6a7a6d",
    "cross_cats_sorted": [
      "cond-mat.dis-nn",
      "math-ph",
      "math.MP"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2025-06-02T20:29:51Z",
    "title_canon_sha256": "1cb53c72f126f80c55f62a1869e35cea67b8bb3b376883cf41ab7f292e87b30d"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2506.02238",
    "kind": "arxiv",
    "version": 1
  }
}