Pith Number

pith:MCUAFF34

pith:2026:MCUAFF346YJIBRFIMOPJQC342Q

not attested not anchored not stored refs pending

From Bogoliubov-de Gennes to Ginzburg-Landau: Critical Points Near $T_{\rm c}$ in the Non-Magnetic Case

Christian Hainzl, Dong Hao Ou Yang, Rupert L. Frank

arxiv:2605.26008 v1 · 2026-05-25 · math.AP · 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{MCUAFF346YJIBRFIMOPJQC342Q}

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	2026-05-26T02:05:23.019163Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

60a802977cf61280c4a8639e980b7cd40217c7d23f163542a2380244bbe6e364

Aliases

arxiv: 2605.26008 · arxiv_version: 2605.26008v1 · doi: 10.48550/arxiv.2605.26008 · pith_short_12: MCUAFF346YJI · pith_short_16: MCUAFF346YJIBRFI · pith_short_8: MCUAFF34

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/MCUAFF346YJIBRFIMOPJQC342Q \
  | 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: 60a802977cf61280c4a8639e980b7cd40217c7d23f163542a2380244bbe6e364

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "5eb485db09e8a7af6f1838cf79b795f5ec3793e5e6cd628ee36bc11075be079a",
    "cross_cats_sorted": [
      "math-ph",
      "math.MP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2026-05-25T16:27:25Z",
    "title_canon_sha256": "7d0410b9e0dad86117ac9bc7983485958bc4268ce3646663bec2427d2aa6aee5"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.26008",
    "kind": "arxiv",
    "version": 1
  }
}