Pith Number

pith:LLHZQ3D2

pith:2016:LLHZQ3D2NPMFQEXO7VTZAAQPWZ

not attested not anchored not stored refs pending

Smoothness and monotone decreasingness of the solution to the BCS-Bogoliubov gap equation for superconductivity

Ken Kuriyama, Shuji Watanabe

arxiv:1609.07224 v1 · 2016-09-23 · math-ph · cond-mat.stat-mech · cond-mat.supr-con · math.AP · math.FA · 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{LLHZQ3D2NPMFQEXO7VTZAAQPWZ}

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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.

Receipt and verification

First computed	2026-05-18T00:49:42.092836Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

5acf986c7a6bd85812eefd6790020fb66e4d26dadc403fbac30695f7a24ca1fc

Aliases

arxiv: 1609.07224 · arxiv_version: 1609.07224v1 · doi: 10.48550/arxiv.1609.07224 · pith_short_12: LLHZQ3D2NPMF · pith_short_16: LLHZQ3D2NPMFQEXO · pith_short_8: LLHZQ3D2

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/LLHZQ3D2NPMFQEXO7VTZAAQPWZ \
  | 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: 5acf986c7a6bd85812eefd6790020fb66e4d26dadc403fbac30695f7a24ca1fc

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "6100dc8fbb0ea2b5885efbf901413b6cb40e5470f31bf49c7b1a1e0661afdcbc",
    "cross_cats_sorted": [
      "cond-mat.stat-mech",
      "cond-mat.supr-con",
      "math.AP",
      "math.FA",
      "math.MP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math-ph",
    "submitted_at": "2016-09-23T04:03:41Z",
    "title_canon_sha256": "39b2658c243a434d82a4964e221ebe184dd92e570c68085c194722c8b93b4a2a"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1609.07224",
    "kind": "arxiv",
    "version": 1
  }
}