Pith Number

pith:YKR4EJKR

pith:2010:YKR4EJKRFDMXHYCXFXFBMU5Z2D

not attested not anchored not stored refs pending

The solution to the BCS gap equation and the second-order phase transition in superconductivity

Shuji Watanabe

arxiv:1006.0765 v3 · 2010-06-04 · math-ph · 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{YKR4EJKRFDMXHYCXFXFBMU5Z2D}

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	2026-05-18T04:18:45.066245Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

c2a3c2255128d973e0572dca1653b9d0ef83b214955f0c74918788cb33166f70

Aliases

arxiv: 1006.0765 · arxiv_version: 1006.0765v3 · doi: 10.48550/arxiv.1006.0765 · pith_short_12: YKR4EJKRFDMX · pith_short_16: YKR4EJKRFDMXHYCX · pith_short_8: YKR4EJKR

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/YKR4EJKRFDMXHYCXFXFBMU5Z2D \
  | 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: c2a3c2255128d973e0572dca1653b9d0ef83b214955f0c74918788cb33166f70

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "3d858a8c9e27b09a365d26a0c7081f61a158abd3c34f876980a98a988adb6dc3",
    "cross_cats_sorted": [
      "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": "2010-06-04T01:46:32Z",
    "title_canon_sha256": "ce08a40cfb6e019c7f6fc152615c17df62826127dea14510433b571de81306e4"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1006.0765",
    "kind": "arxiv",
    "version": 3
  }
}