Pith Number

pith:HCFPLZER

pith:2026:HCFPLZERBNWBK4WPY3WUTH625K

not attested not anchored not stored refs pending

Mathematical Basis for Analyzing Superconducting Phase Transitions Using Catastrophe Theory

Hua Tian, Jiu Hui Wu, Kejiang Zhou

arxiv:2606.11810 v1 · 2026-06-10 · cond-mat.supr-con · quant-ph

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{HCFPLZERBNWBK4WPY3WUTH625K}

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	2026-06-11T01:10:09.255390Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

388af5e4910b6c1572cfc6ed499fdaea9c3f1c720f51658318060eb9656d13f7

Aliases

arxiv: 2606.11810 · arxiv_version: 2606.11810v1 · doi: 10.48550/arxiv.2606.11810 · pith_short_12: HCFPLZERBNWB · pith_short_16: HCFPLZERBNWBK4WP · pith_short_8: HCFPLZER

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/HCFPLZERBNWBK4WPY3WUTH625K \
  | 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: 388af5e4910b6c1572cfc6ed499fdaea9c3f1c720f51658318060eb9656d13f7

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "b8f12505a397fca632b8006569deffde0e4f9e5d7dd0341f4e567ac55a7d1859",
    "cross_cats_sorted": [
      "quant-ph"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "cond-mat.supr-con",
    "submitted_at": "2026-06-10T08:44:30Z",
    "title_canon_sha256": "367944d58cce94e4a14f7f17d398f510d1e4964caa257bc5e6a8ad5920e4fd0e"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2606.11810",
    "kind": "arxiv",
    "version": 1
  }
}