Pith Number

pith:PCECKBSX

pith:2026:PCECKBSXMTI5ZAQKWPMF2RAH73

not attested not anchored not stored refs pending

A Compass on the Quantum State Sphere: The Hopf Ansatz for Arbitrary Pure-State Optimization

Guangxi Li, Ruge Lin

arxiv:2607.14231 v1 · 2026-07-15 · 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{PCECKBSXMTI5ZAQKWPMF2RAH73}

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	2026-07-17T00:20:59.501914Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

788825065764d1dc820ab3d85d4407fed3a4277d69580548e970dab52d6de37d

Aliases

arxiv: 2607.14231 · arxiv_version: 2607.14231v1 · doi: 10.48550/arxiv.2607.14231 · pith_short_12: PCECKBSXMTI5 · pith_short_16: PCECKBSXMTI5ZAQK · pith_short_8: PCECKBSX

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/PCECKBSXMTI5ZAQKWPMF2RAH73 \
  | 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: 788825065764d1dc820ab3d85d4407fed3a4277d69580548e970dab52d6de37d

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "fe939c3c1c26258ad99de853fe555c3239250feb16af2729b80f729861cbc82b",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "quant-ph",
    "submitted_at": "2026-07-15T18:00:41Z",
    "title_canon_sha256": "56d60ddc7daacdbb9bc0282ec72d22772d1052a7cb533285975a8c81aa69232b"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2607.14231",
    "kind": "arxiv",
    "version": 1
  }
}