Pith Number

pith:NOFQPUOV

pith:2026:NOFQPUOVW5QMBDUZ6YA45FHCQB

not attested not anchored not stored refs pending

Optimal classical shadow estimation of unitary channels at Heisenberg limit

Entong He, Noam Scully, Sisi Zhou, Yuxiang Yang, Zihao Li

arxiv:2606.13638 v1 · 2026-06-11 · 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{NOFQPUOVW5QMBDUZ6YA45FHCQB}

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	2026-06-12T01:10:20.393670Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

6b8b07d1d5b760c08e99f601ce94e2807a54e5b47a9a3d695dc07a68039857ed

Aliases

arxiv: 2606.13638 · arxiv_version: 2606.13638v1 · doi: 10.48550/arxiv.2606.13638 · pith_short_12: NOFQPUOVW5QM · pith_short_16: NOFQPUOVW5QMBDUZ · pith_short_8: NOFQPUOV

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/NOFQPUOVW5QMBDUZ6YA45FHCQB \
  | 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: 6b8b07d1d5b760c08e99f601ce94e2807a54e5b47a9a3d695dc07a68039857ed

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "f6d81a64d93a8bd650621916ec3096ce03dcc801b2792841adb98b04745941f2",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "quant-ph",
    "submitted_at": "2026-06-11T17:45:46Z",
    "title_canon_sha256": "c959fdd1c2bea0b67f8ddd97e0b6db96a85aecaf5e5bb8ac64360940a3f60e3a"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2606.13638",
    "kind": "arxiv",
    "version": 1
  }
}