Pith Number

pith:WR6IGKGI

pith:2026:WR6IGKGIQUXGHOPKNIRESPJQ4A

not attested not anchored not stored refs resolved

Combining moment matrices, symmetric extension, and Lov\'asz theta: $\Phi_{\text{E8}}$ is entangled

Felix Huber, Gerard Angl\`es Munn\'e, J\c{e}drzej Stempin, Santiago Llorens

The 14-qubit state Φ_E8 is entangled, certified by an explicit witness from a semidefinite program combining moment matrices and symmetric extension.

arxiv:2605.13832 v1 · 2026-05-13 · quant-ph

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\pithnumber{WR6IGKGIQUXGHOPKNIRESPJQ4A}

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Record completeness

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2 Internet Archive

3 Author claim open · sign in to claim

4 Citations open

5 Replications open

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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.

Claims

C1strongest claim

We solve an open problem in entanglement theory posed by Yu et al., Nature Communications 12, 1012 (2021). The problem is to show, via an entanglement witness, that the 14-qubit state Φ_E8 is entangled.

C2weakest assumption

That the chosen combination of moment matrices and symmetric extension produces a tight enough relaxation whose infeasibility certificate remains valid for the full (unrelaxed) entanglement detection problem without introducing false positives.

C3one line summary

The 14-qubit state Φ_E8 is entangled, certified by an explicit entanglement witness obtained as a rational infeasibility certificate for a semidefinite program that combines moment matrices with symmetric extension.

References

45 extracted · 45 resolved · 2 Pith anchors

[1] (E8) in the arXiv version Ref

[2] Symmetric extension:

[3] Moment matrix: ΦE8 ? = P i piµ⊗2 i Φ(3) E8 ? = P i piµ⊗3 i  ⟨Ea⟩⟨E† b ⟩⟨E† aEb⟩   ⪰0 ∄ ΦE8 is entangled

[4] Combining moment matrices, symmetric extension, and Lov\'asz theta: $\Phi_{\text{E8}}$ is entangled 2026 · arXiv:2605.13832

[5] permutes the tensor factors byS n, and

Cited by

1 paper in Pith

Combining moment matrices, symmetric extension, and Lov\'asz theta: $\Phi_{\text{E8}}$ is entangled

Receipt and verification

First computed	2026-05-18T02:44:15.024399Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b47c8328c8852e63b9ea6a22493d30e01d69ab5c505c01ba3699ae3768cd9e0c

Aliases

arxiv: 2605.13832 · arxiv_version: 2605.13832v1 · doi: 10.48550/arxiv.2605.13832 · pith_short_12: WR6IGKGIQUXG · pith_short_16: WR6IGKGIQUXGHOPK · pith_short_8: WR6IGKGI

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/WR6IGKGIQUXGHOPKNIRESPJQ4A \
  | 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: b47c8328c8852e63b9ea6a22493d30e01d69ab5c505c01ba3699ae3768cd9e0c

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "76227e43fc5d13f4970506aed89a02c94a0b027c095c6d8fd7eba501a7e58534",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "quant-ph",
    "submitted_at": "2026-05-13T17:54:51Z",
    "title_canon_sha256": "bc504ca1be0bbccbab737dc146546fa21528fb97a11e9bdfe7d3dfb489260687"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.13832",
    "kind": "arxiv",
    "version": 1
  }
}