Pith Number

pith:I74HA2PI

pith:2026:I74HA2PIS2H2XL3TBXRCDZGVZZ

not attested not anchored not stored refs pending

Toward a Special \textbf{$E_6\to G(2) \times SU(3)_A$} Embedding for Standard Model and Dark Matter and an $E_7$ Completion Proposal

Nicol\`o Masi

A special non-regular embedding of E6 first breaks to G(2) times SU(3)_A, recovering the Standard Model plus a confining dark sector at low energies.

arxiv:2603.15710 v3 · 2026-03-16 · hep-ph

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\usepackage{pith}
\pithnumber{I74HA2PIS2H2XL3TBXRCDZGVZZ}

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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.

Claims

C1strongest claim

The resulting framework provides a minimal unified, self-consistent exceptional apparatus which includes the Standard Model and a dark matter sector which is secluded by the group-theoretic orthogonality.

C2weakest assumption

The special (non-regular) embedding E6 to G(2) x SU(3)_A exists, permits the full breaking chain without unwanted tree-level leptoquark couplings, and allows construction of a scalar potential whose minima produce the claimed heavy gauge boson spectrum and consistent one-loop unification.

C3one line summary

A special E6 embedding realizes an intermediate G(2) x SU(3)_A stage that breaks to the Standard Model with a hidden dark confining sector, consistent gauge coupling running, and suppressed leptoquark couplings.

Formal links

2 machine-checked theorem links

Receipt and verification

First computed	2026-05-20T00:03:08.376626Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

47f87069e8968fabaf730de221e4d5ce6d65d22cdc6b8349651e279e74ec53e5

Aliases

arxiv: 2603.15710 · arxiv_version: 2603.15710v3 · doi: 10.48550/arxiv.2603.15710 · pith_short_12: I74HA2PIS2H2 · pith_short_16: I74HA2PIS2H2XL3T · pith_short_8: I74HA2PI

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/I74HA2PIS2H2XL3TBXRCDZGVZZ \
  | 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: 47f87069e8968fabaf730de221e4d5ce6d65d22cdc6b8349651e279e74ec53e5

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "be467f3ad4adee88368c6907e47eb62e37c8191d175c3c505ade18b824bd3a45",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "hep-ph",
    "submitted_at": "2026-03-16T13:59:40Z",
    "title_canon_sha256": "55960e0f5b9a0cd84ed9172bc117b9e8873dabd99d38b063cbba9d48a57bd429"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2603.15710",
    "kind": "arxiv",
    "version": 3
  }
}