Pith Number

pith:4QYRMPSZ

pith:2026:4QYRMPSZAZLAALSPPOA4XPK2VA

not attested not anchored not stored refs resolved

Local certification of residual squareclasses in $\mathbb Q(\sqrt{2},\sqrt{pq},\sqrt{ps})$: one-bit, affine, and finite-choice Hilbert-symbol frameworks

Dang Vo Phuc

A single Hilbert symbol at one finite place decides the final squareclass generator for units in Q(√2, √(pq), √(ps)).

arxiv:2605.13888 v1 · 2026-05-12 · math.NT

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\usepackage{pith}
\pithnumber{4QYRMPSZAZLAALSPPOA4XPK2VA}

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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 give an explicit local criterion deciding the parameter μ ∈ {1, ε_pq} left open in recent literature. The criterion is first expressed in terms of Hilbert symbols at a single finite place, and is then sharpened to a residue criterion at a chosen split auxiliary rational prime.

C2weakest assumption

The corrected classification of units in L+ is complete except for the single residual binary indeterminacy in the final generator, as stated in the abstract.

C3one line summary

Local Hilbert-symbol criterion resolves the residual binary choice of unit generator in Q(sqrt(2), sqrt(pq), sqrt(ps)).

References

15 extracted · 15 resolved · 0 Pith anchors

[1] E. Benjamin, F. Lemmermeyer, and C. Snyder,On the unit group of some multiquadratic number fields, Pacific J. Math.230(2007), 27–40. doi:10.2140/pjm.2007.230.27 2007 · doi:10.2140/pjm.2007.230.27

[2] M. M. Chems-Eddin, A. Azizi, and A. Zekhnini,Unit groups and Iwasawa Lambda invariants of some multiquadratic number fields, Bol. Soc. Mat. Mex.27(2021), Article 24. doi:10.1007/s40590-021-00329-z 2021 · doi:10.1007/s40590-021-00329-z

[3] M. M. Chems-Eddin,Unit groups of some multiquadratic number fields and2-class groups, Period. Math. Hung.84(2022), 235–249. doi:10.1007/s10998-021-00402-0 2022 · doi:10.1007/s10998-021-00402-0

[4] M. M. Chems-Eddin,On units of some fields of the formQ( √ 2, √p, √q, √ −ℓ), Math. Bohem.148 (2023), 237–242. doi:10.21136/MB.2022.0128-21 2023 · doi:10.21136/mb.2022.0128-21

[5] M. M. Chems-Eddin, M. B. T. El Hamam, and M. A. Hajjami,On the unit group and the2-class number ofQ( √ 2, √p, √q), Ramanujan J.65(2024), 1475–1510. doi:10.1007/s11139-024-00947-x 2024 · doi:10.1007/s11139-024-00947-x

Formal links

1 machine-checked theorem link

Receipt and verification

First computed	2026-05-17T23:39:19.103196Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e431163e590656002e4f7b81cbbd5aa81744059d9085a541c319bffa32aa0900

Aliases

arxiv: 2605.13888 · arxiv_version: 2605.13888v1 · doi: 10.48550/arxiv.2605.13888 · pith_short_12: 4QYRMPSZAZLA · pith_short_16: 4QYRMPSZAZLAALSP · pith_short_8: 4QYRMPSZ

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/4QYRMPSZAZLAALSPPOA4XPK2VA \
  | 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: e431163e590656002e4f7b81cbbd5aa81744059d9085a541c319bffa32aa0900

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "8429e8ad23bccc7de9f8453702803f5f774f46a6972815b8efe4606ef0193184",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2026-05-12T03:15:04Z",
    "title_canon_sha256": "18d2da843954d5efdf6c1bf477913a7ab6c4def9657a6e1c51063fc83173b3be"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.13888",
    "kind": "arxiv",
    "version": 1
  }
}