Pith Number

pith:DTVYGPKJ

pith:2026:DTVYGPKJ5IB2TM5MTCYQYBVCEZ

not attested not anchored not stored refs pending

Module Lattice Security (Part II): Module Lattice Reduction via Optimal Sign Selection

Ming-Xing Luo

Module lattices reduce to the same quality as ideal lattices by decomposing them into rank-1 submodules and optimizing sign choices.

arxiv:2604.22900 v2 · 2026-04-24 · cs.CR · cs.IT · math.IT · quant-ph

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\usepackage{pith}
\pithnumber{DTVYGPKJ5IB2TM5MTCYQYBVCEZ}

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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

This base module reduction achieves a Hermite factor exp(Õ(√n)) matching the ideal case, with a module reduction factor O(1) independent of the rank, under a balance hypothesis automatically satisfied for MLWE-distributed bases.

C2weakest assumption

All results build on the class number one condition h_k^+=1 established in Part I of this series; the balance hypothesis is assumed to hold automatically for MLWE bases without independent proof here.

C3one line summary

CDPR reduction extends to module lattices with Hermite factor exp(Õ(√n)), O(1) rank-independent module factor under MLWE balance, plus optimal sign discrepancy δ*≈0.4407 from MILP, assuming class number one from Part I.

Receipt and verification

First computed	2026-06-03T01:05:50.644486Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

1ceb833d49ea03a9b3ac98b10c06a22647b6317106c2e784a930765ff9191726

Aliases

arxiv: 2604.22900 · arxiv_version: 2604.22900v2 · doi: 10.48550/arxiv.2604.22900 · pith_short_12: DTVYGPKJ5IB2 · pith_short_16: DTVYGPKJ5IB2TM5M · pith_short_8: DTVYGPKJ

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/DTVYGPKJ5IB2TM5MTCYQYBVCEZ \
  | 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: 1ceb833d49ea03a9b3ac98b10c06a22647b6317106c2e784a930765ff9191726

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "753d4ab5ff835b2e1ea8debe452131b663a8d2a03a4345b4be5edb1822f2f9d7",
    "cross_cats_sorted": [
      "cs.IT",
      "math.IT",
      "quant-ph"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "cs.CR",
    "submitted_at": "2026-04-24T13:54:33Z",
    "title_canon_sha256": "f22d4343e2ae3f58bf1679107170bd675ec8d4262d17856ad5ca3c2b45bcce6b"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2604.22900",
    "kind": "arxiv",
    "version": 2
  }
}