Pith Number

pith:5SCIFHDG

pith:2026:5SCIFHDGTWA2R4KPZ4WJA2Q3ZC

not attested not anchored not stored refs resolved

Residue Number System Comparison revisited, a software perspective

Jean-Marc Robert (UTLN), Laurent-St\'ephane Didier (UTLN), L\'ea Glandus (UTLN), Nadia El Mrabet

A Residue Number System comparison method works over the full dynamic range using one mixed-radix conversion and an extra modulus.

arxiv:2605.18415 v1 · 2026-05-18 · cs.DC

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\usepackage{pith}
\pithnumber{5SCIFHDGTWA2R4KPZ4WJA2Q3ZC}

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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

Our method provides the comparison of two integers in the full range of the RNS base. It does not require moduli of a special form, unlike other state-of-the-art methods that are restricted to specific RNS bases or require bounds on input numbers. Our approach only requires one single conversion to a mixed radix representation with a complexity of O(n2), which can be reduced to O(log(n)) in time with parallelization.

C2weakest assumption

The additional modulus is available without conflicting with the existing RNS base and that the single mixed-radix conversion step correctly determines the ordering for any pair of numbers in the full dynamic range.

C3one line summary

Presents an RNS comparison technique using an additional modulus for full-range comparison via one mixed-radix conversion with O(n²) complexity.

References

24 extracted · 24 resolved · 0 Pith anchors

[1] A new positional characte ristic of non-positional codes and its application 1977

[2] Modular multiplication and base extensions in residue numbersystems 2001

[3] A new euclidean division algorithm for residue number systems 1998

[4] A ne w technique for fast number com- parison in the residue number system 1993

[5] Residue arithmetic and its application to computer te chnology (Nicholas S 1969

Formal links

1 machine-checked theorem link

Receipt and verification

First computed	2026-05-20T00:05:59.585843Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ec84829c669d81a8f14fcf2c906a1bc8b29e62295540be8b9693d52812a9b952

Aliases

arxiv: 2605.18415 · arxiv_version: 2605.18415v1 · doi: 10.48550/arxiv.2605.18415 · pith_short_12: 5SCIFHDGTWA2 · pith_short_16: 5SCIFHDGTWA2R4KP · pith_short_8: 5SCIFHDG

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/5SCIFHDGTWA2R4KPZ4WJA2Q3ZC \
  | 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: ec84829c669d81a8f14fcf2c906a1bc8b29e62295540be8b9693d52812a9b952

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "4b20af858c549afc828ed5b5a57fe9b807f94268a487162b1bf930c9deee1869",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "cs.DC",
    "submitted_at": "2026-05-18T13:52:39Z",
    "title_canon_sha256": "3a18c8523780390119c8f32bd1730542200afae6a64384efb4e942f2b946cef6"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.18415",
    "kind": "arxiv",
    "version": 1
  }
}