Pith Number

pith:RPYVI4DJ

pith:2026:RPYVI4DJ7WYAMEQW6UQPLPJZJT

not attested not anchored not stored refs resolved

$p$-adic Linear Regression for Random Sampling with Digitwise Noise

Tomoki Mihara

A new probabilistic algorithm recovers linear relations from random p-adic samples with digitwise noise.

arxiv:2604.13137 v2 · 2026-04-14 · stat.CO · math.NT · math.ST · stat.TH

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Record completeness

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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 propose a new probabilistic algorithm of p-adic linear regression for random sampling with digitwise noise. This includes a new probabilistic algorithm of modulo p linear regression.

C2weakest assumption

That digitwise noise admits a natural probabilistic model within the p-adic metric that allows a regression algorithm to recover the underlying linear relation with non-trivial success probability.

C3one line summary

Proposes a probabilistic algorithm for p-adic linear regression under digitwise noise, including a modulo p version.

References

22 extracted · 22 resolved · 0 Pith anchors

[1] E.\ Amaldi and V.\ Kann, The complexity and approximability of finding maximum feasible subsystems of linear relations , Theoretical Computer Science, Volume 147, pp.\ 181--210, 1995 1995

[2] S.\ Albeverio, A.\ Khrennikov, and B.\ Tirrozi, p -Adic Dynamical Systems and Neural Networks , Mathematical Models and Methods in Applied Sciences, Volume 09, Issue 09, pp.\ 1417--1437, 1999 1999

[3] V.\ G.\ Berkovich, Spectral Theory and Analytic Geometry over non-\ Fields , Mathematical Surveys and Monographs, Number 33, the American Mathematical Society, 1990 1990

[4] , F.\ Bambozzi and T,\ Mihara, Derived Analytic Geometry for -Valued Functions Part I: Topological Properties , Bulletin of the Iranian Mathematical Society, Volume 50, Issue 4, article number 58, 202 2024

[5] G.\ D.\ Baker, S.\ Mccallum, and D.\ Pattinson, Linear Regression in p -adic Metric Spaces , p -Adic Numbers, Ultrametric Analysis and Applications, Volume 17, Issue 4, pp.\ 333--347, 2025 2025

Formal links

2 machine-checked theorem links

Cited by

1 paper in Pith

$p$-adic Manifold Learning and Benchmark Tasks from Impartial Games

Receipt and verification

First computed	2026-05-20T00:00:37.943361Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

8bf1547069fdb0061216f520f5bd394cfb8fcc3ca79b0f57edf6d38ab96e7ef2

Aliases

arxiv: 2604.13137 · arxiv_version: 2604.13137v2 · doi: 10.48550/arxiv.2604.13137 · pith_short_12: RPYVI4DJ7WYA · pith_short_16: RPYVI4DJ7WYAMEQW · pith_short_8: RPYVI4DJ

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/RPYVI4DJ7WYAMEQW6UQPLPJZJT \
  | 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: 8bf1547069fdb0061216f520f5bd394cfb8fcc3ca79b0f57edf6d38ab96e7ef2

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "7c3cc79ea29e4c3cc74e5b7dce010d5e193ce85fa9a6dbfd6b269bcdb0ba5a57",
    "cross_cats_sorted": [
      "math.NT",
      "math.ST",
      "stat.TH"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "stat.CO",
    "submitted_at": "2026-04-14T11:23:40Z",
    "title_canon_sha256": "cd35ec1597e48ac2a9819a24108e305d436a79ee83e8474d6fc7c8b5a0e3d8a2"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2604.13137",
    "kind": "arxiv",
    "version": 2
  }
}