Pith Number

pith:BONJSSDX

pith:2026:BONJSSDX5CAW4IRTLQ2SYLXCH3

not attested not anchored not stored refs resolved

Problem of Finding an Optimal Piecewise Linear Path Connecting Two Given Points with the Possibility of Making n Turns

Nefedov V.N

Under some condition all interior vertices of an admissible n-turn path between two points lie in a specific region, and every admissible sequence of corner points admits an explicit description.

arxiv:2605.15449 v1 · 2026-05-14 · math.OC

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\usepackage{pith}
\pithnumber{BONJSSDX5CAW4IRTLQ2SYLXCH3}

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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

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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

Under some condition, all interior vertices of an admissible n-turn polygonal line belong to a specific region (Theorem 1); an explicit expression describes the collection of all admissible sequences of corner points (Theorem 2), which is then approximated by a finite family for optimization algorithms.

C2weakest assumption

The unspecified 'some condition' under which the region characterization in Theorem 1 holds; without knowing or verifying this condition the claimed region and subsequent sequence expression may not apply to the general case.

C3one line summary

Characterizes admissible regions and sequences for bounded-turn n-segment paths and builds finite approximations for optimization algorithms.

References

8 extracted · 8 resolved · 0 Pith anchors

[1] Methods of Approximation of Two Dimensional Sets by Finite Sets and Their Application to Some Geometric Optimization 99 Problems 2025

[2] Problem of Finding an Optimal Piecewise Linear Route with n Turns 2025

[3] Dynamic Programming 2010

[4] Cormen, Thomas H., Charles E. Leiserson, Ronald L. Rivest, and Clifford Stein. Introduction to Algorithms. 4th ed. Cambridge, MA: The MIT Press, 2022 2022

[5] Papadimitriou, and Umesh Vazirani 2006

Formal links

2 machine-checked theorem links

Receipt and verification

First computed	2026-05-20T00:00:59.212690Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

0b9a994877e8816e22335c352c2ee23ee3e0645873d71abf3739c945943d70a6

Aliases

arxiv: 2605.15449 · arxiv_version: 2605.15449v1 · doi: 10.48550/arxiv.2605.15449 · pith_short_12: BONJSSDX5CAW · pith_short_16: BONJSSDX5CAW4IRT · pith_short_8: BONJSSDX

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/BONJSSDX5CAW4IRTLQ2SYLXCH3 \
  | 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: 0b9a994877e8816e22335c352c2ee23ee3e0645873d71abf3739c945943d70a6

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "a101dc6d41fcefa4c4039f958d97216b807b35aaae951f057191cc9f39688632",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by-nc-nd/4.0/",
    "primary_cat": "math.OC",
    "submitted_at": "2026-05-14T22:19:03Z",
    "title_canon_sha256": "9303d91a6ba606d240d8cb1b9ecf62c1d86d541a26e2209904c8a694aa0493ad"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.15449",
    "kind": "arxiv",
    "version": 1
  }
}