Pith Number

pith:DL223JQC

pith:2026:DL223JQC2HTGDIY2DHDF3RWG3P

not attested not anchored not stored refs pending

Fibonacci numbers and the probability of polygon formation using random length sticks

Mark Brennan, Noah Callow, Tian Cao Lin

The probability that no p+1 random sticks form a (p+1)-sided polygon equals the product of reciprocals of terms built from the p-step Fibonacci numbers.

arxiv:2604.27573 v2 · 2026-04-30 · math.CO · math.PR

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\usepackage{pith}
\pithnumber{DL223JQC2HTGDIY2DHDF3RWG3P}

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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

the probability that no p+1 sticks can form a (p+1)-sided polygon can be expressed as the product of the reciprocals of a series of terms involving the p-step Fibonacci numbers

C2weakest assumption

Stick lengths are drawn independently from a continuous probability distribution (so that the probability of exact ties is zero and the failure region can be described by strict inequalities on partial sums).

C3one line summary

For n sticks with independent random lengths, the probability that no subset of p+1 sticks satisfies the polygon inequalities is a product of reciprocals involving p-step Fibonacci numbers.

Receipt and verification

First computed	2026-05-26T01:02:34.408946Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

1af5ada602d1e661a31a19c65dc6c6dbc5a167edd46e997931858e938946eec1

Aliases

arxiv: 2604.27573 · arxiv_version: 2604.27573v2 · doi: 10.48550/arxiv.2604.27573 · pith_short_12: DL223JQC2HTG · pith_short_16: DL223JQC2HTGDIY2 · pith_short_8: DL223JQC

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/DL223JQC2HTGDIY2DHDF3RWG3P \
  | 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: 1af5ada602d1e661a31a19c65dc6c6dbc5a167edd46e997931858e938946eec1

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "8bbb663e6c2ee4dbcc23e00aaea3e65633c182361b041b43865251f479aab0db",
    "cross_cats_sorted": [
      "math.PR"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2026-04-30T08:27:53Z",
    "title_canon_sha256": "9b4bae91a57b4b4d74f2e7734a138fad4e1f772ca01ee197a5525d40fe8e732e"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2604.27573",
    "kind": "arxiv",
    "version": 2
  }
}