Pith Number

pith:FFUXJBQY

pith:2026:FFUXJBQYJ5EN5LXGU5CGIQ7FNG

not attested not anchored not stored refs resolved

On the Number of Rational Power Factors in a Finite Word

Shuo Li, Yuan Song

A finite word of length n contains at most one-eighth n squared plus lower-order terms distinct rational power factors.

arxiv:2605.14955 v1 · 2026-05-14 · math.CO

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\usepackage{pith}
\pithnumber{FFUXJBQYJ5EN5LXGU5CGIQ7FNG}

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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

we prove that the number RP(w) of distinct rational power factors of w satisfies RP(w)≤1/8 n² + O(n)

C2weakest assumption

The graph-theoretic representation together with the word equations fully captures every possible finite word and every possible rational power factor without omissions or overcounting.

C3one line summary

The maximum number of distinct rational power factors in a word of length n is at most (1/8)n² + O(n).

References

171 extracted · 171 resolved · 0 Pith anchors

[1] Bidimensional Sturmian Sequences and Substitutions , Url = 2005 · doi:10.1007/11505877

[2] Ali Aberkane and Sre. Suites de m. Actes des Journ

[3] Reversals and palindromes in continued fractions , Volume =

[4] Palindromic continued fractions , Volume =

[5] On Repeated Factors in

Formal links

2 machine-checked theorem links

Receipt and verification

First computed	2026-05-17T23:38:55.347424Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

29697486184f48deaee6a7446443e5699fde12e99095f2b3e8469b64e7e84d51

Aliases

arxiv: 2605.14955 · arxiv_version: 2605.14955v1 · doi: 10.48550/arxiv.2605.14955 · pith_short_12: FFUXJBQYJ5EN · pith_short_16: FFUXJBQYJ5EN5LXG · pith_short_8: FFUXJBQY

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/FFUXJBQYJ5EN5LXGU5CGIQ7FNG \
  | 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: 29697486184f48deaee6a7446443e5699fde12e99095f2b3e8469b64e7e84d51

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "0497009d330b50d64027c48d200f5730c050bec7ae07c732a07084156597926a",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2026-05-14T15:25:12Z",
    "title_canon_sha256": "545ca7762cf22780b4c63214f1a170e3084563afd35d3bf9cd43fee7aa11522d"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.14955",
    "kind": "arxiv",
    "version": 1
  }
}