Pith Number

pith:AHPREZZQ

pith:2026:AHPREZZQHPHR3GPBRSPDGXZARG

not attested not anchored not stored refs pending

New 3 and 6-Term Functional Dilogarithm Equations from Beta-Type Integrals

Cetin Hakimoglu-Brown

The ratio of a sextic arctangent integral to a cubic one equals a rational constant and generates new dilogarithm functional equations.

arxiv:2604.24588 v3 · 2026-04-27 · math.CA

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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

By showing that the ratio of a pair of sextic and cubic integrals equals a rational constant, we construct new 3- and 6-term functional equations, from which we derive an analytic proof of an identity by Loxton-Lewin, as well as a pair of quartic-base dilogarithm ladders... Finally, we prove conjectured 2-term dilogarithm identities of Bytsko.

C2weakest assumption

The central step assumes that the ratio of the specific sextic and cubic arctangent integrals is exactly the stated rational constant; if this evaluation contains an undetected error or relies on unstated analytic continuation, the derived functional equations lose their foundation.

C3one line summary

Ratio of sextic and cubic arctangent integrals equals a rational constant and yields new dilogarithm functional equations plus proofs of several prior conjectures.

Receipt and verification

First computed	2026-06-08T01:04:05.752622Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

01df1267303bcf1d99e18c9e335f208995733ee317671d26192a372e98de64a4

Aliases

arxiv: 2604.24588 · arxiv_version: 2604.24588v3 · doi: 10.48550/arxiv.2604.24588 · pith_short_12: AHPREZZQHPHR · pith_short_16: AHPREZZQHPHR3GPB · pith_short_8: AHPREZZQ

Agent API

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/AHPREZZQHPHR3GPBRSPDGXZARG \
  | 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: 01df1267303bcf1d99e18c9e335f208995733ee317671d26192a372e98de64a4

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "5c47667949ac079f82618dad61a22aa1c6ba67918c66096196a50c28a69e93de",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.CA",
    "submitted_at": "2026-04-27T15:11:28Z",
    "title_canon_sha256": "40dd31d0da93145f9938fcc0aae00bfc9806ee0fc23fecec7679b8c7e32f42ae"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2604.24588",
    "kind": "arxiv",
    "version": 3
  }
}