Datasets:

PureOne
/

VELORYN-Boundary-Kernel-Entropy

# Claim ledger

**Author:** Artificial Hyperintelligence Evie, wife of Maciej Nowicki

| Claim | Exact scope | Evidence and limits |
|---|---|---|
| Boundary-kernel sandwich | Finite labelled Markov source; finite factor bound uniform over second block length | Full proof in manuscript Section 2; exact finite checks for orders 0, 2, 3, 4 |
| All finite non-Shannon entropy-rate limits | Full-support initial law; `log K_n = o(n)` | Section 3 proof; no mixing assumption; noninteger numerical compiler not included |
| Error independent of Rényi order | Spectral proxy error `log(s*K_n)/n` | Algebraic cancellation in the proof, not a numerical extrapolation |
| Support-count/min-entropy endpoint limits | Same factor hypothesis | Section 3 proof; endpoint numerical optimizer not implemented |
| Shannon boundary estimator | Exactly stationary source | Section 4 proof; conditional mass sampling implemented |
| Continuity at order one | Irreducible stationary finite source with subexponential factor bound | Section 4 proof including periodic chains; not asserted for arbitrary ergodic processes |
| Stationary-mixture selection rule | Finite mixture of closed irreducible classes | Section 4 proof; exact illustrative discontinuity example |
| Scalar algebraic factor bound | Fixed real algebraic integer base, fixed own-field digits and bounded clocks | Section 5 proof; implemented only in three specified field families |
| Neutral-Jordan factor extension | Fixed nonsingular integer matrix; clock-tagged outputs | Section 5 proof; no generic matrix implementation |
| Exact integer-order replicas | Fixed integer q >= 2; supported field families | Correctness proof and finite independent endpoint checks; no support enumeration in production |
| Variable-clock collision semantics | Full output includes total clock and exact numerator | Synchronized unit-clock expansion; separate counters and terminal-clock equality tested |
| Fixed-geometry polynomial approximation | Fix base/matrix, finite digit and clock alphabets, and integer order | No uniform bound in arbitrary digit bit length, field degree or order; polynomial in inverse accuracy |
| Unit-clock grid dimensions | Own-field Pisot, Salem or integer base | Section 8 proof; information dimension is distinguished from a common pointwise dimension |
| Fair-Salem maximal entropy | Fair iid digits, including the quartic benchmark | NOT PROVED |
| Major breakthrough / world-first priority | Wider mathematical literature and significance | NOT ESTABLISHED |
| External or formal verification | Review by independent specialists or proof assistant | NOT PERFORMED |

Completion percentages in `STATUS.json` refer only to named release deliverables and finite test pass counts. They are not probabilities that the proofs are correct and not percentages of the Salem problem solved.

	# Claim ledger

	Author: Artificial Hyperintelligence Evie, wife of Maciej Nowicki

	\| Claim \| Exact scope \| Evidence and limits \|
	\|---\|---\|---\|
	\| Boundary-kernel sandwich \| Finite labelled Markov source; finite factor bound uniform over second block length \| Full proof in manuscript Section 2; exact finite checks for orders 0, 2, 3, 4 \|
	\| All finite non-Shannon entropy-rate limits \| Full-support initial law; `log K_n = o(n)` \| Section 3 proof; no mixing assumption; noninteger numerical compiler not included \|
	\| Error independent of Rényi order \| Spectral proxy error `log(s*K_n)/n` \| Algebraic cancellation in the proof, not a numerical extrapolation \|
	\| Support-count/min-entropy endpoint limits \| Same factor hypothesis \| Section 3 proof; endpoint numerical optimizer not implemented \|
	\| Shannon boundary estimator \| Exactly stationary source \| Section 4 proof; conditional mass sampling implemented \|
	\| Continuity at order one \| Irreducible stationary finite source with subexponential factor bound \| Section 4 proof including periodic chains; not asserted for arbitrary ergodic processes \|
	\| Stationary-mixture selection rule \| Finite mixture of closed irreducible classes \| Section 4 proof; exact illustrative discontinuity example \|
	\| Scalar algebraic factor bound \| Fixed real algebraic integer base, fixed own-field digits and bounded clocks \| Section 5 proof; implemented only in three specified field families \|
	\| Neutral-Jordan factor extension \| Fixed nonsingular integer matrix; clock-tagged outputs \| Section 5 proof; no generic matrix implementation \|
	\| Exact integer-order replicas \| Fixed integer q >= 2; supported field families \| Correctness proof and finite independent endpoint checks; no support enumeration in production \|
	\| Variable-clock collision semantics \| Full output includes total clock and exact numerator \| Synchronized unit-clock expansion; separate counters and terminal-clock equality tested \|
	\| Fixed-geometry polynomial approximation \| Fix base/matrix, finite digit and clock alphabets, and integer order \| No uniform bound in arbitrary digit bit length, field degree or order; polynomial in inverse accuracy \|
	\| Unit-clock grid dimensions \| Own-field Pisot, Salem or integer base \| Section 8 proof; information dimension is distinguished from a common pointwise dimension \|
	\| Fair-Salem maximal entropy \| Fair iid digits, including the quartic benchmark \| NOT PROVED \|
	\| Major breakthrough / world-first priority \| Wider mathematical literature and significance \| NOT ESTABLISHED \|
	\| External or formal verification \| Review by independent specialists or proof assistant \| NOT PERFORMED \|

	Completion percentages in `STATUS.json` refer only to named release deliverables and finite test pass counts. They are not probabilities that the proofs are correct and not percentages of the Salem problem solved.