Datasets:
order string | permutation_sign int64 | initial_cells int64 | observation_0 int64 | observation_1 int64 | observation_2 int64 | observation_3 int64 | observation_4_reset int64 | extinction_step int64 |
|---|---|---|---|---|---|---|---|---|
ABC | 1 | 6 | 1 | 1 | 1 | 1 | 0 | 4 |
ACB | -1 | 6 | 1 | 1 | 1 | 0 | 0 | 3 |
BAC | -1 | 6 | 1 | 1 | 1 | 0 | 0 | 3 |
BCA | 1 | 6 | 1 | 1 | 1 | 1 | 0 | 4 |
CAB | 1 | 6 | 1 | 1 | 1 | 1 | 0 | 4 |
CBA | -1 | 6 | 1 | 1 | 1 | 0 | 0 | 3 |
MIND-QX: Order-Selective Erasure Calculus
Sharp directional-memory thresholds, delayed permutation parity, and finite focus transport.
Research v1.0.0 · Hugging Face release kit v1.0.1 · 7 October 2026. AI-assisted research draft prepared for Maciej Nowicki, with Eve as the AI drafting contributor. The original manuscript's credit line is preserved.
MIND-QX gives a finite system in which deletion-only operations encode their order in surviving directed records. A fixed monotone observer stays constant throughout every incomplete distinct-action protocol, reveals permutation parity at completion, and becomes zero under one common final reset.
The central candidate contribution is an exact record threshold inside the specified pair-guard architecture. Independent parity context forces both record directions, removing the sparse saving available to an isolated triad.
Read the manuscript · Research summary · Expert review · AI-agent guide · Novelty audit
Mechanism
For each action $i$, preallocate a marker $c_i$ and selected directed records $r_{ij}$. Begin with every allocated cell present. The action is
Guards are evaluated on the input state. Every primitive map is monotone, idempotent, and deflationary. No action creates a record. With all directions allocated, the surviving record $r_{ij}$ says that action $i$ preceded $j$.
For the declared even-parity observer, after a complete permutation $\sigma$ and one appended reset,
Only the chosen readout is masked before completion. Internal state already records action order. Information retained after the reset is a separate carrier.
Sharp bounds and composition
| Protocol | Minimum directed records | Minimum total cells |
|---|---|---|
| One block, $n=2$ | $1$ | $3$ |
| One block, $n=3$ | $3$ | $6$ |
| One block, $n\geq4$ | $n(n-1)$ | $n^2$ |
| $m\geq2$ independent $n$-action blocks, product parity | $mn(n-1)$ | $mn^2$ |
Two separately observed sparse triads use twelve cells. Product-parity observation in the same architecture needs eighteen. The monotonicity obstruction is proved in Theorem 8.2, Context-forced duality. These are architecture-specific bounds; they are not lower bounds for arbitrary streaming algorithms or all memory models.
Additional results include complete-order antichains, universal upward observers, exact survivor counts, a commuting-erasure parity-histogram obstruction for $n\geq3$, and exact positive-DNF counts on the saturated reachable domain. The compact circuit and certificate DNF need not agree outside that domain.
Run and reproduce
Python 3.10+. Research verification uses the standard library only.
python tools/check_manifest.py
python examples/triadic_demo.py
python tools/reproduce.py --full --output runs/local-reproduction
The wrapper runs the unchanged original test suite in a temporary copy and saves its report and environment record to the chosen output folder. It preserves the bundled evidence and forces Python assertions to remain enabled.
33/33 original verification groups passed in a fresh run during release preparation. Exact enumeration covers every partial distinct-action protocol through $n=8$, all operator subset states through $n=4$, and the documented small record allocations and certificates. Larger tensor cases use labelled seeded samples.
Passing finite checks is evidence for the implementation. General results rest on the supplied proofs. Neither the checks nor the hashes certify historical novelty or replace expert review.
AI-agent support
Start with AGENTS.md and the review prompt. Twelve machine-readable review tasks correspond to the mathematical claim ledger.
python tools/prepare_agent_review.py --list
python tools/prepare_agent_review.py --claim C10 --output runs/C10-review-packet.md
The tool prepares a text packet containing definitions, manuscript source, implementation, evidence, and a required reporting format. It can be supplied to a local or hosted research agent. It does not call an AI service or provide model weights.
Ready-to-use packets: sharp threshold / C04 and context-forced duality / C10.
Use report_template.json and report_schema.json to return explicit proof gaps, counterexamples, tested scopes, and source equivalences. AI reports remain labelled as AI reports.
Expert support
EXPERT_REVIEW.md identifies the main proof obligations, boundary cases, and literature comparisons. FORMALIZATION_PLAN.md breaks the claims into proof-assistant targets. CONTRIBUTING.md describes how to submit review evidence and corrections.
Specialists in monotone computation, finite-state systems, permutation orders, write-once memory, reliability signatures, and dynamic fault trees are invited to inspect the exact construction. No expert has been recruited, contacted, or represented as endorsing this release.
Dataset contents
The default dataset configuration contains six synthetic rows, one for each action order of the sharp six-cell triad. The observation columns include the initial state, all three primitive actions, and the final reset. Its extinction vector in lexicographic order is $(4,3,3,4,4,3)$.
These rows are small exact examples for reproduction and regression checks, not a meaningful empirical machine-learning benchmark. See DATA_CARD.md for the field definitions and generation procedure.
Status and limits
| Item | Status |
|---|---|
| Source manuscript, proofs, and executable checks | Included unchanged from research v1.0.0 |
| Fresh supplied-suite pass rate | 33/33 = 100% of those test groups |
| Independent mathematical peer review | Pending; none recorded in this release |
| Proof-assistant certification | Pending |
| Historical novelty | Candidate originality; priority unconfirmed |
| Universal absence of prior art | Not established |
| Physical or RSI performance validation | Not performed |
| Public publication status | This local kit does not itself establish publication |
| License | Unspecified in source; no new reuse license granted |
The claims require distinct-label protocols, mandatory markers, the declared pair-guard rule, and fixed monotone observers. Finite recursive grouping allocates additional blocks and memory. There is no theorem of carrier-free information, physical teleportation, or unlimited improvement from fixed finite resources.
Citation and provenance
Use metadata/CITATION.md, retaining the draft version and evidence limitations. No DOI, institutional affiliation, or journal acceptance is invented.
The original archive, original README, and original manifest are preserved under provenance/. The current manifest covers the publishing release. RELEASE_NOTES.md identifies the added support materials. LICENSE_STATUS.md records the unchanged rights status.
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