1.1 Purpose and claim boundary

This document is not an “introduction to the theory,” but is written to leave a verifiable public contract. Accordingly, the core is not textual persuasion, but whether the following artifacts exist and reproduce:

• A4 arrangement (arrangement object)

• J_LEDGER (irreversible event ledger)

• Gate verdict ( / )

1.2 Reader guide (tracks + verification-first)

• (Main) Integrated narrative (front matter). §2–§8 provide an integrated description of the applications volume’s design rationale (objects/contracts) and the adjudication structure for minimal claims. KEY \(\rightarrow\) U–J\(\rightarrow\) Gate \(\rightarrow\) Applications is presented as a single flow.

• Application A (Bio EM / neural). §9 organizes the Bio–EM track into (i) a conceptual overview and (ii) gate-based specifications (verification gates). Detailed original text follows Appendix B (text snapshot) and the bundled UJ-REPRO-KIT.

• Application B (Therapeutic concept). §10 includes only the AXIOM-FIX / NO-CAL public scope (qualitative labels + stop rules). Detailed original text is traced via Appendix C and the bundled reproducibility bundle.

• Appendices (traceability / preservation of originals). Appendix A–E preserve key originals and snapshots in service of the “integrative volume that includes all supporting material” goal. In vNext, core definitions/examples in the appendices will be progressively moved into the main body (rearranged) (§12).

1.3 Policy keywords (ASCII)

• AXIOM-FIX: Freeze the meaning of definitions/terms/labels at the version level (core to reproducibility).

• NO-CAL: (therapy track) does not include numerical tuning, dosing, experimental recipes, or clinical procedures. It discloses only qualitative labels + guardrails + stop rules.

• PUBLIC-REFERENCE: (DNA examples) contains no personal genomes/patient data. Human DNA examples use only public standards (references) or publicly available specifications/examples.

• LOCK-DERIVE-GATE: Lock inputs/priors/layouts (LOCK), derive outputs via fixed rules (DERIVE), and fix the verdict as an artifact (GATE).

1.4 Notation and symbol conventions (mm39-compatible)

This document inherits the symbol system of mm39 v1.2-KO(v1.6) verbatim. Any newly introduced symbols/labels are defined without conflicts and used consistently throughout the document.

2.1 What this release adds (beyond mm39 v1.2)

Where mm39 v1.2 presented A4 + J_LEDGER as “interpretation artifacts” and specified how to make them (a pipeline contract), this applications volume bundles, in the same package, what is needed to connect those artifacts to verification specifications and application conclusions.

• Full KEY spec + ontology lock. With and the KEY bundle, the meaning of terms/labels is frozen at the version level (AXIOM-FIX).

• U–J dynamics + Gate specification. To ensure that “explanations” resolve not as text but as artifacts, the package includes gate-name/alias normalization, table headers, and adjudication rules as bundled artifacts.

• Minimal-claim set for Applications A/B. The public scope of Bio–EM (waveguide/soliton/causality) and Ω-LearnSim (IR PAM-Sensitizer) is constrained and fixed as verifiable claims + stop rules.

• Single-upload artifact. Uploading this single release zip to Zenodo is sufficient so that “document + source + bundles + integrity” are preserved together.

2.2 Evidence snapshot (what is checkable in this pack)

2.3 One-line contract (what the whole pack asserts)

KEY (language)  ->  U-J (dynamics ledger)  ->  Gate (\path{PASS/FAIL/INCONCLUSIVE})  ->  Applications
   A4 layout           J_LEDGER                 verdict.json         assurance / risk / stop-rules

2.4 What “deterministic” means here (operational)

2.5 Why applications are possible (objects, not metaphors)

In this framework, an “application” is not a metaphor but object reuse. That is, even across domains, if the same-shaped objects A4, J_LEDGER, and verdict can be shared as inputs/outputs, then the “connection” becomes not philosophy but a formal contract.

2.6 Axiom map (A1–A5) and where gates attach

The axioms (A1–A5) presented in Appendix A (preserved originals) are, in the applications volume, mapped to the following verification points (gates). (We are not trying to prove the axioms “true/false” here; instead we fix which artifacts must fail (FAIL) if an axiom is violated.)

2.7 Rapid verification protocol (reviewer-facing)

A reviewer can quickly check the package’s stated minimal guarantees via the following steps.

1. Integrity: does sha256sum -c CHECKSUMS.txt report all OK?

2. DOI consistency: Do DOI.txt / CITATION.cff / zenodo.json all contain the same DOI?

3. Build: does build under XeLaTeX?

4. Form: are format examples for A4, J_LEDGER, and verdict explicitly shown in the document (§4.3)?

5. Adjudication: are core claims designed to be expressible as Gate (§6, §9, §10)?

3.1 Non-claims (important)

• No claim to “fully solve” biological function or the causes/treatments of disease.

• (therapy track) no provision of experimental recipes, clinical procedures, or dosing/administration guidance (NO-CAL).

• No provision of concrete combinatorial optimization guidance that could facilitate potential misuse (e.g., pathogen design).

3.2 Safety posture (public view)

This release controls risk transparently—without “hiding” it—via warnings, guardrails, and stop rules. In particular, the therapy track is designed to satisfy both of the following:

• Knowledge disclosure (public benefit). Disclose qualitative labels/evidence/risks/stop rules to increase verifiability.

• No action guidance (safety). Do not include dosages, experimental procedures, clinical protocols, or manufacturing recipes.

4.1 Layered architecture and canonical outputs

4.2 Canonical schema snippets (public, schematic)

The example below is a sketch to illustrate the “format,” and does not include actual values (coordinates/numerics/experimental conditions). When needed, redacted fields are denoted <redacted>.

{
  "anchors": [{"id":"ANCHOR-00001","role":"boundary","pos":"<redacted>"}],
  "motors":  [{"id":"MOTOR-00001","role":"driver","pos":"<redacted>"}],
  "loops":   [{"id":"LOOP-00001","from":"ANCHOR-00001","to":"ANCHOR-00002","state":"ACTIVE"}],
  "shells":  [{"id":"SHELL-00001","type":"domain","members":["<redacted>"]}],
  "ontology_lock": "KEYO-v1.0 / AXIOM-FIX"
}

event_id,event_type,label,context,verdict
J0001,transition,"lock_event","baseline",OK
J0002,transition,"boundary_flag","stress",FAIL_LABEL

# gate_table.csv header (normative)
test_id,test_name,gate,result,metric,value,threshold,unit,notes

# verdict.json skeleton
{"gate":"ToF_GATE","result":"PASS","violated_rule":null,"notes":"causal direction preserved (qual.)"}

4.3 Gate naming standardization (global, normative)

The moment the same concept is called by different names across documents, reproducibility breaks. Therefore, Gate names are normalized via an alias map (example; the full set is preserved in the Appendix B snapshot).

gate_alias_map:
  CENTER★: CENTER_STAR
  CENTER_OPT_AX: CENTER_OPT_AX
  CENTER_D_Bridge: CENTER_D_BRIDGE

4.4 Failure labels (public, closed set)

The KEY ontology does not leave failures as “silence”; it fixes them as a closed label set. (The full label set is included in .)

• Input/schema: FASTA_EMPTY, ANNOTATION_MISSING, SCHEMA_INVALID

• Reproducibility: NONDETERMINISTIC_OUTPUT, DOI_AUDIT_FAIL

• Ontology: CLOSED_VOCAB_FAIL, REFERENTIAL_INTEGRITY_FAIL

5.1 Ontology lock (AXIOM-FIX)

The included freezes terms/labels at the version level. For applications, what matters is not “how much data” but consistency of definitions.

• Keep label values as a closed value set.

• Do not change the meaning of existing labels.

• Extend only by adding new labels (no reinterpretation of existing ones).

5.2 Ω-Dictionary term mapping (closure + deterministic fallback)

This release includes, in the main body/appendices, the Ω-Dictionary (integrated DNA dictionary) and a DNA experiment log as public-reference-based material (not personal genomes/patient data). As this layer grows, terminology becomes easier to drift; therefore this release fixes as the Ω-token\(\rightarrow\)KEY object mapping and substitution (fallback) rules. (v1.1/v1.0 are preserved alongside for provenance.)

5.3 KEY classes (snapshot)

5.4 Minimal KEY entry schema (public view)

KEY_ENTRY:
  id: TYPE-NNNNN
  type: {DNA_SITE, RNA, PROTEIN, COMPLEX, CELL_EVENT, FIELD_MODE, ...}
  label: short human name
  arrangement:
    anchors: [...]
    motors:  [...]
    loops:   [...]
    shells:  [...]
  dynamics:
    U2: {increased|decreased|normalized|...}   # qualitative
    U3: {high|medium|low|...}                 # qualitative
    J_events: [ ... ]                         # named irreversible events
  meaning:
    operational_instruction: "what to check / what it implies"
  provenance:
    sources: [ ... ]
    version_lock: "KEYO-v1.0 / AXIOM-FIX"

5.5 Ω-Dictionary (DNA dictionary) layer: grammar vs registry

If KEY is a “grammar book,” then the Ω-Dictionary (DNA dictionary) is a “word list (registry).” That is, KEY fixes the format of how to write a 1D sequence/annotation as an A4 arrangement object, and the Ω-Dictionary records, in public form, which words (genes/proteins/modules/phenomena) are registered to which arrangement/dynamics labels.

This release provides the following together: (i) Ω-Dictionary text snapshot (Appendix D), (ii) Omega-Genesis execution log (DNA_experiment.txt; Appendix E), (iii) Ω-Dictionary\(\rightarrow\)KEY mapping guide (; Appendix F), (iv) mapping coverage report (; Appendix I).

Legacy/provenance note. Prior mapping files (v1.1/v1.0) are preserved as-is in the package to prevent definition drift, and can be viewed as-is in Appendix G/H.

5.6 Mapping fallback policy (when an exact mapping key is absent)

In real data, situations where “the exact key does not exist” (e.g., organisms without CTCF, empty-annotation regions, mismatched domain definitions) necessarily occur. The stance of this integrative volume is simple: do not hide the mapping; fix priorities and fallback rules in public files.

1. Annotation-first. Prefer public annotations (ENCODE/IMGT/PDB, etc.) or curated markers.

2. Structure-first. If boundary/contact evidence exists (e.g., Hi-C boundaries), use it as the next priority.

3. Sequence-only fallback. Use qualitative mapping possible from sequence cues alone (AT/GC, repeats, etc.), and must mark it as source=derived.

4. Unknown label only. Do not fill by guesswork. Leave empty fields as ANNOTATION_MISSING or unknown.

These rules are fixed in machine-readable form in the Appendix F mapping guide, and thereby prevent irreproducibility of the form “we interpreted arbitrarily because no mapping existed.”

6.1 Why U–J is useful in applications

In applications, the U–J decomposition is less a “causal explanation” than a verifiable bookkeeping device. That is, by separating how the system moved (conservative moves) from what changed irreversibly (JEVENT), and recording it as an event ledger, one can verify whether others obtain the same ledger from the same locked inputs.

\[\dot{\Psi} = \mathcal{U}_2[\Psi] + \mathcal{U}_3[\Psi] - \mathcal{J}[\Psi],\]

Here, \(\mathcal{U}_2,\mathcal{U}_3\) are interpreted as conservative paths, and \(\mathcal{J}\) as the dissipative (irreversible) path.

6.2 Residual pressure and “incorrect dynamics”

The residual pressure in Definition 1 is introduced to avoid long “cause narratives” and instead summarize the result of accumulated stress/damage/inflammation/lipid signals as a single qualitative state variable. Accordingly, “incorrect dynamics” is compressed into the following ledger-based description.

Incorrect dynamics = residual-pressure accumulation \(\Rightarrow\) degraded JEVENT efficiency \(\Rightarrow\) functional collapse.

In the therapeutic concept, a “counter-arrangement” is defined as an intervention that restores normal transitions (JEVENT) or returns the system to the Gate PASS region.

6.3 Canonical gate families (registry view)

• Physics / causality: , (EM) ,

• Conservation / bookkeeping: ,

• Stability: prevent runaway transfer gain (e.g., qualitative/quantitative adjudication of \(\rho(G)<1\))

• Identifiability / leakage: IDENTIFIABILITY,

• Domain safety (therapy): selectivity/no-agonism/tolerance (resolves into stop rules)

6.4 Reproducibility snapshot (Bio–EM; computational gates)

This section summarizes minimal results that are checkable not as “words” but as artifacts. All originals are included in , and for reviewer convenience the same contents are also provided as copies under (redundant, but reduces review cost).

7.1 Assurance case skeleton (public)

CLAIM: <what should be true, stated qualitatively>
EVIDENCE: <artifact pointers: gate_table/verdict + doc section + bundle id>
RISKS: <what could go wrong>
STOP_RULES: <conditions that force REVISE/HALT>

8.1 Cross-track translation table (DNA / Bio–EM/ Therapy)

The table below does not aim to claim “identity”; it is a translation convention for locking different domains into the same object shapes.

9.1 Claim boundary (what is and is not claimed)

This track does not aim to “explain the entire brain.” The publicly sharable minimal claim is restricted to the following single sentence:

With a specific arrangement (A4) and priors (A5) locked, the conditions required by the Bio–EM interpretation are designed to be adjudicable via Gate .

That is, “success” of this track is measured not by rhetorical persuasion, but by whether (i) gate definitions exist and (ii) artifacts are produced, and (iii) failures are returned as FAIL_LABEL.

9.2 Conceptual overview (interpretive framing)

This track reframes signal transfer not as microscopic ion trajectories but as a propagation problem of an effective field. Under certain boundary (axon/myelin) conditions, the axon–myelin composite can be approximated by a waveguide model, and total internal reflection (TIR) provides a qualitative frame for minimizing leakage. A balance of nonlinearity and dispersion can be expressed as a soliton-form stable propagation hypothesis, and low-frequency EEG/MEG components can be observed as envelope/beat phenomena of high-frequency carrier interactions—forming a set of testable hypotheses.

However, the “approval” criterion adopted here is not narrative persuasiveness but the Gate verdict. Under input locking (A4, A5), relevant conditions are reduced to , and if FAIL or INCONCLUSIVE is returned, the interpretation is not approved.

9.3 Verification layer (gate-first)

The public claim of this track is limited to whether it passes the defined Gates. Representative Gates (summary):

• : does information transfer respect the causal direction?

• : is there no contradiction in energy/conservation bookkeeping?

• : does a waveguiding (TIR) feasible region exist under boundary conditions?

• : can shape be preserved during propagation without waveform collapse?

• IDENTIFIABILITY / CAL_LEAKAGE: is it identifiable without “custom tuning” (leakage)?

9.4 Assurance card (Bio–EM, public)

CLAIM(EM): "Waveguide/soliton interpretation is accepted only if core gates PASS under locked inputs."
EVIDENCE: bundles/UJ_GATE_SPEC_RELEASE_PACK_v1_0.zip + bundles/UJ-REPRO-KIT_2025-10-22.zip + Appendix B
RISKS: identifiability failure, calibration leakage, alias drift (gate naming), stability violations
STOP_RULES: ToF_GATE FAIL or CAL_LEAKAGE observed => HALT (do not interpret)

10.1 Claim boundary and safety posture (NO-CAL)

This track provides no therapeutic “prescription.” The public scope is restricted by NO-CAL to the following:

• Qualitative labels (qualitative labels): increased/decreased/normalized/minimal, etc.

• Stop-rules: rules that resolve to REVISE/HALT upon risk signals

• Gate framing: a structure that treats selectivity/no-agonism/tolerance risks via

Therefore, the purpose of this track is not “to propose a therapy,” but to fix conceptual claims (what) and safety boundaries (how to stop) in an adjudicable form.

10.2 Problem statement (insulin resistance as incorrect dynamics)

In this framework, insulin resistance is reframed not as “a lack of insulin,” but as a state where micro-arrangement changes of the receptor (IR) and accumulated residual pressure make normal transitions (JEVENT) difficult to complete. That is, even when insulin binds, conformational transitions may fail to complete or proceed with low efficiency, collapsing metabolic signaling (AKT) bias as an instance of “incorrect dynamics”.

10.3 Mechanism snapshot (qualitative, public)

Below is a mechanism snapshot that fixes, qualitatively, “what is being claimed” (it does not include detailed numerics, experimental procedures, or recipes).

insulin present
  -> IR single-insulin state stabilized (qual.)
  -> FnIII-3 approach increased
  -> activation-loop progression normalized
  -> signaling bias shifted toward metabolic (AKT >> ERK)  # qualitative direction only
  -> if selectivity gates PASS and stop-rules not triggered: ACCEPT (concept-level)

10.4 Theory deepening (qualitative): 4D arrangement manifold and maps

To treat the therapy track not as “narrative” but as objects + a map, we lift the minimal definitions used in the bundled Ω-LearnSim pack (v3) into the main text (qualitative).

10.5 Counter-arrangement concept (PATH-A)

The counter-arrangement in the Ω-LearnSim track is defined as follows (qualitative):

• Target: IR interface (L1-\(\alpha\)CT-FnIII-1).

• Goal: in the presence of insulin, stabilize the single-insulin state to normalize FnIII-3 approach/activation-loop progression, and thereby qualitatively strengthen metabolic bias (AKT \(\gg\) ERK).

• Prohibited: operation (agonism) under no-insulin conditions and IGF-1R/Hybrid activation (selectivity failure).

10.6 Governance note (public-interest pledge, summary)

This track asserts not only an “idea” but also public governance. The Appendix C original includes the following principles, which are retained here at a summary level:

• Free distribution / affordability duty: aim for distribution that does not compromise affordability.

• Open governance: update the version log in a Claim–Evidence–Risk–Stop-rules structure.

• Safety first: if selectivity/no-agonism/tolerance stop rules trigger, immediately REVISE/HALT.

10.7 Evidence snapshot (qualitative, versioned)

This proposal assumes versioned accumulation of qualitative labels (v3→v4→vN). That is, rather than a “one-shot narrative,” it is organized so that, per scenario code (A1–D3, N1–N3, E1–E4, etc.), one can check whether label directionality matches/mismatches, and if mismatched, REVISE/HALT is possible. (Details are traced in the Appendix C snapshot and bundled reproducibility bundle.)

10.8 Qualitative label ontology (public, NO-CAL)

Representative labels (summary; full list in Appendix C):

10.9 Stop-rules (public safety rails)

The following conditions imply REVISE/HALT (qualitative):

• (S1) igf1r_activity or hybrid_receptor_signal is elevated.

• (S2) Under no-insulin conditions, activity signs corresponding to hypoglycemia_flag=true (agonism).

• (S3) Under continuous exposure, tolerance_flag=true with tolerance_reversibility=none.

10.10 Assurance card (public, reviewer-facing)

CLAIM(THERAPY): "IR is sensitized only under insulin-present condition, with minimal off-target."
EVIDENCE: Appendix C + bundles/OmegaLearnSim_IR-PAM_v4_FINAL_Reproducibility.zip + Gate framing in §6
RISKS: off-target activation (IGF-1R/Hybrid), hypoglycemia-like behavior, tolerance
STOP_RULES: (S1)-(S3) => REVISE/HALT (public)

10.11 Disclaimer

This track is a research/concept disclosure and is not medical advice. This document does not provide dosages, clinical procedures, or experimental protocols (NO-CAL). Safety/efficacy evaluation must be conducted separately within regulatory and ethical processes.

11.1 Minimal reproducibility steps

# 1) Verify integrity (must be all OK)
sha256sum -c CHECKSUMS.txt

# 2) Build the PDF (XeLaTeX)
xelatex -interaction=nonstopmode -halt-on-error Deterministic_Applications_Whitepaper_v1_2.tex
xelatex -interaction=nonstopmode -halt-on-error Deterministic_Applications_Whitepaper_v1_2.tex

11.2 DOI consistency (MUST)

• DOI.txt contains: 10.5281/zenodo.17979016

• CITATION.cff contains the same DOI

• zenodo.json contains the same DOI and links base DOI 10.5281/zenodo.17963127 as isSupplementTo

11.3 Zenodo upload checklist (suggested, before publish)

• upload_type: publication (publication_type: report)

• license: CC BY 4.0

• keywords/description mention: “integrated applications (KEY + U–J+ Gate + repro)”.

• Attach the release zip as-is (single upload artifact).

13.1 What this pack does not establish

This release demonstrates that “applications are possible” via formal contracts and reproducibility artifacts, but explicitly states that the following are not yet established.

• Measurement-based FULL verification. The Bio–EM track is currently centered on computational “screen” artifacts, and external validation with real ECoG/MEG/in-situ measurement data is a subsequent step.

• Independent reproduction (by other researchers) logs. The package is designed so third parties can reproduce , but multi-institution independent logs are still in the accumulation stage.

• Clinical conclusions on therapeutic efficacy/safety. The Ω-LearnSim track is a NO-CAL-scope concept disclosure and does not replace evaluation under regulatory/ethical procedures.

13.2 Threat model (where errors can hide)

• Alias drift. If Gate names/aliases vary across documents, reproducibility collapses immediately (normalization required).

• Calibration leakage. If calibration parameters leak into evaluation, it becomes “custom tuning” ( gate).

• Boundary domination. If one generalizes interpretations in boundary-dominated regimes, errors grow (§6.5 fail-fast checks).

• Category error. Misuse risk: confusing qualitative labels with “clinical guidance” (NO-CAL fixed).

13.3 Falsification triggers (fast FAIL list)

• Bio–EM: ToF_GATE FAIL or observed \(\Rightarrow\) Halt.

• Bio–EM: TIR_Threshold FAIL \(\Rightarrow\) the waveguide frame is rejected for that input.

• Therapy: (S1) IGF-1R/Hybrid activation rise, (S2) no-insulin agonism, (S3) irreversible tolerance signs \(\Rightarrow\) Halt.