FAQ & Peer Review
Questions, clarifications, and the road to open scientific review
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This page collects common questions about Harmonic Field Theory (HFT) and how the work is evaluated: explicit identity conditions, falsifiable predictions, and an executable checker. Use the quick links to jump to tests, the linter/CLI, or contact for academic review. Plain definitions come first so the rest reads cleanly.
Help me Break this model!
This model is at the point where I am seeking unofficial peer review, so this website is an open call for collaboration to help me submit a formal paper. Any help or comments appreciated!
The current and best path to testing the model is to run this test protocol - it's a scaled down simple version of the model built for onboarding quickly to the models thinking, and pixel typing any equation as a test.
🔗 HFT Test Protocol - Direct Link to Google Doc
🔗 https://docs.google.com/document/d/e/2PACX-1vSLFpcwuKGTQkgRSvqqxR9Yy6-M7Y7x7F6y-LTbVgjXz-_UKbt7rGnYsDpjuEwYQFKEXV2vNN1gvm90/pub​
FAQ & Definitions
Before we start — five quick definitions
Boundary
Where dynamics are compiled into numbers—the interface that extracts the closed part as fact and routes the rest into the ledger.
<detector, horizon, interface, readout code> → one object.
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Mirror check (R² = I)
A two-pass swap on the doubled object; what survives unchanged is admissible, what flips or carries units isn’t.
<conjugate, branch, tilde, normal> → one reflection.
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Invariant (real)
The even, positive, unit-normalized scalar that finishes its loop at the boundary; the piece you can publish.
<fact, observable, scalar, unitless ratio> → one closure.
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Defect (ε)
The oriented, anti-symmetric remainder—the system’s unresolved action. Typed ε^(Ω, η, op): internal conjugacy, causal/handed flow (Tier-4 onset), operator parity. Carried forward on the Möbius ledger, globally balanced (∑σâ‚™εâ‚™ = 0).
<unresolved closure, action, handedness, time’s arrow> → one directed residue.
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Pixel (H-pixel)
The smallest two-face unit (system + mirror) that can close. When it extracts, you get a fact; when it can’t, you get directed ε—the seed of the observed arrow.
<system, mirror, now, readout> → one measurable.
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From these five definitions, some obvious constraints follow:
This is the HFT Constraint program: facts must be mirror-even, positive, and unitless at a boundary; anything that doesn’t close is kept as directed residue (epsilon) rather than thrown away. Pixels (system + mirror) are the minimal units that can produce such facts.
If you’re reading this like a scientist, your thought chain probably goes like this:
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“Our core equations (Hamiltonian, Schrödinger) are invertible. If equations are reversible, shouldn’t processes be reversible too?”
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“Maybe irreversibility is just ignorance: with perfect control I could run time backward.”
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“Echoes (spin/Loschmidt) look like reversals, so doesn’t that settle it?”
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“So why is HFT insisting on two-pass closures and pairing at the boundary?”
This is exactly where the category slip appears: map existence is not event admissibility. Labs implement open channels, not bare inverses; single-pass “undo” would violate standard guardrails (data-processing monotonicity, nonnegative entropy production, and the fact that fluctuation relations compare a forward protocol to a separately defined reversed one). Echoes work precisely because they are paired composites, not rewinds.
Which brings us to Question 0. It’s “0” because it gates everything that follows. If you don’t separate invertible equations from admissible events, you will misread HFT’s boundary rule. Start here:
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Q0. Do “reversible equations” mean real processes can be reversed?
No. Having an inverse map (phi^-t, or U(-t) = U(t)^dagger) is kinematics, not an operational license. Real experiments are open: channels obey data-processing (relative-entropy monotonicity), entropy production is nonnegative, and fluctuation relations compare a forward protocol to a separately defined reversed protocol. So a single-pass “undo” on the system is not a physical event. Echoes are paired composite protocols; that’s why they work.
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Theorem: No single-pass reversal without full control of environment + control record.
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Corollary: No global deletion (Landauer limit; quantum no-deleting).
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Practice: Publish closures from paired protocols; treat “reversal” as a composite.
🔗 Read → HFT-00.1 Supplement - On the Impossibility of Single-Pass Reversal
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Q1. What is the Mirror Law in plain terms?
R² = I: reflect twice to return to identity. Only two-pass closures that survive unit and parity checks are admissible equalities; these yield dimensionless invariants.
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Q2. Why do squares / two-pass structures keep appearing?
Stability here is defined by a two-step closure, which naturally selects quadratic forms (energies, norms, actions) and R-even scalars.
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Q3. What are ε-defects?
Normalized measures of departure from ideal reflection, tracked by defect tensors (conjugacy D^Ω, causal D^η, operator-parity D^op) and aggregated per tier in an ε-ledger.
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Q4. Is HFT meant to replace existing physics?
No. It’s a constraint-first reframing that compresses known structures under one closure rule and then makes testable extensions.
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Q5. How can HFT be tested?
Check whether proposed laws/processes: (a) legally close to a dimensionless invariant, (b) have the right tier/handedness, and (c) show predicted ε-patterns (e.g., parity/birefringence signatures). See Predictions & Tests below.
​​​Core claim, example, predictions​
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The only publishable numbers are those a boundary (detector, horizon, interface) reports the same way under a mirror check done twice (R² = I). Numbers that pass are invariants; anything that fails is kept as defect (ε)—a to-do, not a fudge.
One concrete example (double-slit, minimal)
• Setup: photons hit a camera.
• Bulk math: amplitudes interfere.
• Boundary rule: the camera reports counts per pixel (positive, unit-normalized) that don’t change under the double-mirror check → admissible fact.
• ε signal: any model piece implying negative probability or frame-dependent counts is ε (model/boundary mismatch).
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Predictions (and how to falsify)
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• Readout form: Stable, publishable observables are even and unitless at readout (ratios, squares).
Falsify: demonstrate a robust measurement that must be odd-parity or dimensional to be frame-invariant.
• Boundary discipline: Changing only the boundary (detector model/conditioning) may move distributions, but the reported invariants stay put.
Falsify: same system, two admissible boundaries → different invariant results after proper normalization.
• Coherence ceiling (1–2–4–8): Long-lived, finite-energy coherent compositions won’t require algebra beyond this ladder.
Falsify: a stable, reproducible system that needs >8 composition structure to match data.
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The H-Pixel
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What we mean (plainly):
In HFT, the smallest unit that can yield a reportable fact is a two-face object—a system together with its mirror partner—so that applying the reflection twice returns you to itself (R² = I). We call this pair a H-pixel. At a boundary (detector, interface), only what closes under this double pass becomes a fact (even, positive, unitless). Anything that doesn’t close is kept as ε (typed, directed remainder) and treated explicitly rather than ignored.
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Why a two-face unit?
Because the thing we publish is not the raw state but the closure of a state with its appropriate mirror (conjugate, branch, tilde, normal, etc.). The mirror is domain-specific—not always particle/antiparticle—and the admissible readout is the mirror-even part.
If a system can distinguish "self" from "world" - whether it's a person, a word, a quantum measurement, or a neuron - that distinction must be mathematically precise. You can't have "sort of" self-awareness or "approximately" meaningful language. The boundary either holds or it doesn't.
The H-pixel structure H = (s, ψ) with R² = I isn't just a mathematical convenience - it's the minimal requirement for any stable distinction to exist at all.
Without the perfect involution, the distinction degrades:
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A person who can't cleanly separate self from world has no coherent identity
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A word that doesn't maintain meaning-context distinction has no semantic content
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A quantum system that can't maintain amplitude-outcome distinction has no measurement
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A neuron that can't maintain signal-noise distinction has no information processing
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The scale invariance follows necessarily: the same mathematical constraint (perfect symmetry under the mirror operation) applies at every level because distinction itself requires it.
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So when you find the same R² = I structure in quantum mechanics, neural processing, linguistic meaning, and personal identity, it's not coincidence or analogy - it's the same mathematical necessity manifesting across different substrates.
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The statistical surface (the boundary where distinctions are maintained) has to have the same geometric structure regardless of scale because the mathematical problem it solves is identical: how to maintain a stable distinction without losing coherence.
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Mirror Law: Closure, Boundary, and the Shape of Facts
Statement. The Mirror Law sets a single admissibility rule: only even, unitless, boundary readouts qualify as facts; anything else is a typed remainder ε that must pair with a partner (often at a boundary) to close. Applied consistently, this rule compresses a century of scientific practice into one constraint. Ignored, it reliably inflates mystery, spookiness, and fuzziness.
Historical anchors
From classical field theory to quantum mechanics, progress has leaned on the same move: reflect—and then close.
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Complex conjugation and modulus-squared convert amplitudes to probabilities.
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Adjoint and norm structures discipline what counts as an observable.
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Squaring first-order operators (e.g., Dirac) yields even propagation invariants (e.g., Klein–Gordon).
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Gauss–Stokes and holographic methods turn bulk statements into boundary readouts.
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Boundary terms (e.g., Gibbons–Hawking–York) make variational principles well posed.
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Noether’s theorem casts conservation as scalar invariants.
HFT reads these as one pattern: orientation-sensitive or “odd” content is not a finished report; it must close into an even, unitless, boundary scalar to enter at the equals sign.
Definitions (operational)
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Admissible readout (bullet). A reportable equality that is R-even, unitless, and taken at or through a boundary.
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Typed remainder (ε). Structured obligations that prevent closure until paired:
ε(op) for operator/parity/topology oddness,
ε(Ω) for coherence/topological linking,
ε(η) for metric/boundary incompleteness. -
Two-pass admissibility. Single-pass “reversals” on open subsystems are not admissible events; reversals that close are paired echoes.
These are checker rules. They do not add metaphysics; they constrain what may appear at “=”.
What the rule does when applied
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Eliminates illegal equals. Unitful or orientation-sensitive expressions are not facts; they are ε until paired.
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Routes obligations to boundaries. Bulk topological or metric leftovers close only with boundary partners; the pair is the object.
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Stabilizes measurement. After admissible normalization, invariants are pipeline-stable and basis-independent.
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Disciplines reversals. Echo protocols are admissible closures; one-click rewinds are not.
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Prefers integers and dimensionless equalities. Where possible, closure appears as quantized or strictly unitless relations.
What grows if the rule is removed
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Quantum theory. Measurement ambiguity expands (no unique modulus-squared bullet); entanglement is recast as “action at a distance” rather than a boundary pairing; unitarity feels tacked on.
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Thermodynamics. “Single-pass reversal” proposals proliferate; entropy ledgers drift with pipelines.
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Field theory & geometry. Anomalies look like violations instead of obligations; EH-without-GHY appears acceptable on paper but leaks at the boundary; bulk–boundary equalities look optional and paradox talk expands.
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Units & normalization. Equals signs carry units or orientation; detector pipelines do not stabilize invariants.
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Model building. “Tier chaos” and epicycle fixes multiply; fine-tuning stands in for closure.
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Mind/brain inference. Without closure grammar, observer-centric narratives swell while boundary discipline in sensorimotor loops is lost.
In short: remove the rule and the unpaid ε-debt reappears as mystery, spookiness, and fuzziness.
Representative evidence
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Topological closure. In standard Chern-insulator ribbons, the bulk Chern integer equals the edge spectral-flow integer (per-edge crossings). That is ε(Ω/op) discharged by a boundary partner.
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Metric closure. Discrete Gauss computations give bulk divergence integrals that match boundary flux. That is ε(η) discharged at the boundary.
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Closure hygiene. Mirror squaring, Dirac→Klein–Gordon, normalization to unit readouts, and Noether energy all land on even, unitless closures in ordinary practice.
These are not special pleadings for HFT; they are everyday instances of the rule already at work.
Falsifiers (clear ways to break it)
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Stable illegal bullet. A robust equality that is R-odd or unitful, with no boundary partner, yet is undeniably physical.
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Benign standalone θ-closure. A system where a topological density sits at “=” without boundary inflow and still conserves what it must.
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EH without GHY is well posed. A genuine variational principle on a manifold with boundary that closes without the boundary term.
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Born non-uniqueness. A basis-invariant, unitless, even probability readout distinct from modulus-squared that passes all admissibility checks.
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Beyond 1–2–4–8. A physically necessary coherent composition that exceeds the division-algebra ladder yet still closes legally.
One good counterexample is enough to force revision.
Reviewer checklist (how to use this rule)
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Where is the closure? Is the final report even, unitless, and boundary-located?
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What is the ε-type? If not closed, identify op / Ω / η.
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Where is the partner? What boundary or dual completes the closure?
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What breaks without it? Dropping the partner should re-inflate paradox or drift.
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What is the number? Prefer checks that yield integers or strictly dimensionless equalities.
Why this formulation emerged
A recurring question is simple and productive: If the Mirror Law is set aside, why do “spooky” and “fuzzy” themes return? The answer is methodological: the rule is a single admissibility constraint that has been settling ε-obligations all along. Remove the constraint and the debt resurfaces—first in measurements, then in models, and finally in metaphysics.
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Discipline at the equals sign
Mirror Law is presented here as a unifying admissibility rule. It gathers unit checks, odd→even closures, boundary completions, and anomaly inflow under one constraint:
Only closed, even, unitless boundary readouts are facts; everything odd is an obligation that must be paired.
Keep the rule, and “mystery” sorts into bookkeeping—find the ε, route it to its partner, and close. Remove the rule, and the same content disperses into paradox talk and subjective choices. We didn’t change reality; we changed the rule for when an equality is allowed to count as a fact. It is discipline at the equals sign.
How to read the pairings below:
They are substrate independent structural identities. We suggest each is a stable geometric state under mirror law. Each bracket shows a domain where facts arise from a two-face structure; the exact mirror used by HFT depends on that domain’s mathematics/lawful tier.
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H = <quantum / classical>
<amplitude, readout> → wavefunction evolution in the bulk; |ψ|² at the boundary. -
H = <brain / qualia> (analogy)
<neural dynamics, reported experience> → the reportable is the boundary extraction of a two-face process; non-closing pieces are ε. -
H = <bulk / boundary>
<interior fields, horizon/screen> → well-posed actions require bulk+boundary completion; readouts are boundary-even (e.g., Area/(4Għ)). -
H = <then / now> (operational framing)
<time-reversible bulk laws, irreversible readout> → equations evolve both ways; measurement fixes one mirror-even scalar. -
H = <yes / no>, <0 / 1>
<process, registration> → a bit is a boundary closure of a two-face computation; admissible counts are mirror-even and unitless. -
H = <hidden / visible> (phenomenology placeholder)
<unseen contributions, measured sector> → mismatches appear as typed ε until the boundary/closure is corrected. -
H = <space “lack” / stuff> (metaphor for readout)
<geometric capacity, realized count> → the published number is the closed part; the remainder is tracked, not discarded.
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Caution about causality /acausality:
HFT isn’t claiming “everything causes its opposite.” because that would suppose a sequence. HFT is saying everything that has an opposite, that is what makes it real. It says: facts arise when a system is paired with the right mirror and passes the double-reflection test. The directed remainder (ε) accounts for what does not close (e.g., handed flows, parity-odd pieces), carried forward on the ledger with global balance constraints.
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If you want to test this, not take it on faith:
Use the examples in the “Build it yourself” section: Schrödinger → |ψ|² (passes), Yang–Mills θ-term → ε^op (kept, not extracted), EH+GHY → bulk+boundary closure. The point isn’t rhetoric; it’s that the publishable numbers are the mirror-even ones.
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Build It Yourself:
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Want to see the Mirror Law (R² = I) in action? Our Mirror Notation v7.x compiler takes any equation, restores missing units (like c or ħ), reveals its mirror structure (dual pairs needed for stable facts), and slots it into the table of physics (Tiers 0–8). Each input shows how a boundary readout (like a detector count) must be even, positive, and unitless to be a fact, while the bulk’s primes and ε-defects (typed actions, not errors) drive dynamics like chirality and time’s arrow.
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How It Works​
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Feed an equation into the v7.3 compiler (or follow the logic by hand). It:
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Tiers it: Assigns the lowest algebraic environment (e.g., Tier 5 for quantum measurements).
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Restores units: Balances constants (c, ħ, G) for unitless scalars.
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Checks mirrors: Ensures the boundary output is even under a double flip (R² = I).
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Tags ε: Marks odd or unit-carrying bulk terms as defects (e.g., ε^op for parity issues).
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Builds the table: Slots the equation into Tiers 0–8, showing physics’ structure.
Run these using the CLI: python mnv7.py "[input]" --tier --blocks --lint (see Executable Checker).
mnv7.py is an executable referee for mechanistic claims. It accepts only closed invariants at interfaces (even, unitless scalars) and routes all non-closed structure into a typed ε-ledger that must carry dynamics. It detects algebraic habitat mismatches (tiers) and enforces boundary correctness.​
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Try These Examples
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Schrödinger (Tier 5: Measurement)
Input: i ħ ∂_t ψ = H ψ
What v7.3 Does:-
Tiers to 5 (Hilbert space, quantum states).
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Restores ħ for unitless probability (|ψ|²).
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Boundary mirror: ψ ↔ Hψ, extracts |ψ|² (PASS). Bulk phases? ε^Ω (decoherence).
Output: {ψ ↔ Hψ} → ← •âŠ¸ |ψ|²
Table Slot: Tier 5—probability/measurement.
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Relativistic Dispersion (Tier 4: Dynamics)
Input: E^2 = (m c^2)^2 + (p c)^2
What v7.3 Does:-
Tiers to 4 (Minkowski, relativistic dynamics).
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Restores c for unitless (E/c)².
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Boundary mirror: E ↔ p, closes as even scalar (PASS). Bulk odd terms? ε^op.
Output: {E ↔ p} → ← •âŠ¸ (E/c)^2
Table Slot: Tier 4—propagation/dynamics.
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Yang-Mills + θ-Term (Tier 6: Interaction)
Input: (1/4) F_{μν}F^{μν} + (θ/32π^2) Tr(F ⋆ F)
What v7.3 Does:-
Tiers to 6 (gauge bundle).
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Normalizes trace for unitless F F term.
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Boundary mirror: F_{μν} ↔ F^{μν}, closes (PASS). Bulk θ-term odd, ε^op.
Output: {F_{μν} ↔ F^{μν}} → ← •âŠ¸ Tr(F F), θ → ε^op
Table Slot: Tier 6—interaction/mixing.
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Einstein-Hilbert with Boundary (Tier 4/7: Dynamics/Closure)
Input: √(-g) R + 2 K √|h|
What v7.3 Does:-
Tiers to 4 (Minkowski), advises 7 for holographic closure.
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Restores G, ħ for unitless Area/(4Għ).
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Boundary mirror: bulk ↔ boundary (n↔−n), closes (PASS). No boundary? ε^η.
Output: {√(-g) R ↔ 2 K √|h|} → ← •âŠ¸ Area/(4Għ)
Table Slot: Tier 4 (dynamics), Tier 7 (closure).
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Standard Model Scaffold (Tier 6/7: Interaction/Closure)
Input: --sm --masses 0.51099895,105.6583755,1776.86
What v7.3 Does:-
Tiers to 6 (gauge), 7 (octonionic lock).
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Unitless mass ratios, Koide diagnostic.
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Boundary mirror: masses ↔ triality, closes (PASS). Fourth gen? ε-tagged.
Output: {masses ↔ triality} → ← •âŠ¸ Koide ratio
Table Slot: Tier 6 (interaction), Tier 7 (closure).
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A "Tiered" Hierarchy Structure Emerges -
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Tier 0 (Potential): Basic scalars (e.g., ratios).
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Tier 1 (Phase): Electromagnetic phases (e.g., F=0).
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Tier 2 (Kinematics): Vectors (e.g., F=ma, if paired).
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Tier 3 (Chirality/Spin): Spinors (e.g., Dirac).
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Tier 4 (Propagation/Dynamics): Relativistic laws (E², Einstein).
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Tier 5 (Probability/Measurement): Quantum readouts (Schrödinger).
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Tier 6 (Interaction/Mixing): Gauge fields (Yang-Mills, SM).
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Tier 7 (Closure/Octonions): Holographic locks (GR, Koide).
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Tier 8 (Memory): Entropy, ledger head.
Falsify It
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The Mirror Law fails if:
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A stable, frame-invariant fact is odd or dimensional (e.g., a chiral observable with no dual).
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Two admissible boundaries disagree on normalized invariants (e.g., paired detectors mismatch).
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A reproducible phenomenon needs >8 composition (e.g., 4th fermion generation).
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Predicted ε-patterns (e.g., CMB parity) don’t match data.
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Try It: Download mnv7.py, run the inputs, and see the table build.
What HFT Isn’t Saying (Sidebar)​
To avoid missteps, here’s what HFT and the Mirror Law don’t claim:
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Not about raw stability: HFT doesn’t say every system needs mirrors to function (e.g., integers or reflexes can be stable). It’s about published facts—numbers comparable across frames (like detector counts or error ratios)—needing mirror-dual closures.
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Mirrors aren’t always literal: The mirror (R) is domain-specific (e.g., ψ↔ψ* in quantum, bulk↔boundary in gravity), not just particle/antiparticle.
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ε isn’t a fudge: Defects (ε^Ω, ε^η, ε^op) are typed, directed actions (e.g., parity violations), globally balanced (∑ σ_n ε_n = 0), not errors.
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Not all math needs mirrors: HFT’s 1–2–4–8 cap is for physical systems with coherent readouts, not pure math structures.
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Boundary-constraining, bulk-governing: The Law constrains facts at the boundary (only R-even, unitless scalars publish) and governs bulk evolution via the ε-ledger. Primes mark the inherently anti-mirror steps—handed, forward-moving action on the Möbius strip—that drive the arrow and tier transitions.
The ‘separate’ ideas of <measurement, reflection, observer, symmetry-breaking, qualia> collapse at the boundary (facts), while <primes, chirality, unresolved closure, time’s arrow> organize the bulk (directed ε). Both are the Mirror Law—two faces, one ledger.​​
The questions — plain answers​
What is frame-invariant—and therefore physically real?
The number a boundary reports the same way after the mirror check, once made positive and unit-normalized.
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Why do boundaries/horizons exist, and how do they enforce readout?
They are where equations are forced into reportable numbers; only invariants pass, the rest is ε.
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What is the primitive distinction—the minimal unit of separability?
A pixel: system + mirror partner—just enough to pass the mirror check at a boundary.
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Are quantum “oddities” geometry, not measurement quirks?
Yes: interference lives in the bulk math; counts (the invariant) live at the boundary—hence squaring amplitudes.
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Why are lawful observables quadratic, positive, and unitless at readout?
Because only those forms survive the mirror check and cross-boundary comparison.
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Why is the imaginary unit i required in quantum theory?
It provides a perpendicular direction for amplitudes so the mirror check can separate what flips from what stays.
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Origin of uncertainty and conjugacy?
Two legs of one pixel: extracting one invariant sets a minimum leftover on its partner (an ε floor).
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Why do coherent compositions cap at 1–2–4–8?
Beyond that ladder, mirror closure fails cleanly; coherence leaks into ε instead of yielding stable facts.
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What defines the observer/observed split?
Observer: sets boundary conditions. Observed: what is forced through and reported as invariants.
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Why 3+1 effective spacetime dimensions?
Smallest projection where causality and the mirror check coexist with tolerable defect; higher/lower blow up ε.
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Why is renormalization required; what enforces scale separation?
The boundary accepts only finite, unitless statements; renormalization makes that true.
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Why are fundamental constants “constant”?
They are ratios fixed by admissible structure; drift would signal a boundary/tier change.
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Why does information carry algebra and geometry?
A boundary extracts numbers from algebra on geometry; bits inherit both.
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Gödel/halting in physics?
Basic Rule: A mirror reference frame cannot see itself. As ε regions: places a given boundary cannot decide—signals to change model or boundary.
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Why do theories encode past/future while measurement is only “now”?
Bulk equations run both ways; readout is one-way because it commits to a single invariant. In this model there is no block universe / future. Only <Then/Now> or <Quantum/Classical> as a legal symmetry pair - (Symmetry Pair = H pixel).
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Wavefunction: ontic or epistemic?
Ontic in the bulk (evolves); epistemic at the boundary (only |ψ|² etc. are reported).
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How do space, dimension, and coordinates emerge if not assumed?
By stitching many consistent boundaries; the minimal count that lets stitching work is the effective dimension.
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Why is mathematics so effective in physics?
Physics keeps structures that survive the mirror check—exactly what good math formalizes.
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What makes a law necessary (constraint) rather than a fit?
If breaking it prevents a boundary from reporting a stable invariant, it’s a law, not a curve-fit.
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Is the universe contingent or necessary?
The grammar (mirror check, boundary, 1–2–4–8) is necessary; the story within it is contingent and recorded.|
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​​​Predictions & Tests (scoreboard)​​​​
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Legend:
Aligned= recovers standard results with HFT’s boundary/closure rule.
Reinterpretive= same numerics, clearer organizing principle under HFT.
Speculative = novel prediction with a clean falsifier.
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Recoveries (aligned)
Born readout (|ψ|²)
Where to read: Reflection Mechanics — Part I → Ontology Map → Worked Examples (Schrödinger); also Mirror Admissibility / Admissibility Checklist.
What it establishes: “Facts” at a boundary are even, positive, unit-normalized numbers; the Born norm is the unique admissible closure from complex amplitude (phase stays in the ledger).
How a physicist tests it: Standard counting statistics at detectors. Any model demanding negative or phase-bearing “probabilities” at readout fails admissibility.
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Closed time path (Schwinger–Keldysh) & ThermoField doubling
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Where to read: Reflection Mechanics — Part I → Mirror Admissibility and the Square/Topological Dichotomy.
What it establishes: Observables are swap-even under the branch swap (SK) or tilde swap (TFD); swap-odd components are kept as ε.
How a physicist tests it: Compute branch/tilde components; only the even combinations map to measurable quantities.
GR boundary completion (Einstein–Hilbert + Gibbons–Hawking–York)
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Where to read: Reflection Mechanics — Part I → Worked Examples (EH with boundary).
What it establishes: Well-posed variation requires bulk+boundary pairing even under normal reversal; the boundary term is the closure completion.
How a physicist tests it: Vary EH with a boundary; the missing GHY term shows up as a failure that the completion fixes.
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Area/entropy at the boundary (holography motif)
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Where to read: Reflection Mechanics — Part II → Holography, Entropic Gravity, and the Mirror Law.
What it establishes: Horizon readout is a boundary-even, positive, unitless functional (area/(4Għ)); “facts” live at the boundary.
How a physicist tests it: Use Area/(4Għ) as the admissible scalar; check invariance under normal reversal.
Renormalization as finiteness/ratio admissibility
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Where to read: Mirror Notation v7.x → Scientific Payoff; Mirror-RG (discrete renormalization by tier pairing).
What it establishes: Publishable observables must be finite and unitless; renormalization enforces boundary-admissible statements (ratios). Non-finite or dimensional forms are flagged as ε.
How a physicist tests it: Confirm that only renormalized, dimensionless ratios are compared across experiments; dimensional “observables” are rejected.
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Reversibility (system-only, single pass)
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Where to read: HFT-00.1 Supplement — On the Impossibility of Single-Pass Reversal.
What it establishes: Invertible equations (phi^-t, U(t)^dagger) do not license a single-pass reverse event on the system. Real experiments implement open channels; reversal is a paired protocol (echo), not a solitary pass.
How a physicist tests it: Run a forward protocol on S with uncontrolled environment E, then attempt a single-pass “reverse” on S only. Check three guards:
(1) relative-entropy contraction (data-processing) holds;
(2) mean entropy production >= 0;
(3) Crooks/Jarzynski require a separately defined reversed protocol.
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Observation: No single-pass undo succeeds unless you also control/restore E and the control record (i.e., you’re effectively doing the composite echo).
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Clarifications / Reinterpretive
“Measurement” = boundary closure (no extra postulate)
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Where to read: Reflection Mechanics — Part I → Ontology Map → How to Enter a Law (rubric) and Cold Reader walkthrough; Mirror Notation v7.3 → Using v7.
What it establishes: Measurement is the boundary enforcing admissibility; odd/topological/boundary-only pieces persist as ε (kept, not discarded).
How a physicist tests it: Double-slit—amplitudes interfere in bulk; camera pixels report positive counts only.
Uncertainty as closure cost (pixel trade-off)
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Where to read: Reflection Mechanics — Part I → Mirror Admissibility (square vs topological) and the boundary pixel discussion.
What it establishes: Conjugate legs are two faces of one pixel; extracting one invariant imposes a minimal residual (ε floor) on the partner.
How a physicist tests it: Weak-measurement trade-offs; product bounds persist at readout.
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Constants as ratios (stability = boundary stability)
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Where to read: Mirror Notation v7.3 → ε-Annotated Dynamics; Verified Linter Matrix; Scientific Payoff.
What it establishes: Dimensionless constants are stabilized closures across admissible boundaries; apparent drift implies boundary/tier change.
How a physicist tests it: Long-baseline constancy tests interpreted as boundary stability checks.
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1–2–4–8 coherence ceiling (octonion cap)
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Where to read: Reflection Mechanics — Part II → Tier-7 Closure Forces the Octonions (octonion cap, triality); see also Mirror Notation v7.3 → Duals & Complements.
What it establishes: Coherent compositions that still admit clean closure top out at 8; beyond that, coherence leaks into ε.
How a physicist tests it: Survey stable, finite-energy coherent systems; show whether any require >8 composition algebra (clean falsifier).
Boundary discipline invariance (paired detectors)
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Where to read: Reflection Mechanics — Part I → Admissibility Checklist and Falsifiability Hooks; Mirror Notation v7.3 → Error Checking & Proof Constraints.
What it establishes: Two admissible boundaries probing the same source must agree on the normalized invariant; disagreements indicate mis specification (tier/ε) or a theory fault.
How a physicist tests it: Paired-detector experiments (e.g., different polarization analyzers) with proper normalization must yield the same invariant.
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Speculative but falsifiable
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Cross-boundary invariance stress test
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Where to read: Reflection Mechanics — Part I → Falsifiability Hooks (clean targets); Mirror Notation v7.x → Using v7 (operational framing).
What it asserts: For a fixed system, admissible boundaries must report the same normalized invariant; disagreement is a red card on the assignment or the rule.
How a physicist tests it: Build two admissible readouts with different internals; compare normalized invariants on the same source.
Coherence beyond 8 (no-go)
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Where to read:Reflection Mechanics — Part II → Tier-7 / octonion cap; Mirror Notation v7.x → Duals & Complements.
What it asserts:A reproducible, finite-energy phenomenon that requires composition structure beyond 8 contradicts closure.
How a physicist tests it: Show stable data that cannot be modeled without >8 composition algebra (single counterexample falsifies).
Possible directions (off-board until templates are posted)
ε-pattern templates (e.g., birefringence; parity-odd CMB): keep in reserve unless the explicit ε-tilt fit forms (frequency/sky dependence; twist count by tier) are laid out in the doc—then promote with the fit form and falsifier.
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Admissible boundary (operational sidebar)​
A boundary is any interface that turns equations into numbers (camera pixel, calorimeter, horizon area, readout code). A statement is admissible at that boundary if the reported number is (i) even under the relevant mirror, (ii) positive, (iii) unit-normalized, (iv) unchanged by applying the mirror twice. Anything else is recorded as ε (typed by source: internal conjugacy, causal/handedness, operator-parity) and not thrown away.
Concrete examples: camera counts per pixel; calorimeter energy ratios; horizon area over constants.
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Checker truth table (mnv7 v7.x)
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mnv7.x is an executable referee for mechanistic claims. It accepts only closed invariants at interfaces (even, unitless scalars) and routes all non-closed structure into a typed ε-ledger that must carry dynamics. It detects algebraic habitat mismatches (tiers) and enforces boundary correctness. Use it anywhere a system has mechanism
+ boundary
+ observables.
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• Odd-parity “observable” → FAIL (quarantined as ε^op).
• Dimensional “observable” → FAIL (must reduce to a unitless ratio).​
• Non-finite expression at readout → FAIL (renormalize or restate).
• Normalized, even, positive scalar (R-even under double reflection) → PASS.
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Executable Checker (reproduction kit)
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What it does
Implements the closure rules from Paper 0 – Mirror Notation v7.x: two-pass mirror, unit/scale consistency, tier/handedness legality, R-even extraction, and ε/defect tagging.
Full spec & examples → Technical Papers / Paper 0 – Mirror Notation v7.x
Minimal CLI examples
• Lint a topological density (schematic):
python mnv7.py "(θ/32π²) Tr(F *F)" --tier --blocks --lint
• EH + gauge term: boundary advisory / tier baseline:
python mnv7.py "√(-g) R + (1/4) F_{μν}F^{μν}" --tier --blocks --lint
• SM scaffold with mass diagnostics (e.g., Koide check):
python mnv7.py --sm --masses 0.51099895,105.6583755,1776.86
Readout semantics
PASS: legal closure → even, dimensionless scalar (after normalization).
FAIL: flagged with a defect (unit mismatch, missing boundary term, illegal root, tier leak, parity issue).
ADVISORY: near-closure with a known fix (e.g., add boundary term).
Link to MN7.3 Compiler Paper (python mnv7.py)
https://docs.google.com/document/d/1i0IIEyMdQakPgMf9kOEYMdw2SV3DwFhji82d5RmlAY8/edit?usp=sharing​
Conservation / Global Balance (from Part II)
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Defect tensors per tier: D^Ω (internal conjugacy), D^η (causal; active from Tier-4), D^op (operator-parity).
ε-tilt normalization: combine active defects per tier into εâ‚™.
Global closure (Möbius balance): choose signs σâ‚™ ∈ {±1} such that ∑ σâ‚™ εâ‚™ = 0.
This expresses local asymmetries with exact global compensation, giving concrete targets for where parity/handedness effects should (and shouldn’t) appear.​
Review Policy (how to engage)​
Most useful to reviewers
• Derivation checks against standard formalisms (differential geometry, representation theory, functional methods).
• Counterexamples: laws/setups that pass mainstream checks but fail HFT closure (or vice versa).
• Parameter discipline: places where ε-powers or tier assignments overfit.
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How to cite or respond
Please reference the specific Paper section/line and include a minimal reproducible example (CLI input + expected/actual output).
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Where to send
Submit feedback / request collaboration → Contact, Methodology & Contributions​
Known Issues / Open Questions
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• Mapping certain closures cleanly into standard bundles/categories.
• Tightening ε-power counting to remove residual freedoms.
• Boundary terms: systematic treatment across geometries beyond the canonical EH case.​
Quick Links ​
Back to papers index → Technical Papers
Try guided exploration → Tools: HFT AI
Next → Contact, Methodology & Contributions