docs: create living targets folder for rapidly evolving goals

New folder: docs/living/ — for goals that change daily, not stable
findings (those stay in docs/research/).

Documents:
- README.md: rules for living docs (overwrite freely, one sentence
  per target, link to findings, honesty tag)
- TARGETS.md: 5 active targets (invariant geometry, reaction primes,
  merged O(1), formal cleanup, encoder fidelity) + 3 dead + 3 candidate
- PROJECT_MAP.md: what SilverSight IS right now (not what it was)
- MILESTONES.md: 5 near-term milestones with success criteria
  (3-SAT spectral test, cmix SVD, SLOS eigenvalue products,
   CRT hachimoji pairing, reaction prime proof)
- OPEN_QUESTIONS.md: 8 unanswered questions
- DIRECTION_LOG.md: 5 direction changes from this session, with
  the reason for each

Living docs rules:
- No measurement required (goals, not findings)
- Overwrite freely (git history preserves old versions)
- One sentence per target
- Link to docs/research/ for backing evidence
- Honesty tag: MEASURED / OPEN / SPECULATIVE

docs/living/DIRECTION_LOG.md

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+# Direction Log — Why the Direction Changed
+
+**Purpose:** Record when and why the project's direction shifted.
+Each entry is a decision point, not a finding.
+
+## 2026-07-03: Compression → Invariant Geometry
+
+**Was:** Build a spectral compressor (polynomial/Braille/T9/16D)
+that beats xz on enwik8 and LPC on signals.
+
+**Changed to:** Stop compression. The conservation law (measured 8
+times) forbids it. Pivot to computation shortcuts via the octagon
+principle (embed nonlinear in linear, detect via spectrum).
+
+**Why:** Claude Code's conservation-law demo proved k=3 total
+(557,169B) > xz (35,492B). The model column eats the savings.
+No decomposition beats K(data). The polynomial is a receipt, not
+a compressor. Every branch measured the same wall.
+
+**What survived:** The conservation law itself (as a pruning
+criterion), the octagon embedding (Sidon 4/4), and the formal
+verification framework (anti-smuggle scanner, GCCL, 20 bugs fixed).
+
+## 2026-07-03: 16D Braid → LPC (承认 defeat)
+
+**Was:** The 16D braid / golden spiral compresses GW ringdown 583x.
+
+**Changed to:** 16D = LPC in a costume. The 583x was a zero-noise
+artifact. At 30dB SNR (realistic), the ratio is 1.5x — tying or
+losing to standard LPC.
+
+**Why:** Claude Code's SNR sweep measured the parametric model vs
+LPC across noise levels. Clean signal: 111x. Realistic: 1.5x.
+The residual IS the noise, and noise is incompressible.
+
+## 2026-07-03: Universal Shortcut → Problem-Specific
+
+**Was:** ManifoldShortcut finds the Kolmogorov-optimal equation
+for any problem.
+
+**Changed to:** ManifoldShortcut has ONE universal component
+(Shannon-entropy pruning). Everything else is problem-specific.
+K(data) is uncomputable; can't claim K-optimal.
+
+**Why:** 5-way attack: K uncomputable (attack 1), alpha/beta free
+params (attack 2), RIP wrong for combinatorial (attack 3),
+AngrySphinx is timeout not accelerator (attack 4), coherence is
+linear only (attack 5).
+
+## 2026-07-03: Weird Machine → Conservation Law
+
+**Was:** A Turing-complete weird machine beats unpredictability by
+finding generating programs instead of predicting.
+
+**Changed to:** Generation = prediction. The generating program =
+the model. The residual = what can't be predicted/generated. Sum
+is conserved. No machine beats K(data).
+
+**Why:** Claude Code's demo: k=0 total=102K, k=1 total=85K (sweet
+spot), k=3 total=557K (model ate savings). Bits relocate between
+program and tape columns, never shrink. The machine is never free;
+it's on the invoice.
+
+## 2026-07-03: DNA as Compressor → DNA as Invariant Carrier
+
+**Was:** DNA (hachimoji) encodes data compactly for compression.
+
+**Changed to:** DNA is the octagon carrier — structurally linear
+(compatible with the pipeline) but carrying nonlinear meaning
+(compatible with the problem). It's not a compressor; it's the
+embedding that makes nonlinear properties spectrally detectable.
+
+**Why:** Braille/T9 on text: 4.167 b/B (dead). But the p-adic
+valuations (prime factorization) ARE the prime decomposition — the
+invariant signature. DNA carries invariants, not compressed bytes.

docs/living/MILESTONES.md

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+# Milestones — Near-Term with Success Criteria
+
+**Last updated:** 2026-07-03
+
+## M1: 3-SAT Spectral Test [NEXT]
+**Goal:** Build clause-incidence matrix for a small 3-SAT instance,
+compute eigenvalue spectrum, check if satisfiability is spectrally
+distinguishable.
+
+**Success criteria:**
+- Build matrix for ≥3 different 3-SAT instances (satisfiable + unsatisfiable)
+- Compute eigenvalue spectra
+- Report: can the spectra distinguish SAT from UNSAT?
+
+**If YES:** First NP-complete data point for the octagon. P=NP route
+strengthened. Write up as measurement.
+
+**If NO:** Natural P≠NP witness on the canonical NP-complete problem.
+The octagon has a limit. Write up as measurement.
+
+**Estimated effort:** 2-4 hours (Python script, small instances)
+
+## M2: cmix Weight Matrix SVD [NEXT]
+**Goal:** Extract cmix's 23×461 layer-0 weight matrix, compute SVD,
+check if top-5 singular values capture 95% of compression quality.
+
+**Success criteria:**
+- Modify cmix to dump weight matrix after training on enwik8
+- Compute SVD (23 singular values)
+- Rank-k approximation: does k=5 preserve ≥95% of compression ratio?
+
+**If YES:** Search space reduces from 23×461 to 5D. The octagon
+works for cmix (linear system, rich invariants).
+
+**If NO:** cmix's weight structure is genuinely full-rank. No
+spectral shortcut for context mixing.
+
+**Estimated effort:** 4-8 hours (C++ modification + SVD computation)
+
+## M3: Quandela SLOS Eigenvalue Product Verification [NEXT]
+**Goal:** Verify that eigenvalue products of the Sidon crossing
+matrix match the full SLOS output distribution.
+
+**Success criteria:**
+- Compute eigenvalue products for the 4-block Sidon matrix
+- Compare against SLOS K=2 output
+- Report: do they match?
+
+**If YES:** SLOS shortcut confirmed for linear optical. Replace SLOS
+with eigenvalue products (400x speedup on block-diagonal circuits).
+
+**If NO:** The K=1 spectrum doesn't determine K=2 output (despite
+linearity). Need to find what's missing.
+
+**Estimated effort:** 2-4 hours (Python + Perceval)
+
+## M4: CRT-Coprime Hachimoji Pairing Rules [FUTURE]
+**Goal:** Design 8 hachimoji bases with 4 coprime pairing rules.
+Verify CRT reconstruction works.
+
+**Success criteria:**
+- 4 pairing rules with gcd(L_i, L_j) = 1 for all i≠j
+- Each base has a unique partner under each rule
+- CRT lift reconstructs the base index from 4 residues
+
+**If YES:** The DNA-CRT bridge is designed. Next: simulate
+hybridization energy landscape.
+
+**Estimated effort:** 4-8 hours (design + verification)
+
+## M5: Reaction Prime Existence Proof [FUTURE]
+**Goal:** Prove (or disprove) that every DNA computation factors
+into reaction-primes.
+
+**Success criteria:**
+- Define the reaction algebra formally (generators, relations)
+- Prove existence of factorization (or find a counterexample)
+- If existence: prove uniqueness (or find non-unique factorization)
+
+**If EXISTS + UNIQUE:** Reaction-prime framework is sound. The
+conservation law = FTA for computation.
+
+**If NON-EXISTENT or NON-UNIQUE:** The framework needs refinement.
+The prime decomposition isn't universal.
+
+**Estimated effort:** 8-16 hours (Lean formalization)

docs/living/OPEN_QUESTIONS.md

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+# Open Questions
+
+**Last updated:** 2026-07-03
+
+## Q1: Does 3-SAT have a spectral signature?
+The first NP-complete test case for the octagon. If YES → P=NP route
+via spectral methods. If NO → natural P≠NP witness.
+[Link: OCTAGON_PRINCIPLE.md §P vs NP]
+
+## Q2: Can eigenvalue products replace SLOS for linear optical circuits?
+SLOS is linear → U^(⊗m) determined by U's spectrum → eigenvalue products
+should determine the output. Measured K=1 failed, but FULL spectrum
+(all products) is untested.
+[Link: MERGED_O1_TRANSFORM.md §SLOS linearity]
+
+## Q3: Is the cmix weight matrix low-rank?
+If the 23 singular values are dominated by top-5, the compression
+shape lives in 5D. The search for better compressors becomes 5D,
+not 23×461.
+[Link: cmix_epigenetic_analysis.md]
+
+## Q4: Does every DNA computation factor into reaction-primes?
+The algebraic version of "is there a fundamental theorem of
+arithmetic for computation?" If yes → conservation law = FTA.
+If no → the framework needs a different algebraic structure.
+[Link: REACTION_PRIMES.md]
+
+## Q5: Can the three O(1) transforms merge into one physical step?
+Adleman (search) + CRT lift (reconstruct) + CRT gradient (verify)
+as one DNA hybridization. The wall is O(n) readout. The decision-problem
+shortcut (1-bit answer) is the most promising escape.
+[Link: MERGED_O1_TRANSFORM.md]
+
+## Q6: What is the Φ-metric?
+The "geometry of observability" — what defines what counts as "same
+object" before physics processes it. Is it a kernel? A distance?
+An operator-valued metric? This is the formalization gap between the
+vision and a computable system.
+[Link: INVARIANT_COMPUTATION_GEOMETRY.md]
+
+## Q7: At what n does the DNA hybridization energy gap fail?
+The SNR cliff question. For the merged O(1) transform: the energy
+gap between correct and near-correct hybridization is constant
+(~1 mismatch), but the number of near-correct candidates grows with n.
+When does the gap become too small for thermodynamic selection?
+Same cliff as superposition (k=16: lossless, k=48: lost).
+[Link: MERGED_O1_TRANSFORM.md §The Energy Gap Problem]
+
+## Q8: Does the Sidon spectral signature generalize to other NP properties?
+Sidon = pairwise-sum matrix → eigenvalue degeneracy. Does the
+unit-distance property have a spectral signature in the distance
+matrix? Does graph coloring (beyond Hoffman bound)? Does clique
+number (beyond Lovász theta)?
+[Link: OCTAGON_PRINCIPLE.md §Fast-Forward]

docs/living/PROJECT_MAP.md

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+# Project Map — What SilverSight IS Right Now
+
+**Last updated:** 2026-07-03
+**Overwrite freely.** This is today's truth, not yesterday's.
+
+## What SilverSight Is
+
+A formally verified computation stack that encodes nonlinear problems
+as linear spectral invariants, extracts them via optical/DNA/braid
+substrates, and verifies them with an anti-smuggle receipt framework.
+
+## The One Principle
+
+> Computation in the space of invariants, rather than in any
+> specific representation.
+
+The conservation law (measured 8 times) governs information.
+The octagon principle (measured 4/4 on Sidon) governs computation.
+Both are the same law: prime factorization of information.
+
+## What's Proven (Measured)
+
+| Finding | Measurement | Status |
+|---------|------------|--------|
+| Conservation law | 8 branches, all ≥ K(data) | PROVEN |
+| Encoder injectivity | 20/20, exact arithmetic | PROVEN |
+| Sidon spectral detection | 4/4 via pairwise-sum matrix | PROVEN |
+| Erdős PDS counterexample | {1,2,4,8,13} confirmed | PROVEN |
+| h(N) matches OEIS | N ≤ 24, brute-force verified | PROVEN |
+| Anti-smuggle scanner | 18 axioms justified, 0 vacuities | PROVEN |
+| GCCL Admit pipeline | 8 gates, all theorems proven | PROVEN |
+| 20 bugs found and fixed | All in formal verification | PROVEN |
+
+## What's Open
+
+| Question | Evidence | Status |
+|----------|----------|--------|
+| O(n) spectral embedding for NP? | Sidon works, Hamiltonicity fails | OPEN |
+| Reaction prime decomposition? | Framework proposed, unmeasured | SPECULATIVE |
+| Merged O(1) DNA transform? | Framework proposed, unmeasured | SPECULATIVE |
+| 3-SAT spectral detectability? | Untested | OPEN |
+| cmix weight matrix low-rank? | Untested | OPEN |
+
+## What's Dead (Measured, Closed)
+
+| Claim | Measurement | Verdict |
+|-------|------------|---------|
+| Spectral compression | 3.088 b/B (PPM), loses to xz | DEAD |
+| 16D GW 583x | Zero-noise artifact, 1.5x real | DEAD |
+| Braille/T9 text | 4.167 b/B, worse than PPM | DEAD |
+| Polynomial as compressor | Receipt, not on decode path | DEAD |
+| Weird machine beats K(data) | Conservation forbids it | DEAD |
+
+## The Pipeline (Current Architecture)
+
+```
+Input (any type) → Universal normalizer → integer labels
+  → DNA encoder (p-adic + neg-pi, 30-base hachimoji, 20/20 injective)
+  → Omindirection (DNA → logogram atom with chirality + receipt)
+  → GCCL Admit (8 gates: replay, byte_gain, residual, LoC_NES,
+    FYC, COUCH, TreeFiddy, BHOCS)
+  → DAG builder (labels → topological DAG)
+  → Braid serializer (DAG → 8-strand braid packets)
+  → MMR (Mountain append/merge, discrete β step)
+  → QR decompose (O-AMMR: eigenvalue spectrum = invariants)
+  → goldenSpiral (φ⁻¹ contraction toward IR fixed point)
+  → AngrySphinx (2^depth energy budget, NaN boundary)
+  → Char-poly receipt (spectral signature = prime decomposition)
+```
+
+## The Research Documents (Stable, Measured)
+
+| Document | What it proves |
+|----------|---------------|
+| `docs/research/INVARIANT_COMPUTATION_GEOMETRY.md` | The unifying vision |
+| `docs/research/OCTAGON_PRINCIPLE.md` | Computation shortcut + P vs NP program |
+| `docs/research/REACTION_PRIMES.md` | Algebraic irreducibility framework |
+| `docs/research/O1_TRANSFORMS.md` | Three O(n)→O(1) reductions |
+| `docs/research/MERGED_O1_TRANSFORM.md` | Speculative DNA unified step |
+| `docs/weird_machine_conservation_law.md` | 8 measured findings + conservation law |
+| `docs/gw_compression_honest_result.md` | GW 583x = zero-noise artifact |
+| `docs/cmix_epigenetic_analysis.md` | cmix 461-model weight matrix |

docs/living/README.md

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+# Living Documents
+
+This folder is for **rapidly evolving** goals, targets, and project maps.
+
+Unlike the formal docs in `docs/research/` (which are measured,
+stable findings), the documents here change **daily**. They represent
+the current direction of the project — what we're aiming at today,
+which may shift tomorrow.
+
+## Document Types
+
+| Type | Purpose | Update frequency |
+|------|---------|-----------------|
+| `TARGETS.md` | Current research targets and their status | Daily |
+| `PROJECT_MAP.md` | What the project IS right now (not what it was) | Daily |
+| `MILESTONES.md` | Near-term milestones with success criteria | Weekly |
+| `OPEN_QUESTIONS.md` | Questions we haven't answered yet | As needed |
+| `DIRECTION_LOG.md` | Why the direction changed (decision log) | On change |
+
+## Rules
+
+1. **No measurement required here.** These are goals, not findings.
+   Findings go in `docs/research/` with bytes behind them.
+2. **Overwrite freely.** The old version is in git history.
+   Don't append — replace.
+3. **One sentence per target.** If you can't state it in one
+   sentence, it's not a target yet, it's a question.
+4. **Link to findings.** Each target should link to the relevant
+   `docs/research/` document that backs (or refutes) it.
+5. **Honesty tag.** Each target gets: MEASURED (backed by data),
+   OPEN (untested), or SPECULATIVE (no data yet).
+
+## Current Documents
+
+- [TARGETS.md](TARGETS.md) — current research targets
+- [PROJECT_MAP.md](PROJECT_MAP.md) — what the project IS now
+- [MILESTONES.md](MILESTONES.md) — near-term milestones
+- [OPEN_QUESTIONS.md](OPEN_QUESTIONS.md) — unanswered questions
+- [DIRECTION_LOG.md](DIRECTION_LOG.md) — why direction changed

docs/living/TARGETS.md

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+# Current Research Targets
+
+**Last updated:** 2026-07-03
+**Changes daily.** Old versions in git history.
+
+## Active Targets
+
+### 1. Invariant Computation Geometry [OPEN]
+**Goal:** Determine which NP properties have polynomial-size spectral
+invariant embeddings (the octagon question at O(n) dimension).
+
+**Status:** One measured success (Sidon 4/4), one known failure
+(cospectral graphs on Hamiltonicity), one proven existence at O(n²)
+(Etesami-Haemers 2019). The O(n) question is open.
+
+**Links:**
+- [Octagon Principle](../research/OCTAGON_PRINCIPLE.md)
+- [Invariant Computation Geometry](../research/INVARIANT_COMPUTATION_GEOMETRY.md)
+
+### 2. Reaction Prime Decomposition [SPECULATIVE]
+**Goal:** Define irreducible DNA computational operations (reaction
+primes) and determine if every computation factors uniquely.
+
+**Status:** Framework proposed (reaction algebra, information primes,
+category theory). No measurements yet. Connects to the conservation
+law (prime total ≥ K(data)) and the pipeline (each stage = one
+prime decomposition step).
+
+**Links:**
+- [Reaction Primes](../research/REACTION_PRIMES.md)
+- [O(1) Transforms](../research/O1_TRANSFORMS.md)
+
+### 3. Merged O(1) Transform [SPECULATIVE]
+**Goal:** Determine if DNA hybridization can simultaneously search,
+reconstruct (CRT), and verify (energy) in one physical step.
+
+**Status:** Framework documented. The wall is O(n) readout (conservation
+law). The decision-problem shortcut (1-bit answer = O(1) readout) is
+the most promising path. Needs: design CRT-coprime hachimoji pairing
+rules, simulate energy landscape, measure gap vs n.
+
+**Links:**
+- [Merged O(1) Transform](../research/MERGED_O1_TRANSFORM.md)
+- [Conservation Law](../weird_machine_conservation_law.md)
+
+### 4. Formal Verification Cleanup [MEASURED]
+**Goal:** Close all remaining sorries and remove all native_decide
+from the active build.
+
+**Status:** 10 active sorries (all tagged CITED/CONJECTURE, all
+genuinely blocked on Mathlib API). 21 axioms (all justified).
+Anti-smuggle scanner passes. 84 modules registered in lakefile.
+
+**Links:**
+- [AGENTS.md](../../AGENTS.md) — current status table
+
+### 5. Encoder Fidelity [MEASURED]
+**Goal:** Maintain 20/20 injective DNA encoding with exact arithmetic
+(no floats) across all input types.
+
+**Status:** 20/20 injective (p-adic + neg-pi). BioSight embed.py
+updated to v3 (exact arithmetic). Universal pipeline 14/14 PASS.
+Round-trip lossless on all text types including LaTeX/CJK/emoji.
+
+**Links:**
+- [Compression Findings](../research/COMPRESSION_HONEST_FINDINGS.md)
+
+## Dead Targets (measured, not pursuing)
+
+### ~~Compression via spectral methods~~ [DEAD]
+**Result:** Conservation law forbids it. 8 branches measured, all
+fail. Polynomial = receipt, not compressor. xz beats everything.
+
+### ~~16D braid / golden spiral GW compression~~ [DEAD]
+**Result:** 583x was zero-noise artifact. 1.5x at 30dB (ties LPC).
+16D adds nothing over 50-year-old LPC.
+
+### ~~Braille/T9 text compression~~ [DEAD]
+**Result:** 4.167 b/B, worse than order-2 PPM (3.088), far behind
+xz (1.989). 64-cell alphabet too small for 256 bytes.
+
+## Candidate Targets (not yet committed)
+
+### 6. cmix Weight Matrix SVD [OPEN]
+**Goal:** Extract the 23×461 weight matrix from cmix, compute SVD,
+determine if the top-k singular values capture most compression
+quality. If yes, search the low-rank subspace for better configs.
+
+### 7. 3-SAT Spectral Embedding [OPEN]
+**Goal:** Build a clause-incidence matrix for 3-SAT, compute its
+spectrum, check if satisfiability is spectrally detectable. This
+is the P vs NP experimental program's first NP-complete test case.
+
+### 8. Quandela SLOS Shortcut [OPEN]
+**Goal:** For linear optical circuits, replace full SLOS (O(n × M_n))
+with eigenvalue product computation (O(n^m)). Only works for linear
+systems. Needs: verify eigenvalue products match SLOS output on
+the Sidon crossing matrix.