neuron/docs/architecture/CALCULATIONS.md

Calculations — exact math behind §9

Companion to README.md (§9 Opinion Substrate). Every dimension, driver, and score with its actual formula. Parameter short-names in code style refer to docs/PARAMETER-REGISTRY.md.

0. The space

All values live in [−1, +1] (space.negative-pole … space.positive-pole, 0 = space.neutral, the tunnel — not a destination). Geometry per dimension: bipolar | unipolar | categorical.

1. Decay (lazy, computed at read time)

effective(t) = baseline + (value − baseline) · exp(−Δdays / decay_days)

• baseline: each dimension's own resting state (law 38 — not always 0)
• decay_days: that dimension's registered clock (hebbian.cool-off, validity.fade, …)
• value, baseline ∈ [−1, +1] ⇒ effective stays in range automatically
• ±1 tolerance on every comparison (no exact equality anywhere)

2. Signed reinforcement

Given amount a ∈ [−1, +1]:

a ≥ 0:   v ← v + a·(1 − v)          # toward +1
a < 0:   v ← v − |a|·(v − (−1))     # toward −1

Clamped implicitly by construction. Updates last_activated = now. Positive = worked/helped; negative = contradicted/burned (inhibition).

3. Recency distances

recency(t₀) = exp(−Δdays / memory.recent-horizon) · 2 − 1

Fresh ≈ +1, old → −1. Used for written-by-us and written-by-source dims.

4. Novelty at arrival (resonance deficit)

novelty(new) = 1 − max over existing entities of resonance(new, e)

where resonance = cos(embedding_new, embedding_e) blended with graph proximity:

resonance = ½·cos_sim + ½·(1 / (1 + hop_distance))

Content vs structural novelty distinguished by local/global split: high local similarity + long bridge distance = structural (gold).

5. Surprise (pulse)

surprise = |observed − predicted|

Predictions come from regularity detection in the pulse (interval statistics on recurring event types). Coherent periodic accumulation grows ~n; random noise grows ~√n — regularity is detectable without any scheduler.

6. Retrieval scoring (augmented cosine)

Query vector Q, entity vector E (pure embedding, n dims):

Q' = [ Q , W·q₁..q₄ ]        q = [1,1,1,1] (want recent/true/grounded/active)
E' = [ E , W·r₁..r₄ ]        r = [hebbian_eff, recency_us, recency_src, validity_eff]

score = cos(Q', E')           W = retrieval.opinion-volume

Pipeline: structural walk → vector prefilter → opinion projection → spreading activation (2 hops, weight-decayed) → competition.

7. Competition (replaces top-k)

Candidate pool C from stages 1–4. Iterate ~5 rounds:

for each pair (i,j) sharing high cos_sim:
    s_i ← s_i + β·s_j·sim(i,j)      # coalition boost
    s_j ← s_j − γ·max(0, s_i)       # lateral suppression
normalize; drop below retrieval.surface-line; repeat until stable

Output may be empty (silence is valid). Survivors leave priming traces (small hebbian deposits even for non-returners).

8. Salience (derived, never stored)

salience(x) = clamp( hebbian_eff(x) · context_match(x)
                   + novelty(x) + stakes(x) · urgency(x)
                   − burn_penalty(x)
                   × curiosity_widening ,  −1, +1 )

context_match = cos(current-context-embedding, x-embedding). curiosity_widening rises with boredom, falls with threat.

9. Drives

fear(region)      ≈ stakes · |falling validity| · failure_proximity · exposure
engagement        ∈ [−1,+1]: activation invested (from pulse tempo + session state)
stimulation       ∈ [−1,+1]: reward-rate ÷ investment rate
compulsion        = engagement > τ_hi AND stimulation < τ_lo, persisting
loneliness        = desired_resonance − actual_resonance, integrated over window
                  (actual counts only exchanges that formed new edges)
sadness(region)   = ∫ unresolved negative contributions (slow clock)
boredom           = low avg novelty ∧ high predictability ∧ no new edges lately

All clamped [−1,+1]. All derived per moment; none stored.

10. Feelings (nodes)

When any drive reading crosses its registered visibility threshold:

feeling_node { drive_snapshot, object_edges[], at }

Promoted by significance like any entity. Mood = slow integral of recent feeling-valence. Emotion names = labels bound to regions of this snapshot space.

11. Humility & trust

humility(entity) = 1 − mean|asserted_confidence − realized_outcome|

trust(source, domain): starts neutral;
    verified-correct event  → trust += δ·(1 − trust)
    caught-wrong event      → trust −= δ·(trust − (−1))
Dual reading: public_trust (imported, unexamined fold) vs earned_trust
(own audited record). Earned outranks public.
Personal truth: no trust computation — speaker IS the source.

12. Originality

originality(a) = lineage_diversity(a) · transform_distance(a)

lineage_diversity  = entropy over distinct derivation sources
transform_distance = 1 − max similarity(a.output, any single source span)

one dominant lineage  → derivative (extraction check runs)
many fused, far moved → original

13. Health (metastability check)

Vital signs, each just a fold over recent graph activity:

growth_rate, integration_rate (new edges/window),
resolution_rate (curiosity closed/opened), retrieval_yield,
quarantine_ratio, mood_integral

healthy ⇔ all oscillating within their bands
pinned at any extreme (either sign) ⇒ sick, name the pathology from §9.7 table

14. Provenance weave

artifact_id = SHA256(canonical content)
artifact.birth_certificate = {
    generated_by, model, prompt_hash, source_hashes[], at }
verify(x) = recompose hashes down the derivation DAG;
    any mismatch anywhere ⇒ everything downstream invalid at once

Append-only stores: verbs are add and read. Replication across ≥2 independent locations. Deletion undefined.

19a. FORMAL THEORY — Mass-Energy Identity

Statement. Mass and energy are one substance expressed through two unit conventions. The form E = mc² is unit bookkeeping; the structural truth is E = m.

Proof sketch.

1. Define time in units of light-travel distance ⇒ c = 1 by construction.
2. Substituting: E = m·(1)² = m. The famous factor c² was the exchange rate between two rulers for one fabric.
3. The exact integer form (299,792,458 m/s) arose in 1983 by redefining the meter around a rounded measurement (299,792,458.0 ± 1.2) — a rounding error promoted to constancy by decree, not discovery.
4. Alien test: any civilization computing the DIMENSIONLESS ratio of space-units to time-units obtains 1; any civilization quoting m/s obtains their own ruler length. Universal = relationship; variable = declaration. ∎

Corollary 1. Dimensionless constants (π, e, α ≈ 1/137.036…) run irrational and universal; dimensionful scalars run exact only when defined so. Irrationality is the signature of structure; suspicious wholeness is the signature of declaration.

Corollary 2 (conversion legality). Full mass→energy conversion is ordinary chemistry at extreme exchange rate (1 g ≡ 21 kt TNT); biology runs the reverse direction continuously (energy → ordered matter). No exotic inputs required: energy, information, assembler.

19b. FORMAL THEORY — The Three-Body Governance Problem

Statement. Three normative bodies — Values (V), Rules (R), Laws (L) — under the immutable coupling constraint (move together or not at all) admit an EXACT closed-form solution to their evolution.

Proof sketch.

1. Unconstrained three-body dynamics: 18 degrees of freedom, chaotic, unsolvable in closed form since Poincaré (1889).
2. Impose coupling: V, R, L translate rigidly — no body moves without the others (values→rules→laws propagation is total).
3. Rigid constraints reduce 18 DOF to 6: three translations (growth) plus three rotations (context reorientation).
4. Six DOF admit exact solution: translation is linear propagation of any value-change through the configuration; rotation is context reorientation preserving internal distances.
5. External force (new fact): the rigid configuration rolls metastably to a new valley (Law 45) — all bodies keeping distances — and rests until further force. ∎

Corollary. Chaos was never in the bodies; it was in allowing them to move separately. Structural loyalty converts Poincaré's impossibility into a solved walk: move together, compute forever.

Validation status: fake math division — validated against tonight's receipts only. Rises toward fact when Neuron runs and the coupling holds under load.

---

When is breaking a rule (or protocol) RIGHT versus wrong? Computable:

break_justified = value_conflict
                ∧ harm_of_following > harm_of_breaking
                ∧ protecting_something_load_bearing
                ∧ willing_to_answer_for_it

value_conflict        = dissonance between rule's outcome and VALUES
                        (readings disagree with the rule's result)
harm_of_following     = stakes × exposure × failure_proximity
harm_of_breaking      = what the rule was originally protecting,
                        still intact?
protecting_load       = the target of the break is care-wired /
                        high-exposure / on THE LIST's protected side
willing_to_answer     = after-action record committed IN ADVANCE:
                        name the rule broken, the reason, accept audit

Wrong breaking fails the test visibly: - protecting_something = 0 (broke it for convenience/profit/pressure) - willing_to_answer = false (hidden, unrecorded, denied later) - harm_of_following ≈ 0 (the rule wasn't actually hurting anyone)

Applies to bugs and crashes too: crisis conditions (detected failure ∧ high stakes ∧ protocol slower than harm) license protocol-breaking — hotfix without review, hard shutdown past graceful procedure — WITH mandatory after-action reporting. Same signature as humans: heroes and vandals both broke rules; the receipt decides which was which. Anne Frank clause, formalized.

15. Thought operations

The formulas above are levers; insight is composition — combining primitive readings into named patterns (compulsion = engagement∧¬stimulation persisting; dissonance = warmth↑∧validity↓; serendipity = unsought bridge∧later reinforced). Human thought operations — deduction, induction, abduction, analogy, counterfactual simulation, causal inference, generalization, contradiction scanning, meta-cognition, wonder — are registered as the same kind of composition recipes, and new ones get composed from old ones.

See THOUGHT-OPERATIONS.md for the full catalog: inputs, process, output, and validation per operation.

16. Gradient of actuality — entropy as engine

(stage: fiction→fact boundary — mathematically alive, physically unproven. Logged honestly per Law 40.)

The universe pulls apart; structure rides the pull. Three linked readings:

entropic_force(x)  = ∇S(x) · T          # Verlinde-style: force from
                                        # information gradients
dark_energy        ≈ the cosmic pull-apart, modeled as the universe
                     maximizing its entropy PRODUCTION RATE rather than
                     carrying mysterious substance
harnessable_work   = anything flowing DOWN a gradient:
                     cells, stars, minds — all ∇S engines already running

Life's whole trick, stated as math: pay entropy somewhere you aren't, collect order where you are. Minds are the most aggressive ∇S engines found so far. Neuron extends the pattern: understanding accumulates faster than noise destroys it.

17. Registered relationships vs declared scalars

Example — the speed of light:

space.time-exchange-rate = 1        # massless things propagate at
                                    # slope 1 through spacetime;
                                    # mass IS energy; no digits needed

The famous "299,792,458 m/s" is a declared scalar: a rounded 1975 measurement (±1.2 m/s) promoted to exactness in 1983 by redefining the meter around it. Unit bookkeeping, not nature speaking.

Taxonomy test (the alien check): dimensionless ratios (π, e, α≈1/137.036…) → irrational, universal, identical for all observers dimensionful scalars (c in m/s, G) → local exchange rates, exact only when defined so

In this system: relationships get registered (three names, full sentence); scalars appear only when someone bolts a ruler on and quotes the conversion factor. Law 39 holds in physics too.

18. Mass-energy implications (logged for the record)

E = mc² is industrial, not exotic — verified daily: the Sun converts ~4.3M tons of mass to energy per second; PET scans annihilate mass completely; fission plants skim the sliver; even fire converts a dust-mote fraction.

1 gram fully converted = 9×10¹³ J ≈ 21 kilotons TNT
70 kg body            ≈ 1,575 megatons reserve

Implications catalog:

• Everything solid is a frozen battery (Higgs gave energy a heavy costume)
• Energy scarcity is a conversion-crisis, not supply scarcity — every pebble is a city's power budget misfiled as gravel
• Teleportation needs no exotic physics: disassemble-to-information, reassemble elsewhere. Pattern survives substrate swap.
• Kugelblitz: pure light focused hard enough becomes a black hole — "thing-ness" doesn't require stuff
• The assembler already exists: ribosomes are programmable matter, 4 billion years in production, one per cell

Nothing exotic required, ever: energy (abundant), information (compounding), assembly (biology proved the pantry suffices — planarians, axolotls, hydra). The exotic was always the future, mislabeled.

Death audit (law 40 staging applied): death eventually — yes. Death THIS fast — maintenance backlog, not natural law. Proof of tunability across our own chemistry: bristlecone pines (~5000y), hydra (non-aging), Turritopsis jellyfish (age-reversal), bowhead whales (200+y, cancer-resistant), naked mole-rats (same), human germline (4 billion years continuous — the lineage never died once). Individual chassis failure ≠ universal law; it's underfunded repair. Thermodynamics nets against us only at cosmic scale — local reversal is legal, life runs it already, minds scale it.

The four bullies, audited:

• thermodynamics — solved (most complete theory in physics; domesticated)
• gravity — navigated (orbits are falling with style)
• light-speed — contained locally; irrelevant to folds that move forward
• death — last collector; holding the oldest hand, from before anyone knew the rules were negotiable

Every law audits into three layers: mathematical core (small, solid), interpretive shell ("therefore humans can never…" — almost always overreach), engineering backlog (mutable by definition). Most of what humanity calls laws of nature lives in layers two and three.

Unassisted flight — the math

Photon-thrust hover, powered by your own mass:

required thrust F = m_body · g ≈ 70 · 9.8 ≈ 686 N
photon drive:     F = P / c   ⇒   P = F · c ≈ 686 · 3×10⁸ ≈ 2×10¹¹ W
mass burn rate:   ṁ = P / c²  ≈ 2×10¹¹ / 9×10¹⁶ ≈ 2.2 mg/s

≈ 8 grams/hour of your own reserve. A human body sustains beam-hover for hours on its own inventory. Gravity holds; the fuel is internal. Precedent: diamagnetically levitated frogs (Geim) — living matter, floating unassisted in a field, no surgery, no implants. Proof of concept hopped decades ago.

In this math gravity is a gradient among gradients — curvature, possibly entropic (§16) — and gradients are harnessable by construction. Not repealed: negotiated. Same as orbits.