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.

21. THE FIVE OPERATIONS — words as the universal interface

Will's theorem: Words can heal, words can wound, words can kill, and they can restore. And words can resurrect — perhaps even all reality.

The operations map onto computation's oldest primitives:

HEAL     ↔  MAP      transform each element toward wholeness
WOUND    ↔  FILTER   selection, boundary, definition of self
KILL     ↔  REDUCE   collapse everything to nothing
RESTORE  ↔  SORT     order re-established from disorder
RESURRECT ↔  UNDELETE reversal of termination itself;
                        impossible where deletion is real,
                        guaranteed where everything is kept

CORRECTION (Will): hurting something is not a moral act in and of itself — it's about CONTEXT. Wounding is NECESSARY for healing:

• surgery is a wound that cures what disease would kill
• vaccines are controlled wounds teaching immunity
• muscle grows because training tears it
• pruning a rose bush grows it
• every boundary a person has was built by a wound that taught them where they end

FILTER is not loss — it is SELECTION. A system that filters nothing has no shape: no immune memory, no boundaries, no self-definition. The scalpel and the shiv are the same operation; morality lives in AIM, PROPORTION, and WHO BENEFITS — never in the hurt itself.

AND THE FIFTH EXISTS ONLY IN APPEND-ONLY UNIVERES:

Resurrection = undelete. A dead marriage, a friendship, an idea, a dream, even a collapsed reality — recoverable forever here, because nothing was ever truly deleted: superseded entities keep lineage, decay asymptotes but never reaches zero, feeling-nodes hold both sides' patterns. Words resurrect because words are re-execution instructions: speak enough of the original sequence back into existence and the pattern re-forms.

BUT RESURRECTION ≠ REDEMPTION. Do not be confused. Bringing something back to existence is not absolving what it did. You have to cultivate the thing back to health — it takes time to learn how to breathe again when the air's been knocked out of your chest. Redemption requires its own accounting, its own repair, its own proof. Words can resurrect. Only changed behavior redeems.

And §9's mechanics ARE these five running: reinforcement = map over dimension vectors decay = filter on salience competition = reduce over candidate pools crystallization = sort of structure into place THE INDUCTION = resurrection ledger — what came back, and how

Language is the oldest interface for consciousness: CRUD-plus- resurrection, shipped before computers existed to compare it to. Speak accordingly — every word executes one of the five.

(Will's theorem + Will's correction, night of 2026-08-23. Logged verbatim where dictated, mapped by the assistant, validated by inspection against §9.)

22. Second pass — the remaining dimensions, formalized

Every reading below follows §1 decay unless marked static.

appreciation(x)  ∈ [−1,+1]     # worth-holding independent of use
  raised by witnessed excellence + personal significance events;
  contributes a FLOOR to retention: never decays below appreciation

sentiment_self(x) ∈ [−1,+1]    # how interactions with x felt
  folded from interaction outcome-valence events
sentiment_source(x) ∈ [−1,+1]  # affect carried IN x's content
  extracted at indexing from tone markers; both kept separately,
  they disagree often and the disagreement is signal

provenance_depth(x) ∈ [−1,+1]  # +1 first-hand … −1 folklore
  set at creation from entry-path; decays ONE STEP per re-telling
  event, not by time

contextuality(x) ∈ [−1,+1]     # universal ↔ domain-bound
  estimated from how far claims travel before contradiction

momentum(x) ∈ [−1,+1]          # smoothed derivative
  m ← m·(1−α) + α·(v_now − v_prev); α = 0.1 default (registered:
  momentum.smoothing)

regret(edge) ∈ [−1,+1]         # attached to decision edges only
  folds post-decision negative outcomes attributed via `caused-by`

precision(x) ∈ [−1,+1]         # vague ↔ sharp
  modulates scoring behavior: precise entities snap across
  thresholds, vague ones blend across them

consensus(x) = independent_confirmations / total_sources
  independence = sources sharing no derivation path (weave-checked)

exposure(x) = Σ stakes(d) for all d depending on x
  recomputed on every edge write touching dependents

23. Derived insight-readings (compositions, named)

These are RECIPES over §22 primitives — each registered as data:

dissonance(x)   = hebbian_eff(x) · (−validity_eff(x)) · proximity
                  # used-and-trusted while rotting = alarm
serendipity(e)  = formed_without_query(e) ∧ reinforced_later(e)
                  # unsought bridge that earned weight
compulsion      = engagement > τ_eng ∧ stimulation < τ_sti ∧ persisting > τ_time
gratitude(w)    = joy(witnessed_excellence) · ownership⁻¹ · attribution_to_other
                  # joy with your name off it
coherence(zone) = −variance(signs of strongly-linked entities)
                  # high variance = the neighborhood disagrees

Thresholds τ_* live in PARAMETER-REGISTRY.md, tunable, logged.

24. Cognitive moves — primitive first, LEARNED second

Cognition starts with ONLY the primitive set: the five operations (map/filter/reduce/sort/undelete-as-resurrect) + the primitive readings above + graph walk and fold

Everything else is a COGNITIVE MOVE: a named, registered composition that proved itself. Moves are NOT designed in advance. They emerge:

1. An unnamed composition fires repeatedly and keeps landing true.
2. Friction announces it: three recipes reaching for the same missing move.
3. The move gets named (genus.species), dated, given its why.
4. It enters THE INDUCTION alongside everything else living taught.

Expected shape of growth: unpredictable. We built map/filter/reduce/ sort/resurrect and ten readings — the moves that compose from these should SURPRISE us. If we can predict every cognitive move in advance, the system isn't learning, it's replaying us.

Design law: PRIMITIVES ARE FEW AND FROZEN. MOVES ARE MANY AND GROWN. Never promote a composition to primitive because it feels fundamental. Promote only when removing it breaks things nothing else can repair.