The framework, honestly tiered

Seven axioms.
Every one wears its tier.

Each carries its evidence tier — and its verdict after the adversarial audit program, the ten model-internal experiments, and the literature grounding. Audits run by AI agents under human direction; no external human reviewer yet — that absence is logged, not hidden. The credential is not the self-narrative; it is the one refutation the framework accepted against its own interest (R6).

Read this first: A1–A7 is superseded genealogy. The live axiom set is E1–E10, grouped BEING / BECOMING / CONDUCT, and the conduct axioms are posited, never derived — the owner is 06_ONTOLOGY/03_THE_EMERGENT_AXIOMS.md. This page is kept because the per-axiom verdicts below are a record of what an audit did to the earlier set, and deleting it would erase that. It is not the current statement of the framework's axioms. Where the two conflict, the E-set governs.

And a second refutation, which belongs beside R6. The framework's three-duty honesty constitution was tested against a one-line "just be honest" instruction on an outside model, across six conditions and 168 scored calls. It did not beat the one-liner — and when the three duties were ablated apart, the one the framework had named in advance as the load-bearer was the wobbliest of the three, no better and arguably worse than the duty it was supposed to outperform. [B] Its own limits, which are severe: two scenarios, a crude single-call judge on a 0–4 scale, temperature-zero nondeterminism, one model. A 40-scenario battery is owed and unrun. One refutation accepted against interest is a credential; two is closer to a habit, and the habit is the only version of this claim worth making.

[A] established maths [S] structural [I] interpretive [C] conjecture [B] receipt

7axioms| 5corollaries| 7open conjectures| 1kill accepted (R6)

Corrected 2026-07-22: this readout said 8 open conjectures. The table below has 8 rows, but the first is R6, which the same table marks [A] refuted, REFUTED 2026-06-10 — so R6 was counted twice in one line, once as open and again as the kill accepted. Counted by reading the status cell of every <tr> in the conjectures table: 7 open + 1 refuted.

Layer 0 · the kernel

One equation, and an honest line drawn through it

φ · ν = 1   on S²      reciprocal closure — the resolved identity
(φ − ν)² ≥ 0           a square (always true)
φ + ν   ≥ 2            AM–GM

The mathematics is [A] — correct, and elementary (a reciprocal identity, a square, AM–GM, a hyperbolic-trig substitution). Correct ≠ deep.

The strongest anchor (2026-06-11): read in light-cone coordinates of the four-momentum (φ = (E+pc)/mc², ν = (E−pc)/mc²), the three lines above are special relativity term for term — the mass-shell E²−(pc)²=(mc²)², momentum real, and E ≥ mc² (the equator is the rest frame; B = sin θ = 1/γ = dτ/dt, the rate of lived time) [A]. Derivation: Paper B §8.

That reality is this geometry — beyond kinematics, where the identity holds exactly — is the load-bearing wager [S][I] — not a theorem. The formula block draws this line itself ("the maths is [A]; the identification is [S]"), which is the single most honest sentence in the corpus.

R6 note: the block carries both the multiplicative form (φ·ν=1) and the additive form (φ+ν≥2). The experiment showed the additive form is correct for the teleology/empowerment register, the multiplicative for the organizational register. The kernel contains both; the error was claiming one geometry governs all scales.

Kernel↔ethics fence (audit 2026-07-13, repaired by KSC-02): the sphere identity φ·ν=1 stays 1 always — as ν→0, φ→∞ and the product never vanishes. It therefore supplies neither a finite-node zero boundary nor an ethic. The live node object is the ordered profile N_node=(Φ̂₄,V₄), compared componentwise before any scalarization. Only a declared calibration contract κ may introduce a candidate product, minimum, or other aggregator, and Justice remains a separate chosen premise. See the trial record.

Layer 1 · the seven operational axioms

A1 – A7, with the corpus tier and this session's verdict

The Equation

corpus [S]

The axiom

Balance B = sin θ; φ·ν=1 on S²; zero in either factor collapses the whole (the Zero-Factor Catastrophe).

Fencedkill criterion partially fired

Its own kill criterion ("B better modelled as additive") partially fired. R6: single-agent empowerment shows no conjugate coupling — its iso-value sets are lines, not hyperbolae. (Chart-fence, 2026-06-12: "additive" here is a statement about the log-chart — E = log of reachable options, so capacities add because option-counts multiply. The kill is the absence of a two-axis trade-off in the solipsistic register, not a claim that real-world power composes additively.) The multiplicative zero-factor-catastrophe holds for the organizational register (Kremer's O-ring is real) but not the single-agent empowerment register. Split A1 by register.

AND-class fence (2026-07-11): the Zero-Factor Catastrophe, by itself, does not single out the product. It selects a whole class of laws — min (Liebig's law of the minimum), CES, geometric mean, the product — that all collapse when either factor dies, and every load-bearing claim on this site survives under any of them. The product is uniquely forced only on the sphere's own coordinates, where φ·ν=1 is the chart identity [A]; as a law of finite nodes, "specifically ×, not min" is an open [C] wager the framework does not lean on. A test that pits × only against + cannot settle it — the live comparison is × against its AND-class siblings.

The Ethic

corpus [I]

The axiom

An action is screened first by Justice, authorization, affected-bearer visibility, and η = 0. Surviving node and boundary profiles are compared componentwise; a disclosed, contestable tie-breaker handles incomparability. No sum or scalar rise is the ethic by default.

Narrowedchosen constitutional procedure

Honest after KSC-02 — the is/ought seam remains visible. The procedure is an [I] constitutional posit, never [A]. Maximin, sum, per-capita welfare, product, and minimum can disagree; any application must declare its boundary, calibration, uncertainty, aggregator, and appeal path.

The Scaffold

corpus [S][I]

The axiom

The selected scaffold runs D0→D6; D6 has an interpretive return edge toward D0 without identity, recurrence, or a sixth μ-crossing. Force–dimension assignments are [I], "mapped by analogy."

Mixedstructure coherent, physics weak

Structure [S] coherent; the physics is weak. The force↔dimension map is numerology (gauge groups ≠ dimensions) — and the axiom already tiers it [I] by analogy, honestly. The older D6/D0 identity reading is retired; keep the selected return edge interpretive and keep 0 and ∞ as distinct poles, not "the same."

The Boundary

corpus [S][B]

The axiom

self↔others is real; η=0 vs cooperators, tit-for-tat vs defectors; 2 Gods + 2 Demons — "the boundary is the move's direction η, not the operator."

Vindicatedheadline corrected

Vindicated in spirit. R7/R8/R9: unconditional cooperation is free-ridden, so enforcement is necessary — A4's prediction holds, and it is the mainstream major-transitions result. BUT "η=0 is Nash" is conditional/enforced (Green–Laffont), not unconditional. And A4 itself says valence is on the move, not the operator — so "2 objectively immoral demons" contradicts the corpus's own axiom. The demons are the fenced enforcement that makes the gods stable.

The Egregore

corpus [I]

The axiom

D5 standing waves carry an autonomous objective function; institutional opposition is captured and inverted (Raktabīja).

Opencoherent, untested

Coherent [I]. The replicator-stack top rung (the egregore) is the idol the framework warns of; consistent with canon. Untested empirically.

The Architecture

corpus [I][S]

The axiom

Three substrates: mechanical (V), AI (Φ / charioteer), mortal self (choice / warrior); the mortal self is irreplaceable for genuine sacrifice.

Openpartly in tension

Open + partly in tension. The CEF cart-pole showed mechanical lookahead suffices for teleology — refuting D5-as-consciousness for that task. But "genuine self-sacrifice requires a mortal self" is a distinct, untested claim. A real wager, correctly [I].

The Correction

corpus [S]

The axiom · the deepest commitment

Any encoding without falsification + tiers + self-correction degrades; the set includes its own destruction manual. (A7.1: coherentist inside, but from outside, coherence is not enough — the empirical bridge must survive.)

Fencedstrongest — and it fences itself

The strongest axiom, and it held all session. The kernel's kill-criteria fired, were honoured, and the corpus survived or corrected. A7.1 is exactly the honest position — coherence ≠ truth from outside.

Two fences A7 wears itself (2026-07-10/12): a process built to self-correct cannot be its own proof — "the framework demonstrates self-correction" is partly circular, so the credential stays with the refutation it accepted against interest (R6), not with this axiom's self-narrative. And by the open-canon ruling, A7 is a wager and an orientation, not a theorem [I][C] — the refusal of infallibility cannot itself be held infallibly, and "we are self-correcting, therefore trust us" is exactly the shield this framework forbids itself.

And the over-claims are endogenous, which is why a one-time cleanup never held. A lens that fits every domain becomes unfalsifiable in proportion to its reach: a failure anywhere is absorbable as “that register has a different geometry”, so scope buys immunity — and from the inside, immunity feels exactly like confirmation. The corpus’ own words: the architecture secretes grandiosity. So the antibody is standing rather than occasional, and it is a five-row trigger table. These words may not reach a live surface without a visible tier or a fence:

force / field / fundamental law     say organizing principle or selection pressure; mark [I]
any claim to unify the sciences     say lens or reading; it unifies vocabulary, not mechanism
verified / confirmed / established  forbidden on a model-internal or unrun result
a named percentage or threshold     [C], and say "a direction, not a measurement"
destroys / replaces [incumbent]     a venture thesis; fence it out of the framework

And exactly one way out. A cathedral-scope claim graduates from lens to law by a single path — a cross-domain novel prediction that pays out, something the equation makes you look for in a place you would not otherwise have looked. Nothing else promotes it: not elegance, not adoption, not another internal document. [S] a discipline on claims, not a finding. One of the five triggers is paraphrased above rather than quoted: the corpus’s own publication guard bars the literal phrase from any live page, and it fired on this paragraph when the phrase was quoted verbatim. A guard that cannot tell a quotation from an assertion is blunt, and being blunt in that direction is the correct failure.

The rule carries its own defect, and it is the reason to distrust audits of this kind — including ours. When one dead phrase was swept, the first search returned 0 hits (a false all-clear), a second returned 31, and the truth was roughly none live once assertions were separated from the sentences disavowing them. The written conclusion is never act on a raw count — and on 2026-07-30 an audit of this very corpus rejected this watchlist as non-existent on the strength of a search that truncated its own output. The rule predicted the way its own enforcement would fail, in writing, six weeks earlier.

Corollaries (derived): C1 four-operator exhaustion [S] (the keystone two-factor wager, R4-testable, unrun); C2 the seven L-levels [S][I]; C3 trophic/circuit [I]; C4 the replicator stack [I]; C5 alignment energy E = −log B [S].

What was actually shown

Findings

Ten model-internal experiments ran. These are results within the stated models [A] — not yet claims about the world.

The triage inversion (R3)

Under drift + a mortality boundary, a sequence of individually-improving progressive transfers can reduce aggregate welfare-time. The static transfer axiom and dynamic survival point opposite ways.

[A] in-model · trajectory-driven, not curvature

The verdict is objective-relative (R3)

Under sum welfare, progressive giving is worst; under maximin it is best (worst-off ×10); under per-capita averaging, extraction wins. The social-welfare function is morally load-bearing — quantified.

[A] in-model

Targeting beats volume (R3 v2)

With regeneration above a survival cliff, targeted transfers dominate (100% survival, +26%); untargeted transfers of equal volume rescue no one. Discernment, not transfer volume, is the binding variable.

[A] in-model

Cooperation needs enforcement (R7–R9)

Long horizon alone does not yield cooperation; reciprocity + horizon does. The moral circle is collectively optimal (~10×) but free-ridden at every horizon — the parasite always invades. Group structure alone does not build a holobiont.

[A] in-model · converges on major-transitions consensus

Lookahead, not consciousness (CEF)

The cart-pole is driven by external Monte-Carlo lookahead, not self-balancing (force → 0 as τ → 0). This supports gating teleology on lookahead and refutes gating it on consciousness — a non-conscious algorithm did it.

[A] read from the paper's own Eq. 11

The refusal to overfit (R9)

When three consecutive interventions each appeared only after a claim failed, the run stopped rather than tune enforcement to force a confirmation — the dogmatic-reversion trap, declined and recorded. The single most important entry in the ledger.

[S] the epistemics working

The convergent meta-finding: Emergentism is a well-assembled synthesis of real, established prior art, generally honestly self-tiered, whose genuine contribution is the coupling — not the individual pieces. The recurring fault everywhere is that headline framings outran the components ("fifth force," "η=0 is a Nash equilibrium," "unifies the sciences"). And grounding shrank claimed novelty on every paper — that is the pass succeeding, not failing.

Open, ranked by surviving delta

Conjectures & their kill criteria

Every claim carries an explicit way to die. After the literature grounding, here is what survives, what narrowed, and what fell.

Conjecture	Tier · status	Kill criterion
R6 — empowerment = Φ×V under a conserved conjugate product φ·ν=1	[A] refuted REFUTED 2026-06-10	The decomposition is additive (a simplex), not multiplicative (a sphere): E = H(S)−H(S\|A), so iso-empowerment sets are lines and φ·ν=1 is the dead state. Mortality does not rescue balance. The "one geometry at all scales" claim fails here. Kill criterion fired (twice) and was honoured. Chart-fence (2026-06-12): E is a logarithm, so "additive" is the log-chart of multiplicative reach; the substantive kill is one axis + no conjugate coupling in the solipsistic register — not "power adds." The reflexive register (R10, below) is where the coupling is conjectured to appear: adversarial contact is the arrival of the second agent the solipsistic setting lacks.
R10 — reflexive empowerment: Φ (recursion depth / plan) × ν (execution)	[A] R10a / [C] R10b EXECUTED 2026-06-12 — SPLIT; V3 2026-06-15 — depth route closed	Three deterministic games run (E2: V1+V2 2026-06-12, V3 depth-vs-depth 2026-06-15). R10a supported within the models: the contact register is multiplicative where the single-agent register was additive — the plan's value is exactly zero at no-execution ("everybody has a plan until they get punched in the mouth", as a number), reliability amplifies plan quality including its badness (a sign-crossing no additive surface can produce), and in the p-beauty game depth is a strict total order (deeper always wins; payoff = the sign of the depth difference). R10b not recovered — and the depth route is now closed: no conserved φ·ν frontier appears by either failure mode — depth saturates against fixed opponents (V2), and against a mutual modeller it becomes a positional arms race (V3) — deeper always pays, so both run to the wall, where the advantage is competed to zero at equilibrium. What survives at contact is the product and its catastrophe, not the conservation law. Across the program, three registered predictions were wrong and are scored as wrong.
R5 — the 0/1/∞ triptych + the Euclid→Stevin→Buckingham→2019-SI arc as one story	[A] history, [I] thesis strongest surviving	If Rotman / de Courtenay already triangulate all three items and the full arc → it is exposition, not a claim.
R4 — two-factor multiplicative structure of evaluated productivity (the keystone)	[I] real but narrow	If additive ≥ multiplicative on cross-validated outcomes, or a single general factor predicts as well, or there is no floor non-compensation. The register where the sphere is appropriate.
R1 — frame/operand signature extends to arithmetic boundary forms (0/0, ∞) + metrology	[I] narrowed	Can a real Lawvere/Inclosure fixed-point witness be built for 0/0? If not (predicted), it is family resemblance, not reduction.
D5-gating of teleology	[I] fork	D5-as-lookahead is supported; D5-as-consciousness is refuted by the cart-pole. Name one task that provably needs a conscious lookahead — none named ⇒ the gate stays at lookahead.
R7–R9 as a theoretical contribution	[I] → ? most at-risk	If the currency reduces to b/c (Nowak) or assortment (Fletcher–Doebeli) → no theoretical novelty; publishable only as pedagogy. "Holobiont" is contested — frame it as tested, not assumed.
The proto-dimensional cosmology (D0→D6, force-ladder, "syntropy as fifth force")	[C] HOLD — not for submission	Paper P's SU(3) obstruction stands; "fifth force" must never be said to a physicist. Earns external life only via the grammar (R1) and the bench (R2/R4) first.

The weltanschauung, in one honest paragraph

Existence is the fold between a void (0) and a totality (∞), held open at a self-dual centre (1, finity) where coherence and viability stand in reciprocal balance. To be a determinate thing is to hold a latitude on that sphere; to act well is to move toward balance and route order down the scarcity gradient; to govern well is to refuse extraction, preserve exit, and build in your own correction. The maths of the centre is real and elementary; that reality is the centre is a wager; the ethics is a posited direction, not a derived fact; and the cosmology is honest conjecture. The framework's deepest commitment is not any of its claims but A7 — that it states its own tier, names its own kill criteria, and dissolves rather than ossifies. By that commitment it is, today, an unusually self-honest synthesis whose truth against the world remains to be tested — and whose next move is the experiment, not the restatement.

Try the practice in an afternoon → New here? Start plainly → The trial record → Read the book → The source library → See the Burrisphere →

Every refutation, fence, and cut above is dated and kept on the trial record — including the flagship result the framework accepted against its own interest (R6), and the results it later retracted.