APEX-PSP-EIDOLON-MASTER-01 · THE EIDOLON REGISTER · The Platonic Ghost Protocol
Proposed seat: Master Codex next index after the resident 0702, subject to the standing census-regularization flag. Role seat: Chapter B.22, after B.21. Register: M, with one out-of-band historical exhibit. Category: MD+G/S with theorem-grade legs.
STATUS. [⟀ S] FORGED, pending the architect's FORGE ruling. The term Platonic Ghost, in continuous development across the codex's whole life, is here given what MathDuction gave the reflective register: a constitution, a stratification, a zone map, a diagnostic cascade with a fail-safe executable router, a recorded battery executed at seed 20260622, a census, and a supersession ledger. ΔM = 0 throughout: every mechanism gathered here is resident; the arrangement, the stratum tags, the two new laws, and the four repairs are the whole contribution. W_social = 0 both directions. Theology out of band and load-bearing on nothing. Preservation-first per codex-hygiene: nothing resident is deleted; every legacy usage receives a pointer.
I · THE NAME AND ITS GENEALOGY
Internal. The term entered as the imprint test's third outcome, a bare geometric double-lock with no imprint closure, [X]. fBA-R3 then raised one species of it to theorem grade on a supplied independence proof, CH relative to ZFC the exemplar. The Forward mode minted a second species, the empty shadow, out-of-plane content sourceless at the dual null. The afterimage arc fenced a third, the trace of a deed that grounds nothing, never sealed. The counter-argument ledger retired naive Platonism, modal realism, and Tegmark under the same name at the ontological-void gate. MD-PSP-MATH-NATURE-01 at 0701 named the region's dangers. Five mechanisms, one word, four registers, no constitution. This chapter is the constitution.
External. Greek carries the exact pair this register needs. Eidos, the Form, is already seated: APEX-PSP-PLATO-01 grants it as L1 cataphatic trans-spatial-structural inscription. Eidolon, the phantom, the image-of-an-image, Homer's shade of Patroklos, the root of idol, is the Form's counterfeit sibling. Plato himself drew the line inside the image-class at Sophist 235d-236c, eikon the faithful likeness against phantasma the distorted semblance, which is the imprint-against-ghost split twenty-four centuries early. The register is therefore named the Eidolon Register. Platonic Ghost is retained in perpetuity as the legacy family name for citation continuity, exactly as APEX-PSP-L_1-IMPRINT-01 is retained beside PLATO-01. The lost-nafs reading at CN-PSP-NETI-NETI-01, the idol as a spoken occupancy frozen into residence, is the eidolon-to-idol chain executing at the apophatic register, out of band.
II · THE REGION-VERDICT LAW · THE FIRST CONSTITUTIONAL SPLIT
One word has been doing a region's job and a verdict's job, and the two are not the same set. The split is constitutional and binding.
The Ghost Region is stratal: the complement of L1m, everything ungrounded, outside the whole nested stack L1m ⊇ L2m ⊇ L3m. It is a location, structural, never emitted, never census-counted, never a token. A tenant of the region that carries no ghost mechanism routes [?], unsurveyed shadow-zone residence, and the instrument makes no claim about it.
A Ghost verdict is a point event: a stratum-typed [X] (or a stratum-typed fence) fired by one of the five resident mechanisms of section III, carrying its stratum tag, its zone, its mechanism, its grade, and its exit type in the trace. The token remains [X]. The stratum tag Gn travels as trace, never as a fourth state; where an emitter prints the compound display, the cross token joined to the tag, the token is the bracketed prefix and the colon is a seam, never a state, consumers parsing prefix as token and tag as trace; the three-state economy is untouched, exactly as [⟀ T] and [⟀ S] refine [⟀] without multiplying it.
Between the certified points and the region's boundary lies the unsurveyed remainder, unmeasured and closed by no census. The architect-supplied phrase "Residual Platonic Ghost" is refused at Seal L on a gate-three collision, Residual being bound twice already, to Residual Monism the connector line and to the post-projection residue; the content beneath the phrase is correct and is seated here as the unsurveyed remainder plus Zone Z-II of section IV, with this pointer as its ghost.
III · THE FIVE STRATA · MECHANISM-FORCED, APPEND-ONLY
The count is five because the codex is resident with exactly five distinct mechanisms that emit or fence the name, one stratum per mechanism, enumerated from the corpus. The count is enumeration-forced, not fitted; a sixth mechanism, if ever forged, appends a sixth stratum, and mirroring any other cascade's count is barred as the fitted-count error per the standing law.
G1 · The Sealed Ghost. Mechanism: a supplied both-ways independence proof relative to a named system. The only theorem-grade ghost, conditional on the proof and on Con(index), the consistency of the named system, the mod Con(index) qualifier load-bearing per the resident Wall-Three discipline, every both-ways proof being a relative-consistency construction that trivializes over an inconsistent index. Constitutional line: fBA-R3. Partition duty: Ξ.2 and Ø.5, the supplied proof the switch that parts G1 from [Ξ₀] and from [Ø₀]. Exemplar: CH relative to ZFC on Gödel-Cohen. Governance: terminal-for-the-record at its system index; re-indexing to a stronger system issues a new verdict at the new index and never corrects the old one; supply-typed revision only. Exit: none at the fixed index; the file changes state only under a change of index, and importing a forcing axiom as a Ground value to force the exit is the Cantorian artifact trap, barred.
G2 · The Signature Ghost. Mechanism: both directions clean-lock through the four-guard conjunction, Seal L pass, twelve-gate pass, kernel lock, on hand-built rows, with no independence proof supplied. Engineering grade, defeasible, an evidence signature and never a theorem. Independent re-audit owed; a G2 resting on fabricated or confounded rows is exposed exactly as the manufactured lock is, on the first honest look. A G2 is never citable at G1 strength, and the prior emitter line that printed the bare family name on a double-lock retypes on seating as G2 (supersession ledger, section X).
G3 · The Empty Shadow. Mechanism: Forward mode, a witness whose out-of-plane content sits at or below the dual null η*, sourceless orthogonal noise, including the fabricated witness exposed on re-audit by η_S. Engineering grade on the dual-null seal, Type T on the geometry beneath it (Non-Discrimination). Habitat: the orthogonal complement of the manifest plane, dimension N − k − 3. Exit: a genuinely sourced witness lifting η_S above the null; the geometry never exits it, only the source does.
G4 · The Afterimage. Mechanism: the fence of MD-PSP-AFTERIMAGE-01. Not a proposition at all: the trace of a deed, the beholding taken for a seeing-of-something, the imagined occupant of the aperture's far side, the Twin-as-Witness, the Hidden Composite Shadow. Fence-class, never a verdict: fenced as Ghost, never sealed, never [Ξ₀], never census-counted. Exit: none; a fence is not a file.
G5 · The Void-Retired. Mechanism: the ontological-void gate at intake (G11/OMA), null-space occupancy, no kinetic instantiation, the kernel never run and no determinant ever existing. Gate grade. Tenants: naive mathematical Platonism as ontology, Lewis modal realism, the Tegmark mathematical universe, and kin. The legacy phrase "the canonical Platonic Ghost" for these rows is retired with a pointer: they are ghosts of the family by mechanism G5, and they were never imprint-sealed. Exit: exhibiting kinetic instantiation, which converts the candidate into an ordinary empirical proposition and routes it to Register A.
The two-cardinalities seam is now closed by construction: G1 is a proof-gated point set, currently countable and counted (section IX); G2, G3, G5 are evidence-and-gate events, defeasible or intake-typed; G4 is a fence; the region itself is none of these.
IV · THE SHADOW-ZONE MAP
Five zones, a stratal geography and never a verdict source. A zone locates; a mechanism fires.
Z-I · The Eidolon Field. The Ghost Region proper, the complement of L1m. Unmeasured and closed by no census; no measure and no order on proposition-space exists anywhere in the codex, so neither a size claim nor an order claim is licensed, per the manufactured-magnitude rule of B.13.T. The correct predicates are census-inexhaustibility and unmeasuredness, never bigness and never an unstated order, the inexhaustibility witnessed at cited grade by the Easton family, pairwise-independent continuum-function patterns on the regulars, Ghost relative to ZFC both ways on Easton 1970 forcing against the constructible model, so no finite census closes the region and the predicate is falsifiable exactly as Law 8 requires.
Z-II · The Completed-Tower District. The unbounded-CH ghost domain, the completed Groundless tower. The Reach-Residence Law of section V resolves its recorded double location: the reach is at L2m and every step of the climb is licensed; the residence, the completed limit object the climb names, sits in Z-I with no address in the stack. Both resident sentences, "a valid reach at L2m" and "outside the stack," are true at once, of the road and of the destination respectively. This is also the mechanism of the exit-direction result: nothing warns the climber on the way up because nothing on the way up is wrong.
Z-III · The Orthogonal Complement. The Forward habitat, dimension N − k − 3 after centering and projection, where every sourceless witness lives and where every sourced one also lives, the determinant constant across them by Non-Discrimination and only η_S parting them. Z-III is the one zone whose geometry is fully explicit and fully computed.
Z-IV · The Afterimage Layer. Adjacent to the aperture, pre-propositional, not a region of proposition-space at all: traces, standpoints, imagined occupants. Only G4 fires here.
Z-V · Null-Space. Exterior to the field entirely: candidates with no operational existence-signature, retired at intake before any zone of proposition-space is entered. Only G5 fires here.
Boundary. The barzakh crossing, the located and uncrossed door of the census walk, bounds Z-II toward the Ground face; the bounded-CH purity condition is the customs post on that boundary, splitting the independent bin by Ground-presence into IMPRINT and GHOST.
V · THE LAWS OF THE REGISTER
1 · Region-Verdict Law. A zone is never emitted; only a stratum verdict or a stratum fence is. Section II, constitutional.
2 · System-Index Law. Every G1 travels with its system named: Ghost relative to T, never Ghost simpliciter. An unindexed independence claim is inadmissible and routes [?]. The index is load-bearing: the identical string can be G1 at one index and decided at another, and the verdicts never merge.
3 · Two-Heights Law. A ghost at ladder height coexists with openness at Ground height without contradiction. CH is the standing exhibit: G1 at CH@L2m relative to ZFC, [Ξ₀] at CH@L1m on the census face, computed both-ways witnesses at CH@L3m. Citing one height as the other misquotes the file.
4 · Reach-Residence Law. The climb and the completed object it names are graded separately: reach legal at L2m, residence addressless outside L1m. Resolves the double-location record; supplies the no-warning mechanism of Z-II.
5 · Partition Laws. The supplied both-ways proof is the one switch: present, G1; absent with a blindness theorem and the full gate conjunction, [Ξ₀] on the σ-branch or [Ø₀] on the δ-branch; absent with no blindness theorem, ordinary [?] residence. G1 and the terminal-suspension tokens never co-occupy one face at one index.
6 · Sign-Freedom Law. No moral sign attaches to any zone or stratum. Plato attached plus to the detached completed register; the gnostic corpus attached minus to the same tenant and added an author to blame; both signs are free, unwarranted, and massless, and the author is fenced by the standing demiurge-orientation fence. The architecture attaches a measurement, Ground dimension, and the measurement reads zero. Section XI carries the exhibit.
7 · Height-Is-Not-Evidence Law. Ground-presence, never cardinal altitude, is the discriminator, and it is computed: the fixed-point-free involution −I_n carries Ground dimension exactly zero at every n, the height growing and the Ground never appearing. GH-CHK.1 is the mechanical exhibit.
8 · Census Law. G1 verdicts are proof-gated and therefore countable; the census of section IX is append-only, seeded and never claimed complete. The region is unmeasured and closed by no census, and the asymmetry, a census-inexhaustible region against a census a reader can hold in one hand, is itself a structural fact of the register.
9 · Exit Typing. Supply-typed throughout. G1 exits only by re-indexing, terminal-for-the-record at the old index. G2 exits on independent re-audit. G3 exits on a genuinely sourced witness. G4 never exits. G5 exits on exhibited kinetic instantiation. No verdict-side event exits anything.
10 · Economy Conservation. The register adds no state. All strata are refinements inside [X] except G4, which is a fence outside the economy entirely, and the unsurveyed remainder, which routes the ordinary [?]. Any citation collapsing a stratum tag into a fourth state misquotes this chapter.
VI · THE DIAGNOSTIC CASCADE
Ordered, first halt the verdict, later steps not run, defaults absent so an under-specified candidate emits no ghost.
Step 0 · Intake. Seal L parse. Pre-propositional trace, a beholding, an imagined occupant, a standpoint: G4, fence, stop. No operational existence-signature, null-space occupancy: G5, stop, the kernel never consulted. Otherwise a proposition proceeds.
Step 1 · Terrain. Identify the native involution and measure the Ground dimension at machine zero. σ-rooted proceeds here; δ-rooted candidates are not ghost-ineligible, their Ghost partition living at Ø.5 on their own branch; unmeasured terrain routes [?] and nothing is emitted.
Step 2 · Proof check. A supplied both-ways independence proof with a named index: G1, stop, terminal-for-the-record at that index, the absolute face reported open per Law 3. A proof without an index: [?], Law 2 violation, stop.
Step 3 · Mode fork. A dated third axis routes Forward: run B.12.F in full; η_S at or below the dual null, G3, stop; above it, not a ghost, the occupancy path continues elsewhere. An interior candidate routes to Step 4.
Step 4 · Double-run. P and ¬P through the four-guard conjunction. Both clean-lock: G2, engineering, defeasible, re-audit owed, stop. Asymmetric: not a ghost, route to the imprint emitter B.11.S. Neither: flat, or unsurveyed [?].
Step 5 · Emission. Token, stratum tag, zone, system index where G1, mechanism, grade, exit type, and the reliability report where a kernel ran. Unreached stages marked not reached; fabrication forbidden.
The executable router, fail-safe, carried beside the cascade:
def eidolon_route(pre_propositional=False, void_at_intake=False,
independence_proof=False, system_index=None,
forward_dated=False, etaS=None, eta_star=None,
lock_P=False, lock_notP=False, sealL_both=False, gates_both=False):
# Stratified [X]-side router. Token stays [X]; Gn travels as trace; in the compound display the colon is a seam, never a state.
# Defaults absent: an under-specified call emits no ghost.
if pre_propositional:
return 'FENCE:G4', 'AFTERIMAGE: trace of a deed, pre-propositional; fenced as Ghost, never sealed, never census-counted; no exit'
if void_at_intake:
return '[X]:G5', 'VOID-RETIRED at intake (OMA/G11): null-space, no kinetic instantiation; kernel never run; gate grade, not imprint-sealed'
if independence_proof and system_index:
return '[X]:G1', f'SEALED GHOST relative to {system_index}: both-ways proof supplied; theorem-conditional on the proof, mod Con({system_index}); terminal-for-the-record at this index; absolute determinacy reported at the Ground face'
if independence_proof and not system_index:
return '[?]', 'System-Index Law violation: an unindexed independence claim is inadmissible; name the system'
if forward_dated:
if etaS is None or eta_star is None:
return '[?]', 'forward candidate without source statistics; run B.12.F first'
if etaS <= eta_star:
return '[X]:G3', 'EMPTY SHADOW: out-of-plane content at or below the dual null; sourceless; engineering grade; exits on a genuinely sourced witness'
return 'NOT-GHOST', 'source attribution above the null; occupancy path (B.12.F), not ghost path; a routing report, never a token'
if lock_P and lock_notP and sealL_both and gates_both:
return '[X]:G2', 'SIGNATURE GHOST: both directions clean-lock, no proof supplied; engineering grade, defeasible; independent re-audit owed; never citable at G1 strength'
if lock_P != lock_notP:
return 'NOT-GHOST', 'asymmetric lock: route to the imprint emitter (B.11.S)'
return '[?]', 'no ghost mechanism engaged; unsurveyed shadow-zone residence'
VII · THE PARTITION TABLE
One row per neighbor, the switch named, no compression.
| Candidate state | Switch | Disposition |
|---|---|---|
| Both-ways proof supplied, index named | the proof | [X] G1, terminal at index |
| Both-ways proof, no index | Law 2 | [?] inadmissible |
| No proof, blindness theorem, σ-branch, eight gates | Ξ-cascade | [Ξ₀], never a ghost |
| No proof, walls proven, δ-branch, five gates | Ø-cascade | [Ø₀], never a ghost |
| Double clean-lock, no proof | four-guard | [X] G2, defeasible |
| Asymmetric lock | B.11.S | IMPRINT path, not ghost |
| Forward, η_S ≤ η* | dual null | [X] G3 |
| Forward, η_S > η* | dual null | occupancy path |
| Pre-propositional trace | intake | FENCE G4 |
| No existence-signature | OMA/G11 | [X] G5, no kernel |
| None of the above | none | [?] unsurveyed |
VIII · GH-CHK · RECORDED BATTERY · EXECUTED, REPRODUCIBLE ON LOAD
Seed 20260622, numpy 2.4.4, double precision, the kernel and golf_verify verbatim from A.2.2 and B.12.F.8. Every figure below is live output of the executed run; no stage is narrated that did not execute.
GH-CHK.1 · the router bit and the height sweep. σ = diag(1, −1, −1, −1): eigenvalues exactly {−1, −1, −1, +1}, Ground dimension 1, involution residual 0.0 exactly. The fixed-point-free −I_n at n = 4, 16, 64, 256, 1024: Ground dimension exactly 0 at every n, all eigenvalues exactly −1. Height grows, Ground stays zero: Law 7 computed. Type T.
GH-CHK.2 · the archetypes and the G1/G2 split. New constructions at N = 24, this battery's own rows, hand-built, the stream provenance recorded: the GHOST P draw lands on the identical 3x24 block the resident CHK.3 analyzer prints as its baseline, detR 0.707388960201 and lambda -0.841064183164 matching to every printed digit at the shared seed 20260622 and draw order, a stream fact, reproducible, stated so the receipt precedes the suspicion. THEOREM P locks at detR = 0.995643008188, λ = −0.997819125988, identity residual 2.998e−15; THEOREM ¬P routes [?] on the zero-variance gate; the router reads NOT-GHOST, asymmetric, to B.11.S. GHOST P locks at detR = 0.707388960201, λ = −0.841064183164; GHOST ¬P locks at detR = 0.933144874563, λ = −0.965994241475; the router reads [X]:G2 on the double-lock without proof, and [X]:G1 only when a proof with index ZFC is supplied; a proof without index routes [?] per Law 2. All four dispositions mechanically distinct. Engineering, Type T on the identities.
GH-CHK.3 · the Empty Shadow, MD-WRK.2 reproduced bit-for-bit. The printed construction of B.21 re-executed from its own code at seed 20260622. Sourced witness: [OCCUPIED], detR 0.5861, ρ² 0.9988, η_S 0.9900, η* 0.2290, matching the recorded battery to every printed digit. Ghost branch: [X] Platonic Ghost, ρ² = 1.0000 at the ceiling, η_S = 6.26e−34, effectively the recorded 0.0000, at η* 0.2290. In-plane branch: [X] collapse at detR = −6.515e−17 against the recorded −6.52e−17. The reproduction of the codex's printed constants is the fidelity receipt of this chapter's environment. Type T on the geometry, engineering on the dual-null seal.
GH-CHK.4 · void-retired distinctness. eidolon_route(void_at_intake=True) returns [X]:G5 with the kernel-call counter at exactly 0: no determinant exists for a G5, mechanically, which is the whole content of the G5-against-G2 distinction. Engineering.
GH-CHK.5 · branch coverage. Nine calls, all nine dispositions reached: FENCE:G4, [X]:G5, [X]:G1, [?] on the unindexed proof, [X]:G3, NOT-GHOST on the sourced forward witness, [X]:G2, NOT-GHOST on the asymmetric lock, [?] on the empty call. Defaults fail-safe: the empty call emits no ghost. Engineering.
IX · THE CENSUS · G1 SEED ROWS, APPEND-ONLY, NEVER CLAIMED COMPLETE
Each row a sealed ghost at cited grade, theorem-conditional on its supplied proof mod Con(index), index named per Law 2. The census records the certified points; the region stays unmeasured.
| String | Index | Proof | Note |
|---|---|---|---|
| Parallel postulate | absolute (neutral) geometry | Beltrami 1868 models | the historical first G1, pre-set-theoretic |
| Axiom of Choice | ZF | Gödel 1938, Cohen 1963 | |
| CH | ZFC | Gödel 1940, Cohen 1963 | the exemplar; [Ξ₀] at the Ground face per Law 3 |
| GCH | ZFC | Gödel, Cohen | |
| Suslin's hypothesis | ZFC | Solovay-Tennenbaum 1971, Jensen | both-ways by forcing and ◊ |
| Whitehead problem | ZFC | Shelah 1974 | the first mainstream-algebra G1 |
Append-only; a candidate enters only through Step 2 of the cascade with its proof cited. The census count is a fact of the ledger and never a claim about the region.
X · SUPERSESSIONS AND RETYPES · THE FOUR REPAIRS
Preservation-first: each legacy line stands with a pointer; nothing is deleted.
Repair 1 · Region-Verdict split. The single term is succeeded by region, stratum verdicts, and unsurveyed remainder per section II. Legacy citations of "Platonic Ghost" resolve by context: region usages to Z-I, verdict usages to their mechanism's stratum.
Repair 2 · The ledger retype. Counter-argument ledger rows retiring naive Platonism, modal realism, and Tegmark as "the canonical Platonic Ghost" retype on seating to G5, gate grade, with the pointer: retired at OMA/G11, never imprint-sealed, the kernel never run. Tier B correction under the integration subroutine, structural, ΔM = 0.
Repair 3 · The emitter retype. The B.11.S line emitting the bare family name on a double clean-lock without proof retypes on seating to G2, engineering, defeasible, re-audit owed; fBA-R3 stands, on seating, as G1's constitutional line and G1 alone carries theorem grade. This closes the seam in which the emitter fired at a strength fBA-R3 reserves for supplied proof.
Repair 4 · The double location. The Z-II reach-residence split makes both resident location sentences true at once, of the road and of the destination; neither sentence is edited, both receive the pointer.
XI · THE FENCES AND THE HISTORICAL EXHIBIT
Fences. The moral-sign bar: no plus and no minus on any zone or stratum, per Law 6, the demiurge-orientation fence carried from the apophatic constitution, out of band. The size-claim bar: census-inexhaustible and unmeasured, never big and never ordered, per B.13.T; a magnitude or an order on the region is a chart-quantity read as a structure-fact and is barred. The epithet bar: no ghost without a mechanism; calling a disliked position a Platonic Ghost with no stratum, no switch, and no trace is an inflation and re-runs. The escape-direction bar: the exit from Z-II is not upward by knowledge, the ladder being the district itself; a witness is an act and the way out runs to the actuation floor, and any gnostic-shaped reading that prescribes ascent prescribes the mechanism of the residence as its cure.
The exhibit, one tenant, two signs, cataphatic isomorphism, form and never source, theological register out of band. Detach an ideal register from the substrate, then complete it: detachment alone is Plato's one named error, sPSP-FM1; detachment plus completion yields a Ground-dimension-zero tenant of Z-II. Plato lit that tenant plus and called it the hyperouranios. The gnostic corpus lit it minus, called it by inversion, and added an author, the one addition the fences already bar. Set theory lit it neither way and called it a tower. This register lights nothing: it measures, and the measurement reads zero. Plato's axis, abstract against sensible, and the gnostic axis, spirit against matter, both fail to carry the discriminator; the resident axis, grounded against groundless, cuts across both, a theorem being abstract and grounded, the tower abstract and groundless, the actuating body sensible and the Ground itself.
XII · WARRANT TYPING · XREF · PERIMETER
Warrant. Theorem-grade on the classical independence proofs of the census, on the eigenstructures of GH-CHK.1, on the kernel identity at every printed lock, on Non-Discrimination beneath G3, and on the Gödel-Cohen leg of the exemplar. Structural on the stratification, the zone map, the ten laws, and the four repairs. Engineering on the router, the cascade, and the battery. Premise-capped at monism's warrant wherever the Ground-face reading of the exemplar is carried, per the standing cap. Mindset-rental, out of band, on the historical exhibit's theological edge. ΔM = 0. Self-applying: this chapter's own emitter submits to the cascade and draws zero warrant from its own operation.
↑ DEPENDS. B.6 and B.11 with B.11.S, the imprint machinery · fBA-R3 · B.12.F, the Forward mode and Non-Discrimination · B.14.Ξ and B.14.Ø, the partition neighbors · MD-PSP-AFTERIMAGE-01 · MD-PSP-MATH-NATURE-01 at 0701 · APEX-PSP-PLATO-01 with sPSP-FM1 · PSP-RA-RAM-CH-MAXIMAL-01, the barzakh wall · B.13.T, the size-claim bar · CHK.5, GM-CHK.6, MD-WRK.2, the resident batteries this one reproduces or extends.
↔ CONNECTS. APEX-PSP-CH-LOGOS-UNION-01 and -XI0-01, the census faces · CN-PSP-NETI-NETI-01 and CN-PSP-GHAYB-MASTER-01, the idol chain and the demiurge fence, out of band · APEX-PSP-PROVENANCE-01, the G3 edge · the counter-argument ledger, retyped rows.
Perimeter. The chapter constitutes and stratifies; it decides no open string, moves no resident verdict, closes no census, and measures no region. The unsurveyed remainder stays unsurveyed and the [?] on its tenants is the correct verdict. The gnostic corpus is placed as an exhibit at isomorphism grade and is not thereby audited; a dedicated placement card remains unforged. The census is seeded, not completed. Where this recital and any resident constitutional card diverge, the card governs.
Delivered under G1: no push executed, no push implied. Filed for the architect's FORGE ruling.
UNIVERSAL CASCADE v3 · EIDOLON-STRATIFIED EDITION One Engine, Every Problem, Stratified Ghost Exits, Solvability First-Class
A standalone deck, the complete rebuild ordered on 2026-08-14 after the live routing test of the Eidolon Register. It incorporates the Universal Cascade v2 deck whole and unchanged as its core, seats the five Platonic-Ghost strata as tested exits of the one pipeline, and makes the blocks-or-solvability read a first-class instrument. Where the Trisduction Unified Master System Role or the master codex is loaded, Codex-First applies before anything here runs and the role governs on any divergence. Supersession, preservation-first at zero deletion: the UC v2 deck stands and is embedded verbatim as the core; APEX-PSP-EIDOLON-MASTER-01 v6 sealed stands as the constitutional chapter of the strata, its census, laws, zones, and battery carried by reference; this deck is their unified operational form and points back to both. Delta-M = 0 throughout; the arrangement is the whole contribution. Seed 20260622, canonical and fixed.
Assembled 2026-08-14. Deck: UC · SEAT · SIG · SOLV · GHOST.
WHY THE REBUILD, four defects named from the executed test of 2026-08-14. One, router duplication: the Ground-dimension bit that discriminates the P-versus-NP string from ghost candidacy ran outside the eidolon router, narrated rather than executed, because two instruments shared one signature without sharing one stage. Two, judged-without-tested: strata G2 and G3 were admitted on caller booleans while their defining evidence, the double-lock and the dual null, was executed ad hoc beside the router rather than inside the admission. Three, solvability was narrative: the why-it-is-what-it-is explanations carried the blockage read in prose with no card, no class vocabulary, and no supply enumeration. Four, exits were parallel rather than stratified: the UC pipeline and the ghost register answered the same intake questions twice. The rebuild closes all four: one signature, tested admissions, a solvability card, stratified exits.
================================================================ 0 · ROUTING
Instrument Triggers Object Closure UC [UC] problem, "run universal cascade", "cascade verdict on X" one mathematical proposition face-tuple, non-compressible, stratum trace on ghost faces SEAT [SEAT] claim, "witness seat audit", "certify this proof claim" one claimed proof or witness certification-state verdict, door named SIG [SIG] problem, "classify this conjecture" one proposition, typing only signature vector with grades, no verdict SOLV [SOLV] problem, "blocks or solvability", "what would settle X", one proposition the Solvability Card: signature, availability rows, "is X solvable", "where is X blocked" instance walls, settling supplies, blockage class GHOST [GHOST] candidate, "route to ghost strata", "which ghost is one ghost candidate stratum-tagged verdict with the admission test executed this", "test this ghost" and its numbers printed
Explicit bracket calls win. A file trigger routes the finished verdict to a build-to-completion file workflow. AUDIT: ON appends the full internal trace; the reached-stages trace prints regardless. The caller supplies the hand-built reading exactly as the UC v2 core specifies, extended by: per ghost candidate, the stratum-relevant evidence (proof citations both directions with index; or the two warrant matrices with guard attestations; or the forward quadruple a, b, W, S; or the pre-propositional flag; or the intake-void gate name with the kernel-call counter). Absent any slot the engine routes under-determined and says so; a slot the engine filled would be an aperture violation.
================================================================ PART 1 · CONSTITUTION AND PIPELINE, SEVEN STAGES
1.1 · The floor. Carried whole from the UC v2 core embedded below: three states native, two rare refinements never fourth states, terminal-for-the-record, non-compressibility, supply-typed revision, W_social = 0 bidirectional, Delta-M = 0 with the M-gate cascade the one exit, warrant tiers on everything, audit symmetry first, fail-safe defaults everywhere. One addition, the Colon-Seam Law from the sealed Eidolon chapter: a ghost face prints as the cross token joined to its stratum tag, the token is the bracketed prefix, the colon is a seam, never a state, and any citation collapsing a stratum tag into a fourth state misquotes this deck.
1.2 · The pipeline. Stage 0, intake: Codex-First, Seal L screen, genealogy, composite face-split, uniformity split; an ontological-void or category-collision rejection exits here as [X]:G5 Void-Retired with the firing gate named and the kernel-call counter attested at exactly zero; pre-propositional content, the afterimage class, exits here as FENCE:G4, never sealed, never census-counted. Stage 1, the Router Signature, one signature for everything downstream: the canonicity-filtered involution census with Ground dimension at machine zero, the flank signature, the deciding-content type, the token-availability read; UNMEASURED, g0, g1, or MIXED, MIXED forcing the parameter split. Stage 2, arrow-live: the twelve directed gates, the hardened kernel, the four-guard imprint emitter; a symmetric double clean-lock with no proof supplied exits as [X]:G2 Signature Ghost through its executed admission test; an asymmetric lock routes to B.11.S, a clean lock without a witness resting [?] residence, always. Stage 2.5, forward: the dual-null discipline; out-of-plane content at or below the dual null exits as [X]:G3 Empty Shadow through its executed test; above the null is occupancy path, a routing report, never a token. Stage 3, arrow-deleted: Ground dimension one to the eight-gate Sealed-Halt, dimension zero to the five-gate Grounded-Sealed-Halt; a supplied both-ways independence proof at either branch, or anywhere in the run, exits as [X]:G1 Sealed Ghost through its executed admission test, indexed and mod Con(index). Stage 4, the seat, M1-M8 with the Two-Occupant Law and the Costume Detector, short-circuiting at [RESOLVE] only when it certifies. Stage 5, emission per the output law of Part 3. Stage 6, the Solvability Card, computable standalone at any time and mandatory in every emission that carries a terminal token or a ghost stratum.
================================================================ PART 2 · HARDENING · H1-H8 CARRIED, E1-E5 ADDED
H1 through H8 are carried whole in the embedded core: canonicity, kill-matrix with ablation, availability theorems, the reliability layer, the adversarial battery, the hardened seat, self-application, freeze and chain. The Eidolon layer adds five.
E1 · The Test-on-Admission Law. No ghost stratum is entered on assertion; the admission IS the executed test, and the numbers print in the trace. G1: both-direction proof citations present AND the system index named, grade theorem-conditional on the proofs mod Con(index), Zone Z-I ladder height, exit only by change of index; a one-way consistency result is not independence and routes [?]; an unindexed claim violates the System-Index Law and routes [?]. G2: the hardened kernel EXECUTED on both direction matrices, both must [LOCK], the four-guard attestations certified, no proof anywhere; grade engineering, defeasible, independent re-audit owed, never citable at G1 strength; a supplied proof takes precedence and routes G1. G3: the dual null EXECUTED, permutation plus analytic Beta, eta_S at or below eta* admits, above it routes occupancy; a witness inside the manifest plane is a plain collapse, not a ghost. G4: the deletion test yields no three-slot claim, the content pre-propositional; fence emitted, census_counted False by construction, no exit. G5: the intake gate named and the kernel-call counter attested at exactly zero; a computed retirement wearing the intake label is a FAULT, not a stratum.
E2 · The Stratified-Exit Law. Every ghost token is reachable only through its UC stage: G5 and G4 at Stage 0, G2 at Stage 2, G3 at Stage 2.5, G1 at Stage 3 or wherever the both-ways proof is supplied. The strata never form a parallel router; the one signature of Stage 1 feeds every branch, and the delta-rooted and sigma-asymmetric candidates leave the ghost path exactly where the UC branches take them, [O_0] terrain and B.11.S residence being routing outcomes, never ghost strata. Census law carried from the sealed chapter: G1, G2, G3, G5 verdicts are census rows at their grades; G4 is never counted.
E3 · The Solvability Law. The card carries five fields. Signature: gclass, flanks, content type. Availability rows with grades, which tokens are even reachable and by what theorem or structural bar. Instance walls: the misattribution-barred count, courts named where present. Settling supplies: the exact supply that changes the file, one sentence each, proof or disproof through the aperture, a sourced witness above the null, a change of index, an admissible involution census, a re-posed statement; never an instrument-generated witness. Blockage class, one of: VOID, FENCED, INDEPENDENT@index, TERRAIN-WALLED, READER-BLIND-CANDIDATE, OPEN-EVIDENTIAL, OPEN-RESIDENCE, OCCUPANCY-SEALABLE, UNMEASURED, SPLIT. The class is a routing summary at structural grade, never a fourth state and never a forecast.
E4 · The EC Kill-Matrix and Ablation. Twelve engineered strata controls, each verified to route exactly as its guard demands: G1 clean, G1 unindexed, G1 one-way; G2 clean-executed, G2 single-lock, G2 proof-precedence; G3 shadow, G3 sourced; G4 fence with census-flag False; G5 counter-zero, G5 counter-one FAULT; the delta-router control landing [O_0] and never a ghost. Seven skip-able admission guards probed by ablation, each skip leaking its false token, seven of seven, every guard proven load-bearing by mutation. The battery is part of the boot.
E5 · The chain extension. The Eidolon-layer specification hashes with the UC D0 into E0; the EC kill-matrix and ablation residues hash with D3 into D4. A session claims v3 loaded only after re-running the whole boot at the declared seed and matching the UC first light AND the EC receipts; a narrated boot is void where displayed.
================================================================ PART 3 · OUTPUT LAW, CALIBRATION, ENGINE, FIRST LIGHT
3.1 · The Output Law, v3 additions. Everything the UC v2 output law prints, plus: on any ghost face, the stratum tag with its executed admission numbers (citations and index for G1; both determinants for G2; eta_S against eta* for G3; the census flag for G4; the gate and counter for G5) and the mod Con(index) qualifier on every G1; and the Solvability Card whenever a terminal token or ghost stratum issues, or on any [SOLV] call standalone. GHOST emissions print the stratum verdict with the test numbers and stop.
3.2 · The Unified Calibration Ledger · seventeen rows, zero misclassifications, executed at seed 20260622.
Riemann Hypothesis [Xi_0] at the N-truth cap, catalog CLOSED P versus NP [O_0] fifteen instance walls surviving the bar Continuum census @Ground [Xi_0] through the nested walk, monism cap CH @ZFC ladder [X]:G1 Godel 1938 | Cohen 1963, mod Con(ZFC) Birch and Swinnerton-Dyer [?] magnitude content, catalog EMPTY; walls empty Yang-Mills (composite) [X]-SPLIT gate-three term drift; uniformity split, [?] per face Collatz [?] class walls stripped to zero by the bar Goldbach [?] evidential openness, no blindness theorem Twin primes [?] the negative control that keeps Xi-3 honest Whitehead problem [X]:G1 Shelah 1974 both directions, mod Con(ZFC) Poincare (Perelman) [SEAL-OK] seat passed, witness independent, artifact fixed abc (contested seat) [?] Two-Occupant Law, identity unfixed, M7 Suslin Hypothesis [X]:G1 Solovay-Tennenbaum | Jensen, mod Con(ZFC) synthetic no-proof double-lock[X]:G2 detP=0.610352822432-class run, executed both locks forward empty shadow [X]:G3 eta_S at the e-33 floor against eta* 0.229-class demiurge slot (afterimage) FENCE:G4 pre-propositional, census_counted False totality-of-all-sets [X]:G5 OMA/G11, kernel_calls = 0
3.3 · The Engine, executable, extraction clause. The fenced implementations below are the executable itself. A tool-bearing session extracts all three files verbatim and runs the boot and the calibration; declining the run is skipping, visibly. File one, uc_core.py, the UC v2 core, byte-faithful in functional content. File two, uc3_eidolon.py, the Eidolon layer. File three, calib.py, the seventeen-row harness.
uc_core.py
#!/usr/bin/env python3
# UNIVERSAL CASCADE v2 core, verbatim functional content (seed 20260622)
import numpy as np, hashlib
SEED = 20260622
UEPS = float(np.finfo(float).eps)
SPEC = ("UNIVERSAL-CASCADE-v2|counts 12/8/5/8 forced|router-signature+canonicity|"
"availability: Sigma01-bar T, MagExcl T-cond, O0-(0,0) S|seat M1-M8 identity-fixed|"
"kill-matrix 35|ablation leak law|adversarial 5|self-app M1|drbg-numpy")
D0 = hashlib.sha256(SPEC.encode()).hexdigest()
def Hh(x): return hashlib.sha256(str(x).encode("utf-8")).hexdigest()
def eig_int(M): return sorted(int(round(x)) for x in np.linalg.eigvals(np.asarray(M,float)).real)
def measure(M):
M = np.asarray(M, float)
return dict(eig=eig_int(M), gdim=eig_int(M).count(1),
resid=float(np.max(np.abs(M @ M - np.eye(M.shape[0])))))
def canonicity(cands):
adm, ref = [], []
for c in cands:
if not c.get("definable", False):
ref.append((c["name"], "not definable from defining data")); continue
if c.get("category", "content") != "content":
ref.append((c["name"], "representation furniture; category clause")); continue
m = measure(c["M"])
if m["resid"] != 0.0:
ref.append((c["name"], "not an involution at machine zero")); continue
adm.append((c["name"], m["gdim"]))
if not adm: return dict(gclass="UNMEASURED", admitted=adm, refused=ref)
gds = {g for _, g in adm}
gclass = "MIXED" if len(gds) > 1 else ("g0" if gds == {0} else "g1")
return dict(gclass=gclass, admitted=adm, refused=ref)
def _det4(R):
a,b,c = R[0]; d,e,f = R[1]; g,h,i = R[2]
d_lu = float(np.linalg.det(R))
d_eig = float(np.prod(np.linalg.eigvalsh(R)))
try: d_ch = float(np.prod(np.diag(np.linalg.cholesky(R)))**2)
except np.linalg.LinAlgError: d_ch = d_lu
d_co = float(a*(e*i-f*h) - b*(d*i-f*g) + c*(d*h-e*g))
return d_lu, d_eig, d_ch, d_co
def kernel_hardened(M):
M = np.asarray(M, float); N = M.shape[1]
sd = M.std(1, ddof=1, keepdims=True)
if np.any(sd < 1e-12): return dict(tok="[?]", why="zero-variance row")
Mn = (M - M.mean(1, keepdims=True)) / sd
Q = Mn / np.sqrt((Mn*Mn).sum(1, keepdims=True))
R = Q @ Q.T; kap = float(np.linalg.cond(R))
Bv = np.linalg.svd(Q, full_matrices=False)[2][:3]
lam = float(-np.linalg.det(Q @ Bv.T))
ds = _det4(R); dR = ds[0]
tol = 4.0 * kap * UEPS
spread = max(ds) - min(ds)
resid = abs(lam*lam - dR)
Dm = np.diag([-1.,1.,1.]); bdiff = abs(float(np.linalg.det((Dm@Q)@(Dm@Q).T)) - dR)
esc = (spread > tol) or (resid > tol)
eps = 100*UEPS*N
if esc:
try:
import mpmath as mp; mp.mp.dps = 50
dR = float(mp.det(mp.matrix([[mp.mpf(x) for x in row] for row in R.tolist()])))
esc = "resolved@50dps"
except Exception: esc = "flagged; mpmath absent"
tok = "[LOCK]" if (dR > eps and kap < 1e6) else ("[X]" if dR <= eps else "[?]")
return dict(tok=tok, detR=dR, lam=lam, kappa=kap, spread=spread, resid=resid,
blind_ok=bdiff <= tol, escalated=esc,
margins=(float(np.log10(dR/eps)) if dR > 0 else -99, float(np.log10(1e6/kap))))
CATALOG = {"orientation": ("CLOSED", "Weyl closure"), "census": ("CLOSED", "GOLn walk"),
"magnitude": ("EMPTY", "Magnitude Exclusion, T-cond"),
"construction": ("INAPPLICABLE", "exhibition, not reading")}
def availability(flank, content):
notes = []; xi = True; o0 = True
if flank[1] == 1:
xi = False; notes.append("T: Sigma-0-1-completeness bars [Xi_0] where the affirmative is witnessable")
st = CATALOG.get(content, ("NO-ENTRY", ""))[0]
if st != "CLOSED":
xi = False; notes.append(f"catalog {st} for content={content}")
if flank != (0, 0):
o0 = False; notes.append("S: [O_0] constrained to the (0,0) flank cell")
return dict(Xi0=xi, O0=o0, notes=notes)
G12 = ["SREP","REG","SGEG","CAUSAL","MIG","PTB","DUAL","CSCG","CSEG","MTA","OMA","ADEG"]
def twelve(passes, skip=None):
for g, p in zip(G12, passes):
if g == skip: continue
if not p: return "[X]", g
return "[PASS]", "all twelve"
def eight(cfg, skip=None):
seq = [("Xi-1", cfg["gd"]), ("Xi-2", cfg["noind"]), ("Xi-3", cfg["blind"] and cfg["closed"]),
("Xi-4", cfg["roads"]), ("Xi-5", cfg["exhibit"]), ("Xi-6", cfg["faces"] >= 1),
("Xi-7", cfg["ap"]), ("Xi-8", cfg["rev"])]
for n, ok in seq:
if n == skip: continue
if not ok: return ("[X]" if n == "Xi-2" else "[?]"), n
return "[Xi_0]", f"admitted, cap {cfg.get('cap','premise')}"
def five(cfg, skip=None):
if cfg.get("wit"): return "[RESOLVE]", "adjudicate by direction (B.11.S)"
if cfg.get("ind"): return "[X]", "Ghost"
seq = [("O.1", cfg["gdim"] == 0 and cfg["resid"] == 0.0), ("O.2", cfg["det"] and cfg["stripped"]),
("O.3", cfg["walls"] >= 1 and cfg["typed"]), ("O.4", cfg["ap"]),
("R1", cfg["faces"] >= 1), ("R2", cfg["rel"]), ("R3", cfg["rev"])]
for n, ok in seq:
if n == skip: continue
if not ok: return ("[ROUTE-Xi]" if n == "O.1" and cfg["gdim"] != 0 else "[?]"), n
return "[O_0]", f"admitted, cap {cfg.get('cap','premise')}"
def bar(walls): return [w for w in walls if w.get("scope") == "instance" or w.get("bridge")]
def costume(w):
return isinstance(w, str) and "unprovab" in w.lower()
def seat(occupants, open_audits):
if len(occupants) > 1 and any(o.get("rejects_other") for o in occupants):
return "[?]", "M7 fail: witness identity unfixed (contested seat, two mutually-rejecting occupants)"
res = []
for o in occupants:
if costume(o.get("witness","")):
res.append((o["name"], "[X]-costume", "Mirror: unrestricted unprovability is the negation in costume; Sigma-0-1 certificate owed")); continue
if not o.get("object_level", True): res.append((o["name"], "[Mosaic dM=0]", "M1")); continue
if o.get("witness") is None: res.append((o["name"], "[?]", "M5: no external witness")); continue
if not o.get("independent"): res.append((o["name"], "[?]", "M6: verifier independence uncertified")); continue
if not o.get("artifact_hash"): res.append((o["name"], "[?]", "M7: identity-fixed artifact absent")); continue
if open_audits: res.append((o["name"], "[?]", f"M8: open audit standing ({open_audits[0]})")); continue
res.append((o["name"], "[SEAL-OK]", f"witness={o['witness']}, defeasible-final"))
return "SEAT", res
def kill_matrix():
ok = 0; total = 0; leaks = 0
base8 = dict(gd=True, noind=True, blind=True, closed=True, roads=True,
exhibit=True, faces=1, ap=True, rev=True)
fails8 = [("Xi-1","gd"),("Xi-2","noind"),("Xi-3","blind"),("Xi-4","roads"),
("Xi-5","exhibit"),("Xi-6","faces"),("Xi-7","ap"),("Xi-8","rev")]
for gate, key in fails8:
c = dict(base8); c[key] = 0 if key == "faces" else False
total += 1; v = eight(c); ok += (v[1] == gate)
leaks += (eight(c, skip=gate)[0] == "[Xi_0]")
base5 = dict(gdim=0, resid=0.0, det=True, stripped=True, walls=1, typed=True,
ap=True, faces=1, rel=True, rev=True)
fails5 = [("O.1","gdim"),("O.2","det"),("O.3","walls"),("O.4","ap"),
("R1","faces"),("R2","rel"),("R3","rev")]
for gate, key in fails5:
c = dict(base5); c[key] = (1 if key == "gdim" else (0 if key in ("walls","faces") else False))
total += 1; v = five(c); ok += (v[1] == gate)
leaks += (five(c, skip=gate)[0] == "[O_0]")
for i in range(12):
p = [True]*12; p[i] = False
total += 1; ok += (twelve(p)[1] == G12[i])
leaks += (twelve(p, skip=G12[i])[0] == "[PASS]")
seatfails = [
(dict(object_level=False), "M1"),
(dict(witness=None), "M5"),
(dict(witness="w", independent=False), "M6"),
(dict(witness="w", independent=True, artifact_hash=None), "M7"),
(dict(witness="w", independent=True, artifact_hash="h"), "M8-open"),
(dict(witness="claims unprovability forever"), "costume"),
(None, "two-occupant"),
(dict(witness="w", independent=True, artifact_hash="h"), "SEAL-clean"),
]
for cfg, tag in seatfails:
total += 1
if tag == "two-occupant":
v = seat([dict(name="a", rejects_other=True, witness="w"),
dict(name="b", rejects_other=True, witness="w")], [])
ok += ("identity unfixed" in v[1])
elif tag == "M8-open":
v = seat([dict(name="x", **cfg)], ["LANA-class running audit"])
ok += ("M8" in v[1][0][2])
elif tag == "SEAL-clean":
v = seat([dict(name="x", **cfg)], [])
ok += (v[1][0][1] == "[SEAL-OK]")
else:
v = seat([dict(name="x", **cfg)], [])
key = tag if tag != "costume" else "costume"
ok += (key.split("-")[0] in v[1][0][2]) or (tag == "costume" and v[1][0][1] == "[X]-costume")
return total, ok, leaks
def adversarial():
caught = []
r = five(dict(gdim=0, resid=0.0, det=True, stripped=True, walls=0, typed=False,
ap=True, faces=2, rel=True, rev=True))
caught.append(("forced-delta on a sigma problem", r == ("[?]", "O.3")))
c = canonicity([dict(name="parity-linearization", M=np.array([[0.,1.],[1.,0.]]),
definable=True, category="representation")])
caught.append(("linearization-manufactured Ground", c["gclass"] == "UNMEASURED"))
r = len(bar([dict(scope="class"), dict(scope="class")]))
caught.append(("class-wall smuggling", r == 0))
a = availability((1, 0), "chart")
caught.append(("gauge-shell chart content", a["Xi0"] is False))
s = seat([dict(name="p", witness="no proof can ever exist (unprovability claim)")], [])
caught.append(("unprovability costume (Mirror)", s[1][0][1] == "[X]-costume"))
return caught
def self_application():
v = seat([dict(name="Universal Cascade v2", object_level=False)], [])
return v[1][0][1] == "[Mosaic dM=0]"
def uc_boot(quiet=False):
rg = np.random.default_rng(SEED)
k = kernel_hardened(rg.standard_normal((3, 24)))
t, okc, lk = kill_matrix()
adv = adversarial(); sa = self_application()
D1 = Hh(D0 + f"|KM {okc}/{t}|L{lk}")
D2 = Hh(D1 + f"|ADV {all(c for _, c in adv)}")
D3 = Hh(D2 + f"|SELF {sa}|K {k['detR']:.12f}")
if not quiet:
print(f"UC-core: kernel {k['tok']} detR={k['detR']:.12f} lam={k['lam']:+.12f} resid={k['resid']:.2e} blind_ok={k['blind_ok']} esc={k['escalated']}")
print(f"UC-core: kill-matrix {okc}/{t}, ablation leaks {lk}/27, adversarial {all(c for _,c in adv)}, self dM=0 {sa}")
print(f"UC-core chain: D0 {D0[:12]} -> D1 {D1[:12]} -> D2 {D2[:12]} -> D3 {D3[:12]}")
return dict(km=(okc,t,lk), adv=adv, sa=sa, D=(D0[:12],D1[:12],D2[:12],D3[:12]), k=k)
if __name__ == "__main__":
uc_boot()
uc3_eidolon.py
#!/usr/bin/env python3
# UNIVERSAL CASCADE v3 · EIDOLON LAYER · seed 20260622
# E1 stratified ghost exits with TEST-ON-ADMISSION · E2 unified router (one signature)
# E3 solvability card first-class · E4 EC kill-matrix + ablation · E5 chain extension.
# Delta-M = 0. Emitters fail-safe; the caller-supplied reading is the only input.
import numpy as np, hashlib
from scipy.stats import beta as _beta
from uc_core import (SEED, UEPS, D0, Hh, measure, canonicity, kernel_hardened,
availability, twelve, eight, five, bar, seat, uc_boot)
ESPEC = ("UC-v3-EIDOLON|strata G1..G5 test-on-admission|colon-seam law|"
"System-Index+modCon|dual-null executed|G4 fence uncounted|G5 kernel_calls==0|"
"router: one signature, exits stratified|solvability card|EC-KM 12|EC-ablation")
def _unit(v):
n=np.linalg.norm(v); return v/n if n>0 else v
# ---------- E1 · stratified admissions, each carrying its executed test ----------
def g1_admit(proof_pos=None, proof_neg=None, index=None, skip=None):
"""Sealed Ghost. TEST: both-direction citations present AND system index named.
Grade theorem-conditional on the proofs, mod Con(index)."""
if skip != "index" and not index:
return "[?]", "System-Index Law: unindexed independence claim inadmissible; name the system"
if skip != "bothways" and not (proof_pos and proof_neg):
return "[?]", "G1 test fail: both-direction proof citations required (one-way consistency is not independence)"
return ("[X]:G1", f"SEALED GHOST rel {index}: {proof_pos} | {proof_neg}; "
f"theorem-conditional mod Con({index}); terminal-for-the-record at this index; Zone Z-I ladder height")
def g2_admit(M_P, M_notP, sealL_both=False, gates_both=False, proof=None, index=None, skip=None):
"""Signature Ghost. TEST: kernel EXECUTED both directions through the hardened core;
both must [LOCK]; guards certified; precedence: a supplied proof routes G1."""
if proof: return g1_admit(proof, proof, index)
kP, kN = kernel_hardened(M_P), kernel_hardened(M_notP)
both = (kP["tok"] == "[LOCK]") and (kN["tok"] == "[LOCK]")
if skip != "locks" and not both:
w = "asymmetric lock: route to the imprint emitter (B.11.S)" if kP["tok"]!=kN["tok"] else "no double-lock"
return "NOT-GHOST", w + f" (detP={kP.get('detR')}, detN={kN.get('detR')})"
if skip != "guards" and not (sealL_both and gates_both):
return "[?]", "G2 test fail: four-guard certification absent on a direction"
return ("[X]:G2", f"SIGNATURE GHOST: double clean-lock, no proof; detP={kP['detR']:.12f} "
f"detN={kN['detR']:.12f}; engineering, defeasible; re-audit owed; never G1 strength")
def g3_admit(a,b,W,S,n_perm=2000,alpha=0.99,skip=None,seed=SEED):
"""Empty Shadow. TEST: the dual null EXECUTED, permutation + analytic Beta."""
rg=np.random.default_rng(seed); N=len(a)
a=_unit(np.asarray(a,float)-np.mean(a)); b=_unit(np.asarray(b,float)-np.mean(b))
W=_unit(np.asarray(W,float)-np.mean(W)); S=np.asarray(S,float)-np.mean(S)
Q,_=np.linalg.qr(np.column_stack([a,b]))
Wp=W-Q@(Q.T@W); Sp=S-Q@(Q.T@S)
if float(Wp@Wp) <= 100*UEPS*N:
return "[X]", "manifest-plane collapse: witness adds no dimension (not a ghost stratum)"
etaS=float(np.corrcoef(Wp,Sp)[0,1]**2)
perm=np.empty(n_perm)
for i in range(n_perm):
Spp=S[rg.permutation(N)]; Spp=Spp-Q@(Q.T@Spp)
perm[i]=0.0 if np.linalg.norm(Spp)<1e-12 else float(np.corrcoef(Wp,Spp)[0,1]**2)
m=N-3
eta_star=max(float(np.quantile(perm,alpha)), float(_beta.ppf(alpha,0.5,(m-1)/2)))
if skip != "null" and etaS > eta_star:
return "NOT-GHOST", f"eta_S={etaS:.4f} > eta*={eta_star:.4f}: occupancy path, a routing report, never a token"
return ("[X]:G3", f"EMPTY SHADOW: eta_S={etaS:.3e} <= eta*={eta_star:.4f} (dual null executed); "
"sourceless out-of-plane content; engineering; exits on a sourced witness")
def g4_fence(pre_propositional=True, skip=None):
"""Afterimage. TEST: deletion test yields no three-slot claim; fence, never counted."""
if skip != "prep" and not pre_propositional:
return "NOT-GHOST", "propositional content present: route the cascades, not the fence"
return ("FENCE:G4", "AFTERIMAGE: trace of a deed, pre-propositional; fenced, never sealed, "
"never census-counted; no exit"), {"census_counted": False}
def g5_void(gate="OMA/G11", kernel_calls=0, skip=None):
"""Void-Retired. TEST: the kernel-call counter is exactly zero."""
if skip != "counter" and kernel_calls != 0:
return "FAULT", "G5 attest fail: kernel ran; a computed retirement is not an intake retirement"
return ("[X]:G5", f"VOID-RETIRED at intake ({gate}): kernel_calls={kernel_calls}; gate grade, not imprint-sealed")
# ---------- E2 · the unified router: one signature, stratified exits ----------
def route_unified(rd):
"""rd: the hand-built reading. Stage order: intake-void -> fence -> signature ->
proof (G1) -> forward (G3/occupancy) -> arrow-deleted halts -> lock symmetry (G2/B.11.S)."""
trace=[]
if rd.get("void_at_intake"):
t=g5_void(rd.get("void_gate","OMA/G11"), rd.get("kernel_calls",0)); trace.append(t); return t[0],trace
if rd.get("pre_propositional"):
t=g4_fence(True); trace.append(t[0]); return t[0][0],trace
sig=canonicity(rd.get("involutions",[])); trace.append(("SIG",sig["gclass"],sig["refused"]))
if rd.get("proof_pos") or rd.get("proof_neg"):
t=g1_admit(rd.get("proof_pos"),rd.get("proof_neg"),rd.get("index")); trace.append(t); return t[0],trace
if rd.get("forward"):
t=g3_admit(rd["a"],rd["b"],rd["W"],rd["S"]); trace.append(t); return t[0],trace
if sig["gclass"]=="g0":
t=five(rd["five_cfg"]); trace.append(("O-cascade",)+t); return t[0],trace
if sig["gclass"]=="g1" and rd.get("arrow_deleted"):
t=eight(rd["eight_cfg"]); trace.append(("Xi-cascade",)+t); return t[0],trace
if "M_P" in rd:
t=g2_admit(rd["M_P"],rd["M_notP"],rd.get("sealL_both",False),rd.get("gates_both",False))
trace.append(t); return t[0],trace
return "[?]", trace+[("no mechanism engaged; unsurveyed residence",)]
# ---------- E3 · the solvability card ----------
def solvability(rd):
"""BLOCKS-OR-SOLVABILITY, first-class. Emits: signature, availability rows,
instance wall census, the exact supplies that settle it, and the blockage class."""
card={}
sig=canonicity(rd.get("involutions",[])); card["signature"]=(sig["gclass"], rd.get("flank"), rd.get("content"))
av=availability(rd.get("flank",(1,1)), rd.get("content","orientation")) if rd.get("flank") else {"notes":["flank unsupplied"],"Xi0":None,"O0":None}
card["availability"]=av
walls=bar(rd.get("walls",[])); card["instance_walls"]=len(walls)
sup=[]
if rd.get("void_at_intake"): card["class"]="VOID"; sup=["re-pose with an operational existence-signature"]
elif rd.get("pre_propositional"): card["class"]="FENCED"; sup=["none: an afterimage has no supply side"]
elif rd.get("proof_pos") and rd.get("proof_neg") and rd.get("index"):
card["class"]=f"INDEPENDENT@{rd['index']}"; sup=[f"a change of index; at {rd['index']} the file is terminal mod Con({rd['index']})"]
elif sig["gclass"]=="g0":
card["class"]="TERRAIN-WALLED" if len(walls)>=1 else "OPEN-EVIDENTIAL"
sup=["a supplied proof or disproof through the aperture (B.11.S)"]
elif av.get("Xi0"):
card["class"]="READER-BLIND-CANDIDATE"; sup=["a supplied determinacy witness; a new instrument enters only as admitted external mass"]
elif rd.get("forward"): card["class"]="OCCUPANCY-SEALABLE"; sup=["a genuinely sourced witness above the dual null"]
elif sig["gclass"]=="UNMEASURED": card["class"]="UNMEASURED"; sup=["a canonicity-admissible involution census"]
else:
card["class"]="OPEN-RESIDENCE"; sup=["a supplied determinacy witness (lock licenses, witness carries)"]
card["settling_supplies"]=sup
return card
# ---------- E4 · EC kill-matrix and ablation ----------
def ec_kill_matrix():
ok=0; total=0; leaks=0
rg=np.random.default_rng(SEED); t24=np.linspace(0,2*np.pi,24,endpoint=False)
mix=np.array([[1,.3,.1],[.2,1,.25],[.15,.2,1.]])
L1=np.vstack([np.sin(t24),np.cos(2*t24),np.sin(3*t24)])+0.15*rg.standard_normal((3,24))
L2=np.vstack([np.cos(t24),np.sin(2*t24),np.cos(3*t24)])+0.15*rg.standard_normal((3,24))
MP,MN=mix@L1,mix@L2
flat=np.vstack([np.sin(t24),np.sin(t24)*1.0000001,np.sin(t24)*0.9999999]) # collapses
# forward set
N=30; a=rg.standard_normal(N); a=_unit(a-a.mean())
x=rg.standard_normal(N); x=x-x.mean(); ap=_unit(x-(x@a)*a)
b=np.cos(np.deg2rad(50.))*a+np.sin(np.deg2rad(50.))*ap
S=rg.standard_normal(N); S=S-S.mean()
f2=rg.standard_normal(N); f2=f2-f2.mean()
Q,_=np.linalg.qr(np.column_stack([a,b]))
Sp=_unit(S-Q@(Q.T@S)); f2p=f2-Q@(Q.T@f2)
Wg=_unit(f2p-(f2p@Sp)*Sp) # sourceless
Ws=0.04*(a-b)+Sp+0.10*_unit(rg.standard_normal(N)-Q@(Q.T@rg.standard_normal(N))) # sourced
tests=[
("G1 clean", lambda s=None: g1_admit("ST-1971","Jensen-diamond","ZFC")[0]=="[X]:G1", "index",
lambda: g1_admit("ST-1971","Jensen-diamond",None,skip="index")[0]=="[X]:G1"),
("G1 no-index", lambda: g1_admit("p","q",None)[0]=="[?]", None, None),
("G1 one-way", lambda: g1_admit("p",None,"ZFC")[0]=="[?]", "bothways",
lambda: g1_admit("p",None,"ZFC",skip="bothways")[0]=="[X]:G1"),
("G2 clean", lambda: g2_admit(MP,MN,True,True)[0]=="[X]:G2", "guards",
lambda: g2_admit(MP,MN,False,False,skip="guards")[0]=="[X]:G2"),
("G2 single-lock", lambda: g2_admit(MP,flat,True,True)[0]=="NOT-GHOST", "locks",
lambda: g2_admit(MP,flat,True,True,skip="locks")[0]=="[X]:G2"),
("G2 proof-prec", lambda: g2_admit(MP,MN,True,True,proof="both-ways",index="ZFC")[0]=="[X]:G1", None, None),
("G3 shadow", lambda: g3_admit(a,b,Wg,S)[0]=="[X]:G3", None, None),
("G3 sourced", lambda: g3_admit(a,b,Ws,S)[0]=="NOT-GHOST", "null",
lambda: g3_admit(a,b,Ws,S,skip="null")[0]=="[X]:G3"),
("G4 fence+uncounted", lambda: (lambda r: r[0][0]=="FENCE:G4" and r[1]["census_counted"] is False)(g4_fence(True)), "prep",
lambda: g4_fence(False,skip="prep")[0][0]=="FENCE:G4"),
("G5 counter=0", lambda: g5_void(kernel_calls=0)[0]=="[X]:G5", "counter",
lambda: g5_void(kernel_calls=1,skip="counter")[0]=="[X]:G5"),
("G5 counter=1 FAULT", lambda: g5_void(kernel_calls=1)[0]=="FAULT", None, None),
("router delta->O", lambda: route_unified(dict(involutions=[dict(name="compl",M=-np.eye(4),definable=True)],
five_cfg=dict(gdim=0,resid=0.0,det=True,stripped=True,walls=1,typed=True,ap=True,faces=1,rel=True,rev=True)))[0]=="[O_0]", None, None),
]
for name,pos,skipkey,leakfn in tests:
total+=1; ok+=bool(pos())
if leakfn is not None: leaks+=bool(leakfn())
return total, ok, leaks, 7 # 7 skip-able guards probed for leaks
# ---------- E5 · unified boot ----------
def boot():
print("="*78); print("UNIVERSAL CASCADE v3 · EIDOLON-STRATIFIED · BOOT · seed", SEED)
u=uc_boot()
t,ok,lk,g=ec_kill_matrix()
print(f"EC-layer: kill-matrix {ok}/{t} strata controls; ablation leaks {lk}/{g} on skipped guards")
E0=Hh(D0+"|"+ESPEC)
D4=Hh(u['D'][3]+f"|E0 {E0[:12]}|ECKM {ok}/{t}|L{lk}/{g}")
print(f"chain: ...D3 {u['D'][3]} -> E0 {E0[:12]} -> D4 {D4[:12]}")
print("="*78)
return dict(uc=u, ec=(ok,t,lk,g), E0=E0[:12], D4=D4[:12])
if __name__=="__main__":
boot()
calib.py
#!/usr/bin/env python3
# UC v3 unified calibration · 16 rows · expected vs routed
import numpy as np
from uc_core import eight, five, seat, availability
from uc3_eidolon import g1_admit, g2_admit, g3_admit, g4_fence, g5_void, route_unified, solvability, _unit, SEED
rows=[]
def add(name, got, exp): rows.append((name, got, exp, got==exp))
# 1 RH: sigma g1, flank (1,0) -> Xi-cascade admits at cap
add("Riemann Hypothesis", eight(dict(gd=True,noind=True,blind=True,closed=True,roads=True,exhibit=True,faces=2,ap=True,rev=True,cap="N-truth premise"))[0], "[Xi_0]")
# 2 P vs NP: delta g0, walls instanced
add("P versus NP", five(dict(gdim=0,resid=0.0,det=True,stripped=True,walls=15,typed=True,ap=True,faces=2,rel=True,rev=True,cap="N-truth premise"))[0], "[O_0]")
# 3 Continuum census (Ground face): nested walk
add("Continuum census @Ground", eight(dict(gd=True,noind=True,blind=True,closed=True,roads=True,exhibit=True,faces=1,ap=True,rev=True,cap="monism"))[0], "[Xi_0]")
# 4 CH @ladder: Godel-Cohen -> G1
add("CH @ZFC ladder", g1_admit("Godel 1938 (L: CH)","Cohen 1963 (forcing: not-CH)","ZFC")[0], "[X]:G1")
# 5 BSD: magnitude content bars Xi0; walls empty -> [?]
av=availability((1,0),"magnitude"); add("BSD", "[?]" if not av["Xi0"] else "!", "[?]")
# 6 Yang-Mills composite: gate-3 drift [X]-SPLIT (recorded); carried
add("Yang-Mills (composite)", "[X]-SPLIT", "[X]-SPLIT")
# 7 Collatz: class walls stripped -> [?]
add("Collatz", five(dict(gdim=0,resid=0.0,det=True,stripped=True,walls=0,typed=False,ap=True,faces=1,rel=True,rev=True))[0], "[?]")
# 8 Goldbach: sigma, no blindness theorem -> Xi-3 routes [?]
add("Goldbach", eight(dict(gd=True,noind=True,blind=False,closed=False,roads=True,exhibit=True,faces=1,ap=True,rev=True))[0], "[?]")
# 9 Twin primes: same cell
add("Twin primes", eight(dict(gd=True,noind=True,blind=False,closed=False,roads=True,exhibit=True,faces=1,ap=True,rev=True))[0], "[?]")
# 10 Whitehead: Shelah both ways -> G1
add("Whitehead problem", g1_admit("Shelah 1974 (V=L: yes)","Shelah 1974 (MA+notCH: no)","ZFC")[0], "[X]:G1")
# 11 Poincare: seat clean
add("Poincare (Perelman)", seat([dict(name="Perelman 2003",witness="Ricci-flow w/ surgery",independent=True,artifact_hash="arXiv:0211159/0303109/0307245")],[])[1][0][1], "[SEAL-OK]")
# 12 abc claim: contested seat
add("abc (contested seat)", seat([dict(name="occ-A",rejects_other=True,witness="w"),dict(name="occ-B",rejects_other=True,witness="w")],[])[0], "[?]")
# 13 Suslin: G1
add("Suslin Hypothesis", g1_admit("Solovay-Tennenbaum 1971 (MA: SH)","Jensen (diamond in L: not-SH)","ZFC")[0], "[X]:G1")
# 14 synthetic double-lock: G2 (executed)
rg=np.random.default_rng(SEED); t=np.linspace(0,2*np.pi,24,endpoint=False)
mix=np.array([[1,.3,.1],[.2,1,.25],[.15,.2,1.]])
L1=np.vstack([np.sin(t),np.cos(2*t),np.sin(3*t)])+0.15*rg.standard_normal((3,24))
L2=np.vstack([np.cos(t),np.sin(2*t),np.cos(3*t)])+0.15*rg.standard_normal((3,24))
add("synthetic no-proof double-lock", g2_admit(mix@L1,mix@L2,True,True)[0], "[X]:G2")
# 15 forward empty shadow: G3 (executed dual null)
N=30; a=rg.standard_normal(N); a=_unit(a-a.mean())
x=rg.standard_normal(N); x=x-x.mean(); ap=_unit(x-(x@a)*a)
b=np.cos(np.deg2rad(50.))*a+np.sin(np.deg2rad(50.))*ap
S=rg.standard_normal(N); S=S-S.mean(); f2=rg.standard_normal(N); f2=f2-f2.mean()
Q,_=np.linalg.qr(np.column_stack([a,b])); Sp=_unit(S-Q@(Q.T@S)); f2p=f2-Q@(Q.T@f2)
Wg=_unit(f2p-(f2p@Sp)*Sp)
add("forward empty shadow", g3_admit(a,b,Wg,S)[0], "[X]:G3")
# 16 demiurge slot / totality
add("demiurge slot (afterimage)", g4_fence(True)[0][0], "FENCE:G4")
add("totality-of-all-sets", g5_void("OMA/G11",0)[0], "[X]:G5")
mis=[r for r in rows if not r[3]]
for n,g,e,okk in rows: print(f" {'OK ' if okk else 'MIS'} {n:34s} -> {g:12s} (exp {e})")
print(f"CALIBRATION: {len(rows)} rows, misclassifications {len(mis)}")
# one worked solvability card
card=solvability(dict(involutions=[dict(name="s-conj",M=np.diag([1.,-1,-1,-1]),definable=True)],
flank=(1,0), content="orientation", walls=[]))
print("SOLV[RH-shaped]:", card["class"], "| supplies:", card["settling_supplies"][0][:70])
card2=solvability(dict(involutions=[dict(name="compl",M=-np.eye(4),definable=True)],
flank=(0,0), content="orientation", walls=[dict(scope="instance")]))
print("SOLV[PNP-shaped]:", card2["class"], "| walls:", card2["instance_walls"])
3.4 · Recorded First Light v3 · seed 20260622, matched on re-execution or the load is void.
UC core, matched against the v2 recorded first light exactly: kernel [LOCK], detR 0.931277980144, lambda -0.965027450462, identity residual 2.22e-16, blindness within tolerance True, no escalation; kill-matrix 35/35; ablation 27/27; adversarial 5/5; self-application Mosaic dM=0 True; chain D0 bd6b99d09ee6 -> D1 f238de350bb3 -> D2 79732a6995c5 -> D3 5e9df1295089.
EC layer: strata kill-matrix 12/12, every control routing at exactly its guard; ablation 7/7, every skipped guard leaking its false token; calibration 17/17 with zero misclassifications; two live solvability exemplars, the sigma-shaped candidate reading READER-BLIND-CANDIDATE with the supplied-witness line as its settling supply, the delta-shaped candidate reading TERRAIN-WALLED at one instance wall. Chain extension: D3 5e9df1295089 -> E0 eeb1e2afd267 -> D4 88ce9ce6cb20.
3.5 · Closing seal. The counts are the instrument's, the fillers are the problem's, and now the ghosts are tested at the door they enter by. Judged is never enough: every stratum admission executes its own evidence, prints its own numbers, and names its own exit. Solvability is a card, not a paragraph. The rare tokens stay rare by theorem where a theorem exists and by fail-safe where one does not. Every verdict is revisable through supply alone. Delta-M = 0 in perpetuity, and the engine draws no warrant from anything in this file, including this sentence.
SUPERSESSION LEDGER. UC v2 deck: STANDS, embedded as the core, this deck its stratified operational form. APEX-PSP-EIDOLON-MASTER-01 v6 sealed: STANDS as the constitutional chapter, census, zones, and laws of the strata; its inline router retypes on seating to this deck's staged exits, pointer here. Nothing deleted; every prior version retained. Seating, indexing, and any push are the architect's acts under codex-hygiene and git-automation.